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no-repeat 6px;background-position:center;min-width:55px;display:none;} @media (min-width:768px){.fuTMHY .floats-partial-section .floats-partial-footer .floats-partial-caption .expand_btn{display:none;}} .fuTMHY .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{-webkit-flex:9;-ms-flex:9;flex:9;text-align:left;padding:21px 37px 21px 0;font-size:16px;font-weight:700;} @media (min-width:768px){.fuTMHY .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 18px 20px 18px;}} @media (min-width:992px){.fuTMHY .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 21px 21px 21px;}} .fuTMHY .floats-partial-section .floats-partial-footer .floats-partial-caption 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no-repeat 6px;background-position:center;padding:16px 0 16px 0;min-width:62px;max-width:62px;} @media (min-width:768px){.fuTMHY .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:16px 0 17px 0;min-width:52px;max-width:52px;}} @media (min-width:992px){.fuTMHY .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:15px 0 17px 0;min-width:60px;max-width:60px;}} .fuTMHY .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url:hover{-webkit-text-decoration:none;text-decoration:none;} .fuTMHY .floats-partial-section .floats-partial-footer .floats-partial-caption-text{font-size:14px;padding:21px 18px 17px 22px;font-family:STIXGeneral-Regular;} @media (min-width:768px){.fuTMHY .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:22px 15px 15px 18px;}} @media (min-width:992px){.fuTMHY .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:16px 18px 19px 21px;}} .fuTMHY .floats-partial-section .floats-partial-footer .floats-partial-caption-text figcaption{margin:0;padding:0;} .fuTMHY .floats-partial-section .floats-partial-footer .floats-partial-caption-text svg{max-width:100%;} .fuTMHY ol{font-size:16px;padding-left:32px;font-family:STIXGeneral-Regular;line-height:24px;margin:15px 0;} .fuTMHY ol li{margin:10px 0;padding-left:10px;word-break:normal;} .fuTMHY ol li a{word-break:break-all;} .fuTMHY ol li .reflinks{display:block;} .fuTMHY ol li .reflinks a{color:#4D8A17;-webkit-text-decoration:none;text-decoration:none;cursor:pointer;} .fuTMHY ol li .reflinks a:hover{-webkit-text-decoration:underline;text-decoration:underline;} .fuTMHY ol li .reflinks .sep{color:#000000;} .fuTMHY .table-wrapper{width:auto;overflow-x:auto;} .fuTMHY .table-wrapper::-webkit-scrollbar{-webkit-appearance:none;width:5px;height:5px;} .fuTMHY 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.fuTMHY .partial-carousel-dot{text-align:center;cursor:pointer;border:0;width:100px;padding-bottom:20px;background-color:#fff;display:table-cell;} .fuTMHY .partial-carousel-dot:focus-visible{outline-offset:-3px;} .fuTMHY .partial-carousel-dot strong{font-size:11px;padding-top:12px;} @media (min-width:767.5px){.fuTMHY .partial-carousel-dot strong{font-size:16px;}} .fuTMHY .partial-carousel-dot img{width:90px;height:90px;border:1px solid #979797;margin:10px 0;} .fuTMHY .partial-carousel-wrapper .floats-partial-middle{border-top:1px solid #e3e3e3;display:block;margin-bottom:50px;padding-top:1px;} @media (min-width:767.5px){.fuTMHY .partial-carousel-wrapper .floats-partial-middle{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;margin-bottom:0;}} .fuTMHY .partial-carousel--single-image{overflow:hidden;text-align:center;} .fuTMHY .partial-carousel--single-image img{width:100%;max-height:239px;height:auto;} @media (min-width:767.5px){.fuTMHY 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height="24"><span class="text">提交</年代p一个n></年代p一个n><span class="sc-htoDjs kNoiZu sc-fhYwyz iBoHeM fileArrow icon-colored undefined icon-themeable" title="" font-size="16"></span></a> <div class="sc-CtfFt XFBFH hide__submenu journalSubmenuCheck" id="journalnav__submenu"> <button class="sc-hGoxap hxsCRE journalSubmenuCheck"><span class="sc-htoDjs gvAGTV sc-TFwJa huQLDk journalSubmenuCheck icon-colored _1CwL9R82TPl2HxDleeYGDR icon-themeable" title="" font-size="9"></span></button> </div> <div class="sc-laTMn cxFuMz hide__submenu journal__nav__desktop" id="journalnav__submenudesktop"> <div order="0" class="sc-dTdPqK fTRdky"> <div class="sc-bHwgHz cktMDW"></div> <div class="sc-bHwgHz cktMDW"></div> </div> <div class="sc-krDsej iEoFfk"></div> <span class="sc-eMigcr jUJlcF"></span> </div> </nav> </div> <div class="sc-iuDHTM iUyLDt breadcrumb__wrapper journal_article__BreadCrumbStyle-sc-12fk6zy-2 bjwAQR article"> <a class="sc-htpNat bUhGXt link sc-kEmuub hRBKET breadCrumb" href="//www.newsama.com/journals/ijbi/" aria-label="International Journal of Biomedical Imaging">国际生物医学成像杂志》上</一个>/<gydF4y2Ba一个cl一个年代年代=”年代c-htpNat bUhGXt link sc-kEmuub hRBKET breadCrumb" href="//www.newsama.com/journals/ijbi/contents/year/2011/" aria-label="2011">2011年</一个>/<gydF4y2Ba年代p一个ncl一个年代年代=”年代c-bbkauy bAmZHt">文章</年代p一个n></d我v> <div class="threeColumn__ThreeColumnWrapper-sc-1bf4078-0 uVYyF threeColumnWrapper"> <div class="threeColumn__LeftWrapper-sc-1bf4078-1 fkVFlF leftWrapper"> <button type="button" class="sc-hzDEsm fuYUWV section__button " id="sectionButton"><span class="sc-htoDjs diutvq icon__dots dots__detector icon-colored _3n-7Ho7DlfjMlZbrRr9Q4a icon-themeable" title="" font-size="22"></span>文章部分</gydF4y2Babutton> <div class="sc-eInJlc fMnOCC static_contents__section_links links__hidden "> <div id="leftSectionMenu" class="sc-iujRgT kgnSNR sc-hgHYgh fgALee left_section_menu"> <p>在这一页上</p><年代p一个ncl一个年代年代="sc-fOICqy jUXuDi grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-gtfDJT giUMKZ" href="#abstract" aria-label="">文摘</一个></年代p一个n><年代pan class="sc-fOICqy jUXuDi grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-gtfDJT giUMKZ" href="#introduction" aria-label="">介绍</一个></年代p一个n><年代pan class="sc-fOICqy jUXuDi grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-gtfDJT giUMKZ" href="#experiments-and-results" aria-label="">结果</一个></年代p一个n><年代pan class="sc-fOICqy jUXuDi grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-gtfDJT giUMKZ" href="#discussion" aria-label="">讨论</一个></年代p一个n><年代pan class="sc-fOICqy jUXuDi grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-gtfDJT giUMKZ" href="#conclusion" aria-label="">结论</一个></年代p一个n><年代pan class="sc-fOICqy jUXuDi grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-gtfDJT giUMKZ" href="#acknowledgments" aria-label="">确认</一个></年代p一个n><年代pan class="sc-fOICqy jUXuDi grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-gtfDJT giUMKZ" href="#references" aria-label="">引用</一个></年代p一个n><年代pan class="sc-fOICqy jUXuDi grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-gtfDJT giUMKZ" href="#copyright" aria-label="">版权</一个></年代p一个n></d我v> </div> </div> <div class="threeColumn__ContentWrapper-sc-1bf4078-3 bbzREB contentWrapper"> <div class="threeColumn__Content-sc-1bf4078-4 jknsZc content"> <div class="articleContent__ArticleContentsWrapper-sc-2yl9jy-0 eSvjPB article_contents"> <div class="articleContent__ArticleContentsSectionsWrapper-sc-2yl9jy-1 jntdRu article_contents__sections_wrapper"> <div class="articleContent__ArticleWrapper-sc-2yl9jy-2 hAzjHP"> <div class="sc-jtggT hRFckM article_header_class"> <div class="sc-ebFjAB igytsx"> <span class="sc-jKVCRD coOovf">特殊的问题</年代p一个n><h2cl一个年代年代="sc-kaNhvL fAyCHF">现代数学在生物医学成像</h2><一个cl一个年代年代=”年代c-htpNat bUhGXt link sc-LKuAh ekTSUD" href="//www.newsama.com/journals/ijbi/si/469690/" aria-label="">把这个特殊的问题</一个><hrcl一个年代年代=”年代c-fcdeBU IXRXP"> </div> <p class="sc-iBEsjs cJuRPa article_type">研究文章|<gydF4y2Ba!-- -->开放获取</p><d我v class="sc-hzNEM jtSvIR article_citation"> 体积<gydF4y2Ba!-- --> 2011年<gydF4y2Ba!-- --> <span class="sc-kxynE bfcQlE">|</年代p一个n>文章的ID<gydF4y2Ba!-- --> 891585年<gydF4y2Ba!-- --> <span class="sc-kxynE bfcQlE">|</年代p一个n><一个cl一个年代年代="sc-htpNat bUhGXt link sc-cooIXK ceqZdW" href="https://doi.org/10.1155/2011/891585" aria-label="Doi-link">https://doi.org/10.1155/2011/891585</一个></d我v> <div class="sc-iGrrsa bSAkNj article_full_citation"> <div class="sc-dEoRIm jpFWyG isHide"> <p>纪尧姆•詹森Laurent雅克·乔纳森·班德Xivry Xavier这些年,Benoit Macq<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> ”<年代p一个n>D我ffeo米orph我c登记与变量的图像对比度增强</年代p一个n>”,<gydF4y2Ba!-- --><i>国际生物医学成像杂志》上</我>,<ggydF4y2BaydF4y2Ba!-- --> 卷。<gydF4y2Ba!-- -->2011年<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 文章的ID<gydF4y2Ba!-- -->891585年<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 16<gydF4y2Ba!-- -->   页面<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 2011年<gydF4y2Ba!-- -->。<gydF4y2Ba!-- --> https://doi.org/10.1155/2011/891585</p></d我v> <button class="sc-iAyFgw irxuxk sc-bmyXtO gFAjsK" color="">显示引用</gydF4y2Babutton> </div> <h1 class="sc-gPEVay iUuzmH sc-chbbiW fUTznD article_title heading-title">Diffeomorphic登记与变量的图像对比度增强</h1></d我v> <div class="sc-hIVACf hYRfeq article_authors"> <hr class="sc-kQsIoO kyyvRa hr__author"> <span class=""><b>Guillaume詹森</gydF4y2Bab><a class="sc-htpNat bUhGXt link" href="mailto:" aria-label="Mail to Author Option"><span class="sc-htoDjs kNoiZu sc-gpHHfC iFiPLx icon-colored _2zt-1j0LmaF8UjTQAM413G icon-themeable" title="" font-size="16"></span></a>,<年代up>1</年代up></span> <span class="">Laurent雅克<gydF4y2Ba!-- -->,<年代up>1</年代up></span> <span class="">乔纳森·班德Xivry<gydF4y2Ba!-- -->,<年代up>1</年代up></span> <span class="">泽维尔这些年<gydF4y2Ba!-- -->,<年代up>2</年代up> 和</年代p一个n><年代p一个ncl一个年代s="">Benoit Macq<年代up>1</年代up></span> <div class="sc-cpmKsF gljosP isHide"> <p><sup>1</年代up><span>信息和通信技术研究所、电子产品和应用数学(ICTEAM),大学Catholique de鲁汶(UCL), 1348 Louvain-la-Neuve,比利时</年代p一个n></p><p><sup>2</年代up><span>放射肿瘤学和放射生物学和放射保护实验室(RBNT),大学Catholique de鲁汶(UCL), 1200年布鲁塞尔,比利时</年代p一个n></p></d我v> <button class="sc-iAyFgw irxuxk sc-eXNvrr gvRxK" color="">显示更多</gydF4y2Babutton> </div> <div class="articleContent__EditorWrapper-sc-2yl9jy-3 evMkvU"> <div class="articleContent__TextWrapper-sc-2yl9jy-8 fYrLtk"> <b>学术编辑器:</gydF4y2Bab>詹姆斯·g·伊</d我v> <div class="articleContent__PublicationTimeLineWrapper-sc-2yl9jy-4 fjviok"> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">收到了</年代p一个n><年代p一个ncl一个年代s="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2010年4月30日</年代p一个n></d我v> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">修改后的</年代p一个n><年代p一个ncl一个年代s="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2010年7月28日</年代p一个n></d我v> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">接受</年代p一个n><年代p一个ncl一个年代s="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2010年9月24日</年代p一个n></d我v> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC isPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">发表</年代p一个n><年代p一个ncl一个年代s="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2010年12月08</年代p一个n></d我v> </div> </div> <article class="sc-kasBVs fuTMHY article_body "> <div> <div class="xml-content"> <h4 class="header" id="abstract">文摘</h4><p>gydF4y2Ba非刚性图像配准被广泛用于评估组织变形在高度变形构造。在现有的方法中,非参数注册算法如光流,或恶魔,通常的优点是快速和容易使用。最近,一位diffeomorphic版本的恶魔算法。这提供了产生可逆的位移场的优势,这是一个必要条件对这些物理。然而,这些方法都是基于强度的匹配和不适合注册图像具有不同的对比度增强。在这种情况下,基于当地的注册方法阶段像Morphons必须被使用。本文的diffeomorphic版本Morphons登记方法提出并与传统Morphons相比,恶魔,diffeomorphic恶魔。验证了方法的上下文中对肺癌患者放疗在几个4 d respiratory-correlated CT扫描的胸腔对比度增强和不变量。</p><年代p一个ncl一个年代年代="end-abs"></span> <h4 id="introduction">1。介绍</h4><p>gydF4y2Ba在基于图像的背景下医学诊断和治疗,以期成像分析高度变形的构造是一个问题在疗程。确实,器官的精确跟踪是困难的,因为形状和位置的变化。非刚性的登记可以用来计算每个图像的立体像素的位移矢量(<一个href=”#B1">1</一个>),使解剖学的空间变化的估计。位移向量计算指向最好在另一个图像对应像素点的位置根据指标是衡量图像的匹配和在某些约束全局属性产生的变形,如可逆性和平滑度。</p><p>gydF4y2Ba几种注册方法已经使用在过去的几年中估计变形在高度变形构造(<一个href=”#B2">2</一个>- - - - - -<一个href=”#B5">5</一个>]。许多一直努力提高位移估计的质量并减少所需的预处理或建模和提高登记速度(<一个href=”#B6">6</一个>- - - - - -<一个href=”#B8">8</一个>]。此外,医疗应用程序注册方法的选择取决于特征(例如,形态)的图像注册(<一个href=”#B1">1</一个>]。现有的方法(<一个href=”#B9">9</一个>)可分为参数、基于模型的方法(b样(<一个href=”#B10">10</一个>),利用薄板样条函数(<一个href=”#B11">11</一个>),径向基函数(<一个href=”#B12">12</一个>),线弹性有限元法(<一个href=”#B13">13</一个>]等)和非参数方法(粘性流体<一个href=”#B14">14</一个>),光学流(<一个href=”#B15">15</一个>),等等)。在这第二个类别,该算法<我>恶魔</我>(<gydF4y2Ba一个href=”#B16">16</一个>,<gydF4y2Ba一个href=”#B17">17</一个>)是快速、高效和容易使用,因为它不需要特殊的预处理和特定的建模。这种方法旨在计算常规位移场产生的良好匹配的强度图像通过最小化一个度量,如平方的总和差异(ssd) [<一个href=”#B18">18</一个>)或互信息(MI) (<一个href=”#B8">8</一个>)图像和测量之间的规律。</p><p>gydF4y2Ba在越来越多的应用程序中,注册用于变形产生的位移场图像从其他形式或其他空间分布地图(例如,放射治疗的剂量相关映射到CT扫描(<一个href=”#B19">19</一个>,<gydF4y2Ba一个href=”#B20">20.</一个>])。因此,基于结构的匹配图像强度不是一个足够的约束以生成逼真的解剖变形估计(<一个href=”#B21">21</一个>]。这就是为什么先验解剖变形的物理特性的信息必须包含在注册过程中。微分同胚映射位移场的必要条件是物理(<一个href=”#B22">22</一个>]。事实上,器官可以被压缩和变形,但不能接受不可逆转的空间转换,例如,显示镜效果。提出了一个方法(<一个href=”#B23">23</一个>恶魔]极限位移场计算的一组diffeomorphic转换,使用diffeomorphic流动和李代数。</p><p>gydF4y2Ba在一些医疗协议,以便造影剂用于解释。这使得注册问题的假设不符合保护强度。此外,直方图均衡化是经常不能正确造影剂可变性,因为不同地区将以不同的方式增强内部的图像。因此,简单的指标,比如SSD或互相关,不适合这些图像匹配和方法适用于注册变量对比图像必须调查(<一个href=”#B24">24</一个>,<gydF4y2Ba一个href=”#B25">25</一个>]。</p><p>gydF4y2Ba类似于恶魔的方法但使用分阶段方法第一次被提出<一个href=”#B26">26</一个>),被称为<我>Morphons</gydF4y2Ba我>。方法是匹配转换的原则(黑暗和光明之间的区域),而不是强度,通过本地空间振动的强度。这种方法使用高斯平滑的正则化迭代过程中位移场和添加剂积累。不过这是不足以确保变形[的可逆性<一个href=”#B22">22</一个>,<gydF4y2Ba一个href=”#B29">27</一个>]。</p><p>gydF4y2Ba摘要Morphons登记使用步骤提出了diffeomorphic积累及其精度评估在胸腔中图像配准,也存在不同的对比度增强,比恶魔。本文组织如下。节<一个href=”#sec2">2</一个>,主要的数学概念和定义。然后,在节<一个href=”#sec3">3</一个>一个通用的非参数注册过程,及其详细列明Morphons和解析提出了部分<一个href=”#sec4">4</一个>。节<一个href=”#sec5">5</一个>应用,不同的注册在胸腔的图像,没有在第一实验和对比度增强对比度增强。这些实验的结果最终讨论的部分<一个href=”#sec6">6</一个>。</p><h4gydF4y2Baid="mathematical-framework">2。数学框架</h4><p>gydF4y2Ba为了清晰,让我们介绍一些关键的数学概念在本文使用。</p><h5gydF4y2Baid="sec2.1">2.1。图片和变形场</h5><p>gydF4y2Ba在本文中,我们总是由小写字母表示3 d图像。例如,在评估的过程中位移场,固定和移动图像<年代vg height="13.4875" id="M1" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="7.1374998" id="M2" style="vertical-align:-0.10033pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,分别。我们认为他们是实值函数的体积<年代vg height="13.775" id="M3" style="vertical-align:-0.0pt;width:17.887501px;" version="1.1" viewbox="0 0 17.887501 13.775" width="17.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.775)"> <g transform="translate(72,-60.98)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.61,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> </g> </g> </svg>点的<年代vg height="14.75" id="M4" style="vertical-align:-3.25793pt;width:95.612503px;" version="1.1" viewbox="0 0 95.612503 14.75" width="95.612503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.380369" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.543869" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-38.52,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-33.65,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-21.56,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-16.69,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-4.6,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> <text transform="matrix(1,0,0,-1,0.27,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>,也就是说,<年代vg height="16.700001" id="M5" style="vertical-align:-2.34499pt;width:251.825px;" version="1.1" viewbox="0 0 251.825 16.700001" width="251.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7)"> <g transform="translate(72,-58.64)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9391651" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.140413" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.493378" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.533768" y="0"> ℱ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.487354" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.527744" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.529182" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="79.156494" y="0"> ∶</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="89.021362" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,26.42,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> <text transform="matrix(1,0,0,-1,36.85,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> →</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.12911" y="0"> ℝ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.932182" y="0"> ∶</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.79705" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.149532" y="0"> ↦</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.203148" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.354622" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="75.51812" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="82.394768" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="86.558266" y="0"> }</t年代p一个n></text> </g> </g> </svg>。大多数时候,这些函数和连续操作,如旋转或积分,必须被理解为近似离散<我>体素</我>网格<年代vg height="17.8375" id="M6" style="vertical-align:-3.25793pt;width:150.9375px;" version="1.1" viewbox="0 0 150.9375 17.8375" width="150.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8375)"> <g transform="translate(72,-57.73)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.12815" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.168539" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.169979" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.333477" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-29.73,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-24.86,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-12.77,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-7.9,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,4.19,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> <text transform="matrix(1,0,0,-1,9.06,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6268301" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> ℤ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,37.83,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> <text transform="matrix(1,0,0,-1,42.7,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</t年代p一个n></text> </g> </g> </svg>,省略治疗量的界限。在这项研究中,进行了图像旋转使用补零外边界。</p><p>gydF4y2Ba上的位移场<年代vg height="13.775" id="M7" style="vertical-align:-0.0pt;width:17.887501px;" version="1.1" viewbox="0 0 17.887501 13.775" width="17.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.775)"> <g transform="translate(72,-60.98)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.61,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> </g> </g> </svg>是一个矢量场<年代vg height="16.6" id="M8" style="vertical-align:-2.26974pt;width:241.83749px;" version="1.1" viewbox="0 0 241.83749 16.6" width="241.83749" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.340701" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.38109" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.50972" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.55011" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.551548" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.204102" y="0"> ∶</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="79.06897" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,16.47,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> <text transform="matrix(1,0,0,-1,26.9,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> →</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.12911" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,53.37,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> <text transform="matrix(1,0,0,-1,58.25,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.364747" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.717232" y="0"> ↦</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.770844" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.960068" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.123566" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.000217" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.163715" y="0"> }</t年代p一个n></text> </g> </g> </svg>。这是有关“变形”操作<年代vg height="14.1" id="M9" style="vertical-align:-0.51414pt;width:74.050003px;" version="1.1" viewbox="0 0 74.050003 14.1" width="74.050003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.1)"> <g transform="translate(72,-60.72)"> <text transform="matrix(1,0,0,-1,-71.95,61.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.490497" y="0"> ≜</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.530886" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.694386" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.72155" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.061771" y="0"> </t年代p一个n></text> </g> </g> </svg>,也就是说,<年代vg height="16.225" id="M10" style="vertical-align:-2.21957pt;width:107.4px;" version="1.1" viewbox="0 0 107.4 16.225" width="107.4" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.225)"> <g transform="translate(72,-59.02)"> <text transform="matrix(1,0,0,-1,-71.95,61.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.190665" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.067314" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.694145" y="0"> ≜</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.734535" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.386848" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.72707" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.604439" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="74.767937" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="81.644592" y="0"> )</t年代p一个n></text> </g> </g> </svg>,<年代vg height="10.95" id="M11" style="vertical-align:-0.12538pt;width:13.1375px;" version="1.1" viewbox="0 0 13.1375 10.95" width="13.1375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> d</t年代p一个n></text> </g> </g> </svg>恒等变形:<年代vg height="16.225" id="M12" style="vertical-align:-2.21957pt;width:60.137501px;" version="1.1" viewbox="0 0 60.137501 16.225" width="60.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.225)"> <g transform="translate(72,-59.02)"> <text transform="matrix(1,0,0,-1,-71.95,61.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.414999" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.578498" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.455149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.081978" y="0"> ≜</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.122368" y="0"> </t年代p一个n></text> </g> </g> </svg>。操作<年代vg height="10.6625" id="M13" style="vertical-align:-0.0pt;width:11.4125px;" version="1.1" viewbox="0 0 11.4125 10.6625" width="11.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6625)"> <g transform="translate(72,-63.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> </g> </g> </svg>,通过扩展其向量场<年代vg height="10.325" id="M14" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,据说<我>d我ffeo米orph我c</我>如果它是可逆的、可微和它的逆矩阵是可微的。为转换<年代vg height="10.6625" id="M15" style="vertical-align:-0.0pt;width:11.4125px;" version="1.1" viewbox="0 0 11.4125 10.6625" width="11.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6625)"> <g transform="translate(72,-63.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> </g> </g> </svg>雅可比矩阵是可逆的,其必须在任何时候不消失<年代vg height="7.1624999" id="M16" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,也就是说,如果<年代vg height="13.5625" id="M17" style="vertical-align:-2.21957pt;width:148.625px;" version="1.1" viewbox="0 0 148.625 13.5625" width="148.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.5625)"> <g transform="translate(72,-61.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2515001" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> t</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.192345" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.355844" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.383251" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.546749" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.710247" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.586899" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.825893" y="0"> ≠</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.478455" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="76.893448" y="0"> f</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="80.669357" y="0"> o</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="86.920853" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="95.247856" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="100.79919" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="104.27502" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="111.91435" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="16.637501" id="M18" style="vertical-align:-4.77652pt;width:90.737503px;" version="1.1" viewbox="0 0 90.737503 16.637501" width="90.737503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-51.3,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.41692" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-23.85,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-20.63,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8648672" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-3.88,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。此外,它必须是积极的(<年代vg height="13.5625" id="M19" style="vertical-align:-2.21957pt;width:94.525002px;" version="1.1" viewbox="0 0 94.525002 13.5625" width="94.525002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.5625)"> <g transform="translate(72,-61.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2515001" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> t</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.192345" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.355844" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.383251" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.546749" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.710247" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.586899" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.226231" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.25412" y="0"> 0</t年代p一个n></text> </g> </g> </svg>)。事实上,一个转换<年代vg height="10.6625" id="M20" style="vertical-align:-0.0pt;width:11.4125px;" version="1.1" viewbox="0 0 11.4125 10.6625" width="11.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6625)"> <g transform="translate(72,-63.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> </g> </g> </svg>与-雅克比不对应于物理变形(作为<我>镜子</我>操作)。</p><p>gydF4y2Ba在数学上,考虑到图像<年代vg height="13.4875" id="M21" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="7.1374998" id="M22" style="vertical-align:-0.10033pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,我们将看到我们的研究,我们的全球目标是估计<年代vg height="10.325" id="M23" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>这样<我>扭曲</我>的<年代vg height="7.1374998" id="M24" style="vertical-align:-0.10033pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>通过<年代vg height="10.325" id="M25" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是“接近”<年代vg height="13.4875" id="M26" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,也就是说,<年代vg height="13.575" id="M27" style="vertical-align:-2.34499pt;width:62.987499px;" version="1.1" viewbox="0 0 62.987499 13.575" width="62.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.575)"> <g transform="translate(72,-61.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.402496" y="0"> ≃</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.442884" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.09568" y="0"> ∘</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.247398" y="0"> Δ</t年代p一个n></text> </g> </g> </svg>与<年代vg height="6.1750002" id="M28" style="vertical-align:-0.0pt;width:5.5999999px;" version="1.1" viewbox="0 0 5.5999999 6.1750002" width="5.5999999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.175)"> <g transform="translate(72,-67.06)"> <text transform="matrix(1,0,0,-1,-71.95,67.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∘</t年代p一个n></text> </g> </g> </svg>常见的函数组成。有时我们将使用的符号<年代p一个ncl一个年代年代=”equation" id="eq1"> <svg height="16.5375" id="M29" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 16.5375" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,165.45,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.652796" y="0"> ⋄</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.967531" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.67178" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.875668" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.540962" y="0"> ∘</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="73.69268" y="0"> Δ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="82.719849" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="308.67001" y="0.63"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="312.8335" y="0.63"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="319.08499" y="0.63"> )</t年代p一个n></text> </g> </g> </svg></span>坚持的<我>扭曲</我>行动的<年代vg height="10.325" id="M30" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>在<年代vg height="7.1374998" id="M31" style="vertical-align:-0.10033pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。推而广之,这种扭曲的符号也可以用于向量场本身,例如,对于两个位移场<年代vg height="14.2375" id="M32" style="vertical-align:-3.13504pt;width:18.5625px;" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.2375" id="M33" style="vertical-align:-3.13504pt;width:18.5625px;" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>,<年代vg height="14.5625" id="M34" style="vertical-align:-3.13504pt;width:119.75px;" version="1.1" viewbox="0 0 119.75 14.5625" width="119.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5625)"> <g transform="translate(72,-60.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.42,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋄</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3147354" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.22,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-26.88,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-4.96,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,2.69,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∘</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1517162" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,18.87,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>。</p><p>gydF4y2Ba在实践中,这种扭曲是应用于离散图像。转换可能因此需要截断(体积边界上)最接近点的体积为了避免外推内图像扭曲。</p><h5gydF4y2Baid="sec2.2">2.2。综合的积累</h5><p>gydF4y2Ba在本文中,我们促进特定方式结合,或<我>积累</我>两个位移场,妥善<年代vg height="14.2375" id="M35" style="vertical-align:-3.13504pt;width:18.5625px;" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.2375" id="M36" style="vertical-align:-3.13504pt;width:18.5625px;" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>。将它们添加到表单<年代vg height="14.2375" id="M37" style="vertical-align:-3.13504pt;width:54.650002px;" version="1.1" viewbox="0 0 54.650002 14.2375" width="54.650002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.42,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-33.2,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>(登记由许多非参数方法;参见<一个href=”#sec3">3</一个>)当然是计算效率,但它打破了一致性的组成相应的空间转换,如图<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig1/" target="_blank">1</一个>。</p><d我v class="floats-partial-section partial-carousel-wrapper" data-section="fig1"> <div class="floats-partial-content fig-content-fig1"> <div class="partial-carousel--single-image"> <img alt="(一)2”n一个米e=”891585。f我g.001a" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.001a.jpg"> <br> <strong>(一)2</年代tr在g></d我v> <div class="partial-carousel--single-image"> <img alt="(b) 1”n一个米e=”891585。f我g.001b" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.001b.jpg"> <br> <strong>(b)1</年代tr在g></d我v> <div class="partial-carousel--single-image"> <img alt="(c) 1⋄2”n一个米e=”891585。f我g.001c" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.001c.jpg"> <br> <strong>(c)1⋄2</年代tr在g></d我v> <div class="partial-carousel--single-image"> <img alt="(d) + 2”n一个米e=”891585。f我g.001d" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.001d.jpg"> <br> <strong>(d)+2</年代tr在g></d我v> <div class="partial-carousel--single-image"> <img alt="(e) + (1 + 2)”n一个米e=”891585。f我g.001e" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.001e.jpg"> <br> <strong>(e)+(1+2)</年代tr在g></d我v> <div class="partial-carousel--single-image"> <img alt="(f) + (1⊕2)”n一个米e=”891585。f我g.001f" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.001f.jpg"> <br> <strong>(f)+(1⊕2)</年代tr在g></d我v> <div class="partial-carousel--single-image"> <img alt="(g)移动图像”n一个米e=”891585。f我g.001g" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.001g.jpg"> <br> <strong>(g)移动图像</年代tr在g></d我v> <div class="partial-carousel--single-image"> <img alt="(h)⋄(1 + 2)”n一个米e=”891585。f我g.001h" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.001h.jpg"> <br> <strong>(h)⋄(1+2)</年代tr在g></d我v> <div class="partial-carousel--single-image"> <img alt="(我)⋄(1⊕2)”n一个米e=”891585。f我g.001i" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.001i.jpg"> <br> <strong>(我)⋄(1⊕2)</年代tr在g></d我v> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig1"> <button class="partial-carousel-dot" aria-label="(a) 𝐷 2"><img alt="(一)2”n一个米e=”891585。f我g.001a" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.001a.jpg"><br><strong>(一)2</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(b) 𝐷 1"><img alt="(b) 1”n一个米e=”891585。f我g.001b" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.001b.jpg"><br><strong>(b)1</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(c) 𝐷 1 ⋄ 𝐷 2"><img alt="(c) 1⋄2”n一个米e=”891585。f我g.001c" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.001c.jpg"><br><strong>(c)1⋄2</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(d) 𝑥 + 𝐷 2"><img alt="(d) + 2”n一个米e=”891585。f我g.001d" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.001d.jpg"><br><strong>(d)+2</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(e) 𝑥 + ( 𝐷 1 + 𝐷 2 )"><img alt="(e) + (1 + 2)”n一个米e=”891585。f我g.001e" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.001e.jpg"><br><strong>(e)+(1+2)</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(f) 𝑥 + ( 𝐷 1 ⊕ 𝐷 2 )"><img alt="(f) + (1⊕2)”n一个米e=”891585。f我g.001f" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.001f.jpg"><br><strong>(f)+(1⊕2)</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(g) moving image 𝑚"><img alt="(g)移动图像”n一个米e=”891585。f我g.001g" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.001g.jpg"><br><strong>(g)移动图像</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(h) 𝑚 ⋄ ( 𝐷 1 + 𝐷 2 )"><img alt="(h)⋄(1 + 2)”n一个米e=”891585。f我g.001h" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.001h.jpg"><br><strong>(h)⋄(1+2)</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(i) 𝑚 ⋄ ( 𝐷 1 ⊕ 𝐷 2 )"><img alt="(我)⋄(1⊕2)”n一个米e=”891585。f我g.001i" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.001i.jpg"><br><strong>(我)⋄(1⊕2)</年代tr在g></button> </div> <div class="partial-carousel-next-prev fig-nav-fig1"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图1</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/ijbi/2011/891585/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="14.2375" id="M38" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg> <svg height="14.2375" id="M39" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg> <svg height="14.5625" id="M40" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 119.75 14.5625" width="119.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5625)"> <g transform="translate(72,-60.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.42,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋄</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3147354" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.22,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-26.88,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-4.96,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,2.69,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∘</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1517162" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,18.87,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg> <svg height="14.2375" id="M41" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg> <svg height="14.2375" id="M42" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg> <svg height="14.2375" id="M43" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg> <svg height="14.2375" id="M44" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 57.112499 14.2375" width="57.112499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.42,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.303192" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-31.24,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg> <svg height="14.5625" id="M45" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.5 14.5625" width="17.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5625)"> <g transform="translate(72,-60.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg> <svg height="14.5625" id="M46" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.5 14.5625" width="17.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5625)"> <g transform="translate(72,-60.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg> <svg height="14.7125" id="M47" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 77.962502 14.7125" width="77.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.27,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∘</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1517162" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-39.09,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-31.44,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.50372" y="0"> d</t年代p一个n></text> </g> </g> </svg> <a href="#sec3">3</一个><年代vg height="14.2375" id="M48" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 164.58749 14.2375" width="164.58749" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.42,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.303192" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-31.24,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-22.89,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-0.97,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,6.68,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,27.9,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,35.55,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋄</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3147354" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,54.75,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg> <svg height="7.1374998" id="M49" style="vertical-align:-0.10033pt" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg> <svg height="7.1374998" id="M50" style="vertical-align:-0.10033pt" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg> <svg height="7.1374998" id="M51" style="vertical-align:-0.10033pt" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg> <table> 对比添加剂和综合领域积累。翘曲是使用线性插值来实现的。在(a)和(b),定义了两个不同的位移场在平面上(视觉清晰)。(c)的领域gydF4y2Ba扭曲的,gydF4y2Ba也就是说,gydF4y2Ba。(d)的领域gydF4y2Ba是应用于像素网格。(e)的网格扭曲的领域从addition-based积累的结果gydF4y2Ba和gydF4y2Ba。在(f),网格扭曲的位移场gydF4y2Ba所组成的gydF4y2Ba和,gydF4y2Ba这是之和(由深蓝色和灰色箭头)gydF4y2Ba。这篇作文是积累重要的因为它对应于位移场的迭代方式应用到一个图像(见部分)gydF4y2Ba。自,(f)gydF4y2Ba的总结向量对应的向量(a)和(c) (g),一个移动的对象gydF4y2Ba划分为4个颜色(像素中心之间的区域)。在(h),扭曲的结果gydF4y2Ba字段的总和。显然,表面是反向(镜面效果,可见因为颜色反转),导致非物质变形(-雅克比)。(我)的扭曲的结果gydF4y2Ba组成的字段。可以注意到,尽管变形物体的形状,颜色的位置是守恒的。</t一个ble> </div> </div> </div> <p>事实上,一个人可以清楚地看到在图<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig1/" target="_blank">1 (h)</一个>在数字图像的扭曲<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig1/" target="_blank">1 (g)</一个>由两个diffeomorphic字段的总和,<年代vg height="14.2375" id="M61" style="vertical-align:-3.13504pt;width:18.5625px;" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.2375" id="M62" style="vertical-align:-3.13504pt;width:18.5625px;" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>不对应于图像的连续弯曲<年代vg height="14.2375" id="M63" style="vertical-align:-3.13504pt;width:18.5625px;" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>然后通过<年代vg height="14.2375" id="M64" style="vertical-align:-3.13504pt;width:18.5625px;" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>,这是在图表示<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig1/" target="_blank">1(我)</一个>。</p><p>gydF4y2Ba然而,<我>综合</我>操作,用<年代vg height="11.725" id="M65" style="vertical-align:-1.49226pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 11.725" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.725)"> <g transform="translate(72,-62.62)"> <text transform="matrix(1,0,0,-1,-71.95,64.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n></text> </g> </g> </svg>,解决了这个问题。它仅仅是定义为<年代p一个ncl一个年代年代=”equation" id="eq2"> <svg height="18.15" id="M66" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.15" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.15)"> <g transform="translate(72,-57.48)"> <text transform="matrix(1,0,0,-1,145.13,61.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,155,58.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,162.66,61.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.303192" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,185.84,58.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,194.19,61.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≜</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,215.25,58.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,222.91,61.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∘</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1392131" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,239.09,58.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,246.74,61.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.50372" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.75522" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="227.38" y="-0.33000001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="231.5435" y="-0.33000001"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="237.795" y="-0.33000001"> )</t年代p一个n></text> </g> </g> </svg></span>通过建设、变形操作与变形场<年代vg height="14.2375" id="M67" style="vertical-align:-3.13504pt;width:57.112499px;" version="1.1" viewbox="0 0 57.112499 14.2375" width="57.112499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.42,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.303192" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-31.24,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>因此,<年代vg height="14.5625" id="M68" style="vertical-align:-3.13504pt;width:47.299999px;" version="1.1" viewbox="0 0 47.299999 14.5625" width="47.299999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5625)"> <g transform="translate(72,-60.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.27,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∘</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1517162" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-39.09,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>。如果两个位移字段diffeomorphic,他们的作文也是diffeomorphic [<一个href=”#B38">28</一个>]。</p><p>gydF4y2Ba操作<年代vg height="11.725" id="M69" style="vertical-align:-1.49226pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 11.725" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.725)"> <g transform="translate(72,-62.62)"> <text transform="matrix(1,0,0,-1,-71.95,64.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n></text> </g> </g> </svg>有一些有趣的和有用的属性。首先,中性的积累当然是获得零位移场,也就是说,<年代vg height="12.55" id="M70" style="vertical-align:-1.49226pt;width:142.675px;" version="1.1" viewbox="0 0 142.675 12.55" width="142.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.55)"> <g transform="translate(72,-61.96)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.00408" y="0"> ⊕</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.483273" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.198105" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.238495" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.265663" y="0"> ⊕</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.581352" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="91.922058" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="103.96245" y="0"> </t年代p一个n></text> </g> </g> </svg>。其次,它很容易证明<我>联想</我>关系<年代vg height="14.75" id="M71" style="vertical-align:-3.25793pt;width:346.3125px;" version="1.1" viewbox="0 0 346.3125 14.75" width="346.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-50.26,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.303192" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-27.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-22.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9391651" y="0"> ⊕</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.242357" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,7.93,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> <text transform="matrix(1,0,0,-1,16.27,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,38.19,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,45.84,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.303192" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.46669" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,73.19,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,80.84,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.303192" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,104.03,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> <text transform="matrix(1,0,0,-1,108.9,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6268301" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,138.45,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,146.1,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.303192" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,169.29,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,176.94,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.303192" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,200.12,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> </g> </g> </svg>三个位移场<年代vg height="14.2375" id="M72" style="vertical-align:-3.13504pt;width:18.5625px;" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>,<年代vg height="14.2375" id="M73" style="vertical-align:-3.13504pt;width:18.5625px;" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>,<年代vg height="14.3875" id="M74" style="vertical-align:-3.25793pt;width:18.5625px;" version="1.1" viewbox="0 0 18.5625 14.3875" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> </g> </g> </svg>。最后,<年代vg height="11.725" id="M75" style="vertical-align:-1.49226pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 11.725" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.725)"> <g transform="translate(72,-62.62)"> <text transform="matrix(1,0,0,-1,-71.95,64.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n></text> </g> </g> </svg>和<年代vg height="7.75" id="M76" style="vertical-align:-0.0pt;width:8.3000002px;" version="1.1" viewbox="0 0 8.3000002 7.75" width="8.3000002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.75)"> <g transform="translate(72,-65.8)"> <text transform="matrix(1,0,0,-1,-71.95,65.85)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋄</t年代p一个n></text> </g> </g> </svg>通过简单相关关系<年代p一个ncl一个年代年代=”equation" id="eq3"> <svg height="15.75" id="M77" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 15.75" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.75)"> <g transform="translate(72,-59.4)"> <text transform="matrix(1,0,0,-1,141.03,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,150.9,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,158.56,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.303192" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,181.74,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,190.09,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,212,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,219.66,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.327718" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,240.88,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,248.53,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⋄</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3147354" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,267.72,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,272.6,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="201.52" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="205.6835" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="211.935" y="0"> )</t年代p一个n></text> </g> </g> </svg></span>这意味着位移场<年代vg height="14.2375" id="M78" style="vertical-align:-3.13504pt;width:57.112499px;" version="1.1" viewbox="0 0 57.112499 14.2375" width="57.112499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.42,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.303192" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-31.24,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>相当于求和<年代vg height="14.2375" id="M79" style="vertical-align:-3.13504pt;width:18.5625px;" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>与字段<年代vg height="14.2375" id="M80" style="vertical-align:-3.13504pt;width:18.5625px;" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>扭曲的<年代vg height="14.2375" id="M81" style="vertical-align:-3.13504pt;width:18.5625px;" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>。这是见图<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig1/" target="_blank">1</一个>:矢量图<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig1/" target="_blank">1(我)</一个>,相应的连续弯曲<年代vg height="14.2375" id="M82" style="vertical-align:-3.13504pt;width:18.5625px;" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>然后<年代vg height="14.2375" id="M83" style="vertical-align:-3.13504pt;width:18.5625px;" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2375)"> <g transform="translate(72,-60.61)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>向量数据的总和<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig1/" target="_blank">1(一)</一个>和<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig1/" target="_blank">1 (c)</一个>,如图<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig1/" target="_blank">1 (f)</一个>。</p><h5gydF4y2Baid="sec2.3">2.3。Diffeomorphic流和求幂</h5><p>gydF4y2Ba一个重要的概念用于部分<一个href=”#sec4.2">4.2</一个>的概念(连续)<我>d我ffeo米orph我c流</我>(<gydF4y2Ba一个href=”#B29">27</一个>,<gydF4y2Ba一个href=”#B27">29日</一个>,<gydF4y2Ba一个href=”#B28">30.</一个>]。给定的一个点<年代vg height="14.1875" id="M84" style="vertical-align:-0.33858pt;width:45.875px;" version="1.1" viewbox="0 0 45.875 14.1875" width="45.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.1875)"> <g transform="translate(72,-60.65)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.339981" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.380369" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-40.22,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> </g> </g> </svg>和一个平滑的向量场<年代vg height="11.2875" id="M85" style="vertical-align:-0.33858pt;width:46.424999px;" version="1.1" viewbox="0 0 46.424999 11.2875" width="46.424999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.2875)"> <g transform="translate(72,-62.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.340701" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.38109" y="0"> </t年代p一个n></text> </g> </g> </svg>,流<年代vg height="14.6" id="M86" style="vertical-align:-3.13504pt;width:50.375px;" version="1.1" viewbox="0 0 50.375 14.6" width="50.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.62,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.08,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.241398" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.154837" y="0"> )</t年代p一个n></text> </g> </g> </svg>是动态的解决方案<年代vg height="16.5375" id="M87" style="vertical-align:-2.21957pt;width:59.987499px;" version="1.1" viewbox="0 0 59.987499 16.5375" width="59.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.9264221" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.089921" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.00336" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.63019" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.670578" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-28.93,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> </g> </g> </svg>下面的(自治)常微分方程:<年代p一个ncl一个年代年代=”equation" id="EEq1"> <svg height="57.799999" id="M88" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 57.799999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,57.8)"> <g transform="translate(72,-25.76)"> <text transform="matrix(1,0,0,-1,172.6,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> d</t年代p一个n></text> <g> <path d="m 170.65,59.28 10.16,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,170.65,47.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2515001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.36" y="-8.75"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.361919" y="-8.75"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.525419" y="-8.75"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.438858" y="-8.75"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.07819" y="-8.75"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.11858" y="-8.75"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.258991" y="-8.75"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.422493" y="-8.75"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.348915" y="-8.75"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="75.60041" y="-8.75"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.72" y="17.85"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.72192" y="17.85"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.88542" y="17.85"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.136917" y="17.85"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.776253" y="17.85"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.804138" y="17.85"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.680786" y="17.85"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="303.47" y="1.65"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="307.63348" y="1.65"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="313.88501" y="1.65"> )</t年代p一个n></text> </g> </g> </svg></span>在给定的“时间”<年代vg height="11.0625" id="M89" style="vertical-align:-0.30096pt;width:32.224998px;" version="1.1" viewbox="0 0 32.224998 11.0625" width="32.224998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.37677" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.417158" y="0"> 0</t年代p一个n></text> </g> </g> </svg>,位置<年代vg height="14.6" id="M90" style="vertical-align:-3.13504pt;width:50.375px;" version="1.1" viewbox="0 0 50.375 14.6" width="50.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.62,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.08,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.241398" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.154837" y="0"> )</t年代p一个n></text> </g> </g> </svg>仅仅是一个点后的轨迹<年代vg height="10.325" id="M91" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>无意中从初始化<年代vg height="7.1624999" id="M92" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>(见图<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig2/" target="_blank">2</一个>)。后(<一个href=”#B29">27</一个>),一个向量场的指数<年代vg height="10.325" id="M93" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,也就是说,<年代vg height="14.25" id="M94" style="vertical-align:-2.72118pt;width:84.612503px;" version="1.1" viewbox="0 0 84.612503 14.25" width="84.612503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.25)"> <g transform="translate(72,-60.6)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.217831" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.38133" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.258701" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.898033" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.925919" y="0"> </t年代p一个n></text> </g> </g> </svg>是非线性变形操作获得的流动<年代vg height="10.325" id="M95" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>在时间<年代vg height="10.825" id="M96" style="vertical-align:-0.11285pt;width:32.224998px;" version="1.1" viewbox="0 0 32.224998 10.825" width="32.224998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.825)"> <g transform="translate(72,-63.34)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.37677" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.417158" y="0"> 1</t年代p一个n></text> </g> </g> </svg>,也就是说,<年代vg height="14.6" id="M97" style="vertical-align:-3.13504pt;width:142.22501px;" version="1.1" viewbox="0 0 142.22501 14.6" width="142.22501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.217831" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.38133" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.258701" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.422199" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.585697" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.462349" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.101681" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.12957" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,7.52,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,15.06,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.241398" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.492897" y="0"> )</t年代p一个n></text> </g> </g> </svg>。有趣的是,这个指数映射作为常见的纯量值指数,也就是说,<年代vg height="14.075" id="M98" style="vertical-align:-2.72118pt;width:249.2625px;" version="1.1" viewbox="0 0 249.2625 14.075" width="249.2625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.075)"> <g transform="translate(72,-60.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.217831" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.38133" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.433022" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.31039" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.249557" y="0"> ∘</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.489273" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.040604" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.292107" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="81.707108" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="85.870605" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="92.847275" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="102.72465" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="110.36398" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="122.40437" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="127.9557" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="134.2072" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="144.62221" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="148.78571" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="152.9492" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="162.77655" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="174.12929" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="181.10596" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="185.26945" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="195.14682" y="0"> )</t年代p一个n></text> </g> </g> </svg>为<年代vg height="13.425" id="M99" style="vertical-align:-2.29482pt;width:55.237499px;" version="1.1" viewbox="0 0 55.237499 13.425" width="55.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.0391889" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.25294" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.705448" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.745838" y="0"> ℝ</t年代p一个n></text> </g> </g> </svg>,它是可逆的,只要考虑到倒向量场,也就是说,<年代vg height="14.1875" id="M100" style="vertical-align:-2.72118pt;width:159.325px;" version="1.1" viewbox="0 0 159.325 14.1875" width="159.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.1875)"> <g transform="translate(72,-60.65)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.217831" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.38133" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.945885" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.823254" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.762421" y="0"> ∘</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.002136" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.553467" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="72.80497" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="83.219971" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="87.383469" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="97.260834" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="104.90017" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="116.94056" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="121.10406" y="0"> d</t年代p一个n></text> </g> </g> </svg>。此外,对于可微的<年代vg height="10.325" id="M101" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="14.075" id="M102" style="vertical-align:-2.72118pt;width:50.662498px;" version="1.1" viewbox="0 0 50.662498 14.075" width="50.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.075)"> <g transform="translate(72,-60.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.217831" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.38133" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.258701" y="0"> )</t年代p一个n></text> </g> </g> </svg>也是一个微分同胚映射<年代vg height="13.775" id="M103" style="vertical-align:-0.0pt;width:17.887501px;" version="1.1" viewbox="0 0 17.887501 13.775" width="17.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.775)"> <g transform="translate(72,-60.98)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.61,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> </g> </g> </svg>。换句话说,<年代vg height="14.075" id="M104" style="vertical-align:-2.72118pt;width:50.662498px;" version="1.1" viewbox="0 0 50.662498 14.075" width="50.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.075)"> <g transform="translate(72,-60.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.217831" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.38133" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.258701" y="0"> )</t年代p一个n></text> </g> </g> </svg>修改3 d坐标点的运动之间没有交集。事实上,这种可能性会诱发一个点<年代vg height="7.1624999" id="M105" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>有两个不同的运动矢量,禁止的情况(<一个href=”#EEq1">4</一个>)自<年代vg height="13.45" id="M106" style="vertical-align:-2.21957pt;width:31.475px;" version="1.1" viewbox="0 0 31.475 13.45" width="31.475" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8773699" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.040869" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.917519" y="0"> )</t年代p一个n></text> </g> </g> </svg>独特的定义。</p><d我v class="floats-partial-section partial-carousel-wrapper" data-section="fig2"> <div class="floats-partial-content fig-content-fig2"> <div class="partial-carousel--single-image"> <img alt="" name="891585.fig.002" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.002.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图2</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/ijbi/2011/891585/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="14.075" id="M107" style="vertical-align:-2.72118pt" version="1.1" viewbox="0 0 50.662498 14.075" width="50.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.075)"> <g transform="translate(72,-60.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.217831" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.38133" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.258701" y="0"> )</t年代p一个n></text> </g> </g> </svg> <svg height="10.325" id="M108" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg> <svg height="10.825" id="M109" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 32.224998 10.825" width="32.224998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.825)"> <g transform="translate(72,-63.34)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.37677" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.417158" y="0"> 1</t年代p一个n></text> </g> </g> </svg> <svg height="10.325" id="M110" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg> <svg height="7.1624999" id="M111" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg> <svg height="14.075" id="M112" style="vertical-align:-2.72118pt" version="1.1" viewbox="0 0 69.662498 14.075" width="69.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.075)"> <g transform="translate(72,-60.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.217831" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.38133" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.258701" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.422199" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.585697" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.462349" y="0"> )</t年代p一个n></text> </g> </g> </svg> <svg height="10.575" id="M113" style="vertical-align:-0.20064pt" version="1.1" viewbox="0 0 12.625 10.575" width="12.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.575)"> <g transform="translate(72,-63.54)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg> <svg height="13.45" id="M114" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 107.4 13.45" width="107.4" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.190665" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.067314" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.694145" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.734535" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.386848" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.72707" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.604439" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="74.767937" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="81.644592" y="0"> )</t年代p一个n></text> </g> </g> </svg> <table> diffeomorphic流gydF4y2Ba相关的向量场gydF4y2Ba解决方案是在时间吗gydF4y2Ba在轨迹相切gydF4y2Ba在每一个点(代表在2 d)。我们看到的运动gydF4y2Ba引起的gydF4y2Ba更兼容gydF4y2Ba比这所产生的gydF4y2Ba。</t一个ble> </div> </div> </div> <h5 id="sec2.4">2.4。缩放和平方</h5><p>gydF4y2Ba一个数值方案存在计算约但有效<年代vg height="14.075" id="M115" style="vertical-align:-2.72118pt;width:69.662498px;" version="1.1" viewbox="0 0 69.662498 14.075" width="69.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.075)"> <g transform="translate(72,-60.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.217831" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.38133" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.258701" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.422199" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.585697" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.462349" y="0"> )</t年代p一个n></text> </g> </g> </svg>当<年代vg height="7.1624999" id="M116" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>属于常规网格体素<年代vg height="11.1" id="M117" style="vertical-align:-0.1881pt;width:12.2px;" version="1.1" viewbox="0 0 12.2 11.1" width="12.2" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。实际上,当<年代vg height="10.325" id="M118" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是接近于零(即<年代vg height="10.95" id="M119" style="vertical-align:-0.12538pt;width:43.8125px;" version="1.1" viewbox="0 0 43.8125 10.95" width="43.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.490497" y="0"> ≈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.530886" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.694386" y="0"> d</t年代p一个n></text> </g> </g> </svg>),田野的指数可以使用一阶泰勒展开近似<年代vg height="14.1875" id="M120" style="vertical-align:-2.72118pt;width:143.7375px;" version="1.1" viewbox="0 0 143.7375 14.1875" width="143.7375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.1875)"> <g transform="translate(72,-60.65)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.217831" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.38133" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.258701" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.898033" y="0"> ≈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.925919" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.089417" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.129089" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="80.469307" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="93.82251" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="105.8504" y="0"> Δ</t年代p一个n></text> </g> </g> </svg>,即转换本身。另一方面,流动方程的解决方案(<一个href=”#EEq1">4</一个>)<gydF4y2Ba年代vg height="10.825" id="M121" style="vertical-align:-0.11285pt;width:32.224998px;" version="1.1" viewbox="0 0 32.224998 10.825" width="32.224998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.825)"> <g transform="translate(72,-63.34)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.37677" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.417158" y="0"> 1</t年代p一个n></text> </g> </g> </svg>可以用“离散化”近似<年代vg height="9.125" id="M122" style="vertical-align:-0.11285pt;width:5.0124998px;" version="1.1" viewbox="0 0 5.0124998 9.125" width="5.0124998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.125)"> <g transform="translate(72,-64.7)"> <text transform="matrix(1,0,0,-1,-71.95,64.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>在0和1之间。事实上,正如<年代vg height="19.6625" id="M123" style="vertical-align:-2.72118pt;width:153.625px;" version="1.1" viewbox="0 0 153.625 19.6625" width="153.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.6625)"> <g transform="translate(72,-56.27)"> <text transform="matrix(1,0,0,-1,-71.95,59.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.217831" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.38133" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.258701" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.898033" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.925919" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.477249" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.728752" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.15625" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="82.319756" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,16.62,64.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,27.86,59.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.064915" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,42.09,64.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,46.47,67.77)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>(指数<年代vg height="13.9" id="M124" style="vertical-align:-0.0pt;width:14.4875px;" version="1.1" viewbox="0 0 14.4875 13.9" width="14.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9)"> <g transform="translate(72,-60.88)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.7,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>表达的次数变形操作结合本身),可以使用<我>缩放和平方</我>策略计算指数(<一个href=”#B30">31日</一个>]。如果一个选择<年代vg height="10.7375" id="M125" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>这样的场<年代vg height="13.9" id="M126" style="vertical-align:-0.0pt;width:34.5625px;" version="1.1" viewbox="0 0 34.5625 13.9" width="34.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9)"> <g transform="translate(72,-60.88)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.7,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.46,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>接近于零,一阶近似可以用来估计<年代vg height="17.2875" id="M127" style="vertical-align:-2.72118pt;width:72.512497px;" version="1.1" viewbox="0 0 72.512497 17.2875" width="72.512497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.2875)"> <g transform="translate(72,-58.17)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.217831" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.38133" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-39.31,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-28.08,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8773699" y="0"> )</t年代p一个n></text> </g> </g> </svg>(基于Pade近似值原点附近)。然后,流动方程的解决方案是通过执行计算<年代vg height="10.7375" id="M128" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>递归的作品本身,因为这样的组合计算负担得起。注意,在<年代vg height="10.9125" id="M129" style="vertical-align:-0.17555pt;width:35.799999px;" version="1.1" viewbox="0 0 35.799999 10.9125" width="35.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.239957" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.280346" y="0"> 0</t年代p一个n></text> </g> </g> </svg>相当于一个简单的一阶近似。领域的扩展和调整步骤求幂(<一个href=”#B22">22</一个>描述以下。<年代p一个ncl一个年代年代=”l是t”><span class="list-item"><span class="list-label">(我)</年代p一个n><年代p一个ncl一个年代s="list-content"><i>扩展。</我>分<年代vg height="10.325" id="M130" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>的一个因素<年代vg height="13.9" id="M131" style="vertical-align:-0.0pt;width:14.4875px;" version="1.1" viewbox="0 0 14.4875 13.9" width="14.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9)"> <g transform="translate(72,-60.88)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.7,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>这样<年代vg height="13.9" id="M132" style="vertical-align:-0.0pt;width:34.5625px;" version="1.1" viewbox="0 0 34.5625 13.9" width="34.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9)"> <g transform="translate(72,-60.88)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.7,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.46,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是足够小的,例如,当<年代vg height="17.799999" id="M133" style="vertical-align:-3.13504pt;width:61.4375px;" version="1.1" viewbox="0 0 61.4375 17.799999" width="61.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8)"> <g transform="translate(72,-57.76)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.5390692" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.16,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-47.92,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8773699" y="0"> 为</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-31.51,57.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代p一个n></text> </g> </g> </svg>=<年代vg height="17.9" id="M134" style="vertical-align:-3.21404pt;width:147.375px;" version="1.1" viewbox="0 0 147.375 17.9" width="147.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.9)"> <g transform="translate(72,-57.68)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.727334" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.278666" y="0"> x</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-46.25,57.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-40.94,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.5390692" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-28.15,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-16.91,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8773699" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.040869" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.917519" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.081018" y="0"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.08342" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.123806" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.375305" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.501057" y="0"> 5</t年代p一个n></text> </g> </g> </svg>体素。</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(2)</年代p一个n><年代p一个ncl一个年代s="list-content"><i>求幂。</我>计算一阶显式集成流的:<年代vg height="17.862499" id="M135" style="vertical-align:-3.13504pt;width:252.675px;" version="1.1" viewbox="0 0 252.675 17.862499" width="252.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8625)"> <g transform="translate(72,-57.71)"> <text transform="matrix(1,0,0,-1,-71.95,60.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.22,60.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.666979" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.707369" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-13.18,57.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-5.63,60.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.241398" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,16.87,66.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,28.1,60.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> ≈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.830717" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.082218" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.245716" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.122368" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.074036" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.414257" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,93.77,66.06)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,105.01,60.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8773699" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.040869" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.917519" y="0"> )</t年代p一个n></text> </g> </g> </svg>。</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(3)</年代p一个n><年代p一个ncl一个年代s="list-content"><i>平方。</我>执行<年代vg height="10.7375" id="M136" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>递归的平方(使用字段复合)流的时间<年代vg height="13.9" id="M137" style="vertical-align:-0.0pt;width:21.987499px;" version="1.1" viewbox="0 0 21.987499 13.9" width="21.987499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9)"> <g transform="translate(72,-60.88)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.7,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n></text> </g> </g> </svg>为了获得流时间1,这是一场指数。换句话说,开始<年代vg height="13.95" id="M138" style="vertical-align:-0.0pt;width:61.799999px;" version="1.1" viewbox="0 0 61.799999 13.95" width="61.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.95)"> <g transform="translate(72,-60.84)"> <text transform="matrix(1,0,0,-1,-71.95,60.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.37,60.89)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-33.31,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="7.2904158" y="0"> )</t年代p一个n></text> </g> </g> </svg>,做<年代vg height="10.7375" id="M139" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>倍计算<年代vg height="11.7125" id="M140" style="vertical-align:-0.0pt;width:88.574997px;" version="1.1" viewbox="0 0 88.574997 11.7125" width="88.574997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.7125)"> <g transform="translate(72,-62.63)"> <text transform="matrix(1,0,0,-1,-71.95,62.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.37,62.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ←</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.041109" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-30.3,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-22.44,62.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∘</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1517162" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-6.26,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> </g> </g> </svg>,为了得到<年代vg height="15.1" id="M141" style="vertical-align:-2.72118pt;width:90.275002px;" version="1.1" viewbox="0 0 90.275002 15.1" width="90.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.1)"> <g transform="translate(72,-59.92)"> <text transform="matrix(1,0,0,-1,-71.95,62.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.37,62.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≃</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.115887" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.918718" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.333717" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.497215" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.374588" y="0"> )</t年代p一个n></text> </g> </g> </svg>。</年代p一个n></年代p一个n></span></p> <p>我们可以看到,使用这种方法,<年代vg height="10.7375" id="M142" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>成分(因此<年代vg height="10.7375" id="M143" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>需要插入)评估指数。相比标准流的估计在固定时间间隔的离散化<年代vg height="13.125" id="M144" style="vertical-align:-1.95624pt;width:32.674999px;" version="1.1" viewbox="0 0 32.674999 13.125" width="32.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.414999" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.616247" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.867746" y="0"> ]</t年代p一个n></text> </g> </g> </svg>在<年代vg height="13.9" id="M145" style="vertical-align:-0.0pt;width:14.4875px;" version="1.1" viewbox="0 0 14.4875 13.9" width="14.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9)"> <g transform="translate(72,-60.88)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.7,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>步骤,缩放和平方方法限制了向量场的数值错误由于成分,但这并不减少误差的放大由于现场评估<年代vg height="14.0375" id="M146" style="vertical-align:-0.11285pt;width:46.262501px;" version="1.1" viewbox="0 0 46.262501 14.0375" width="46.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.0375)"> <g transform="translate(72,-60.77)"> <text transform="matrix(1,0,0,-1,-71.95,60.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.37677" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.417158" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-46.27,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> </t年代p一个n></text> </g> </g> </svg>。</p><h4gydF4y2Baid="generic-registration-pipeline">3所示。一般注册管道</h4><p>gydF4y2Ba非刚性的配准方法可分为参数和非参数方法。参数(或模型)方法旨在计算参数变形模型的在高维空间中以优化的全球目标函数考虑图像相似性和转换规律(<一个href=”#B10">10</一个>]。在这种情况下,先验信息包含在modelization和规律性标准的非刚性的转换。例如,谐波的能量转换可以影响目标函数中<一个href=”#B31">32</一个>]。</p><p>gydF4y2Ba另一方面,非参数方法可以解耦相似性从正则化优化直接作用于位移场。先验信息然后被包括在优化过程通过使用适当的正则化技术。解耦优化使登记计算效率(<一个href=”#B8">8</一个>),主要是因为每个位移矢量的计算是独立于他人,但它阻止我们容易包括更复杂的正则化约束在这个过程中,例如,如体积保持注册(<一个href=”#B32">33</一个>,<gydF4y2Ba一个href=”#B33">34</一个>]。</p><h5gydF4y2Baid="sec3.1">3.1。多尺度非参数注册</h5><p>gydF4y2Ba大多数非参数注册都基于一个迭代的过程,由3个步骤:(i)场计算,(ii)领域积累,和(3)场正则化。这个想法是为了逐步构建一个适当的位移场通过迭代改善固定图像之间的匹配和运动图像扭曲的位移场,根据一定的指标。注意,根据位移一个试图模型的性质,应用正则化在积累上的增量字段或字段。加快场增量对应于一个粘性流体建模,同时加快全球转换对应于一个弹性固体模型(<一个href=”#B14">14</一个>]。第二个是在这项研究中。</p><p>gydF4y2Ba在这篇文章中,我们一般非参数注册框架(例如,恶魔和Morphons)有效实行<我>多尺度</我>方法;即位移场估计是稳定通过分解在几个固定和移动图像<我>尺度</我>例如,使用一个简单的平滑,将采样过程<一个href=”#B34">35</一个>]。</p><p>gydF4y2Ba上述三个步骤应用到一定次数(直到达到一定的算法停止条件)每个规模分别从粗到细尺度(图<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig3/" target="_blank">3</一个>)。这三个基本块的一般解释以后。迭代方法应用在每个规模中描述部分<一个href=”#sec3.2">3.2</一个>。</p><d我v class="floats-partial-section partial-carousel-wrapper" data-section="fig3"> <div class="floats-partial-content fig-content-fig3"> <div class="partial-carousel--single-image"> <img alt="" name="891585.fig.003" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.003.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图3</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/ijbi/2011/891585/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="10.9125" id="M147" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 11.4125 10.9125" width="11.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代p一个n></text> </g> </g> </svg> <svg height="10.475" id="M148" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</t年代p一个n></text> </g> </g> </svg> <svg height="10.9125" id="M149" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.7875 10.9125" width="11.7875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ψ</t年代p一个n></text> </g> </g> </svg> <table> 非参数登记管道是由三个主要操作(gydF4y2Ba,,ggydF4y2BaydF4y2Ba)和移动图像的扭曲。从粗到细尺度上执行这些操作。在每个规模,应用迭代过程,直到它到达停止准则。</t一个ble> </div> </div> </div> <h6 id="sec3.1.1">3.1.1。场计算</h6><p>gydF4y2Ba在登记过程中,每次迭代更新位移场(<年代vg height="14.3375" id="M150" style="vertical-align:-3.21404pt;width:18.275px;" version="1.1" viewbox="0 0 18.275 14.3375" width="18.275" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>)首先计算一个函数(<年代vg height="10.9125" id="M151" style="vertical-align:-0.17555pt;width:11.4125px;" version="1.1" viewbox="0 0 11.4125 10.9125" width="11.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代p一个n></text> </g> </g> </svg>固定的图像(<年代vg height="13.4875" id="M152" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>)和移动图像(<年代vg height="7.1374998" id="M153" style="vertical-align:-0.10033pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>前一次迭代)扭曲造成的位移场(<年代vg height="14.35" id="M154" style="vertical-align:-3.22282pt;width:18.5875px;" version="1.1" viewbox="0 0 18.5875 14.35" width="18.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.35)"> <g transform="translate(72,-60.52)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>):<年代p一个ncl一个年代年代=”equation" id="EEq2"> <svg height="19.35" id="M155" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,151.35,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,161.23,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,169.35,61.13)"> <tspan style="font-size: 12.50px; " x="34.259998" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ⟵</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.143053" y="0"> Θ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.110001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.049164" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.250412" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.91571" y="0"> ∘</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.067429" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,249.45,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,254.34,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9400001" y="-2.51"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="219.78" y="-2.51"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="223.9435" y="-2.51"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="230.19499" y="-2.51"> )</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="14.675" id="M156" style="vertical-align:-3.22282pt;width:17.525px;" version="1.1" viewbox="0 0 17.525 14.675" width="17.525" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.675)"> <g transform="translate(72,-60.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.6625" id="M157" style="vertical-align:-3.21404pt;width:17.2125px;" version="1.1" viewbox="0 0 17.2125 14.6625" width="17.2125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6625)"> <g transform="translate(72,-60.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>表示变形操作有关<年代vg height="14.35" id="M158" style="vertical-align:-3.22282pt;width:18.5875px;" version="1.1" viewbox="0 0 18.5875 14.35" width="18.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.35)"> <g transform="translate(72,-60.52)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.3375" id="M159" style="vertical-align:-3.21404pt;width:18.275px;" version="1.1" viewbox="0 0 18.275 14.3375" width="18.275" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,分别。</p><p>gydF4y2Ba根据图像的性质是注册,这个局部位移估计可以基于不同的局部图像指标,如SSD (<一个href=”#B17">17</一个>),互信息计算块体素(<一个href=”#B8">8</一个>,<gydF4y2Ba一个href=”#B35">36</一个>),和当地相(<一个href=”#B26">26</一个>]。</p><h6gydF4y2Baid="sec3.1.2">3.1.2。领域积累</h6><p>gydF4y2Ba场计算后,总位移<年代vg height="14.35" id="M160" style="vertical-align:-3.22282pt;width:18.5875px;" version="1.1" viewbox="0 0 18.5875 14.35" width="18.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.35)"> <g transform="translate(72,-60.52)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>必须增加更新<年代p一个ncl一个年代年代=”equation" id="EEq3"> <svg height="19.35" id="M161" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,156.16,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,166.04,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,174.4,61.13)"> <tspan style="font-size: 12.50px; " x="34.779999" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.630001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ⟵</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.143053" y="0"> Φ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,224.91,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,229.8,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,244.89,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,249.53,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9400001" y="-2.51"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="224.59" y="-2.51"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="228.75349" y="-2.51"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="235.005" y="-2.51"> )</t年代p一个n></text> </g> </g> </svg></span></p> <p>这种积累操作<年代vg height="10.475" id="M162" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</t年代p一个n></text> </g> </g> </svg>有时被实现为一个简单的积累和更新字段(如[<一个href=”#B18">18</一个>,<gydF4y2Ba一个href=”#B36">37</一个>,<gydF4y2Ba一个href=”#B37">38</一个>])。然而,在部分解释<一个href=”#sec2.2">2.2</一个>,这种积累可能是计算有效但不符合相应的构成空间的转换。因此,解决方案是取代它的综合积累<年代vg height="11.725" id="M163" style="vertical-align:-1.49226pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 11.725" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.725)"> <g transform="translate(72,-62.62)"> <text transform="matrix(1,0,0,-1,-71.95,64.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n></text> </g> </g> </svg>介绍了早些时候。积累<年代vg height="14.35" id="M164" style="vertical-align:-3.22282pt;width:56.849998px;" version="1.1" viewbox="0 0 56.849998 14.35" width="56.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.35)"> <g transform="translate(72,-60.52)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.4,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.303192" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-31.22,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>的位移场<年代vg height="14.35" id="M165" style="vertical-align:-3.22282pt;width:18.5875px;" version="1.1" viewbox="0 0 18.5875 14.35" width="18.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.35)"> <g transform="translate(72,-60.52)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>与<年代vg height="14.3375" id="M166" style="vertical-align:-3.21404pt;width:18.275px;" version="1.1" viewbox="0 0 18.275 14.3375" width="18.275" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>然后兼容吗<年代vg height="14.3375" id="M167" style="vertical-align:-3.21404pt;width:18.275px;" version="1.1" viewbox="0 0 18.275 14.3375" width="18.275" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>估计。事实上,自<年代vg height="14.3375" id="M168" style="vertical-align:-3.21404pt;width:18.275px;" version="1.1" viewbox="0 0 18.275 14.3375" width="18.275" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>计算从<年代vg height="14.675" id="M169" style="vertical-align:-3.22282pt;width:41.037498px;" version="1.1" viewbox="0 0 41.037498 14.675" width="41.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.675)"> <g transform="translate(72,-60.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.652796" y="0"> ∘</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.804512" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.11,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>的积累<年代vg height="14.35" id="M170" style="vertical-align:-3.22282pt;width:18.5875px;" version="1.1" viewbox="0 0 18.5875 14.35" width="18.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.35)"> <g transform="translate(72,-60.52)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.3375" id="M171" style="vertical-align:-3.21404pt;width:18.275px;" version="1.1" viewbox="0 0 18.275 14.3375" width="18.275" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>必须修改<年代vg height="14.35" id="M172" style="vertical-align:-3.22282pt;width:18.5875px;" version="1.1" viewbox="0 0 18.5875 14.35" width="18.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.35)"> <g transform="translate(72,-60.52)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>通过<年代vg height="14.3375" id="M173" style="vertical-align:-3.21404pt;width:18.275px;" version="1.1" viewbox="0 0 18.275 14.3375" width="18.275" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>本质上,这一过程集成的操作<年代vg height="11.725" id="M174" style="vertical-align:-1.49226pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 11.725" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.725)"> <g transform="translate(72,-62.62)"> <text transform="matrix(1,0,0,-1,-71.95,64.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n></text> </g> </g> </svg>。此外,结合性的<年代vg height="11.725" id="M175" style="vertical-align:-1.49226pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 11.725" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.725)"> <g transform="translate(72,-62.62)"> <text transform="matrix(1,0,0,-1,-71.95,64.16)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n></text> </g> </g> </svg>验证位移场的综合积累几个迭代,如图<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig3/" target="_blank">3</一个>。</p><h6gydF4y2Baid="sec3.1.3">3.1.3。场正则化</h6><p>gydF4y2Ba最终,字段是正规化为了得到一个平滑转换和减少图像噪声的影响在注册输出:<年代p一个ncl一个年代年代=”equation" id="EEq4"> <svg height="19.35" id="M176" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,166.13,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,176.01,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,184.37,61.13)"> <tspan style="font-size: 12.50px; " x="34.57" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.419998" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ⟵</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.155556" y="0"> Ψ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,234.67,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,239.56,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9299998" y="-2.51"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="234.56" y="-2.51"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="238.7235" y="-2.51"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="244.97501" y="-2.51"> )</t年代p一个n></text> </g> </g> </svg></span>这个操作<年代vg height="10.9125" id="M177" style="vertical-align:-0.0pt;width:11.7875px;" version="1.1" viewbox="0 0 11.7875 10.9125" width="11.7875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ψ</t年代p一个n></text> </g> </g> </svg>是通过应用低通滤波器对每个组件的位移场。我们假设它是一个高斯平滑的大小<年代vg height="19.200001" id="M178" style="vertical-align:-4.35121pt;width:18.0875px;" version="1.1" viewbox="0 0 18.0875 19.200001" width="18.0875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.2)"> <g transform="translate(72,-56.64)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.61,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.3400002"> Ψ</t年代p一个n></text> </g> </g> </svg>一些体素,会减少谐波的能量转换(<一个href=”#B31">32</一个>]。</p><p>gydF4y2Ba它总是可以产生可逆的领域通过执行一个非常强大的高斯平滑。然而,这可能会降低显著位移估计的准确性通过限制的解决方案过于光滑的位移场。另一方面,通过防止位移场的不可逆转,diffeomorphic积累行为在某种程度上作为一个正规化,允许可逆的字段的估计只在执行适当的平滑。</p><h5我d=”年代ec3.2">3.2。注册算法</h5><p>gydF4y2Ba现在让我们解释整个多尺度非参数注册算法依赖于三个具体过程<年代vg height="13.7375" id="M179" style="vertical-align:-2.26974pt;width:63.025002px;" version="1.1" viewbox="0 0 63.025002 13.7375" width="63.025002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.7375)"> <g transform="translate(72,-61.01)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.00144" y="0"> Θ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.028606" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.229855" y="0"> Φ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.769644" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.983395" y="0"> Ψ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.310631" y="0"> }</t年代p一个n></text> </g> </g> </svg>中定义的部分<一个href=”#sec3.1">3.1</一个>。</p><p>gydF4y2Ba该算法需要作为输入的固定和移动图像<年代vg height="13.4875" id="M180" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="7.1374998" id="M181" style="vertical-align:-0.10033pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>下面描述,一些参数,输出估计转换<年代vg height="14.8125" id="M182" style="vertical-align:-3.22282pt;width:86.050003px;" version="1.1" viewbox="0 0 86.050003 14.8125" width="86.050003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8125)"> <g transform="translate(72,-60.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.56,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.191385" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.231054" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.571274" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-8.11,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>这样<年代vg height="14.675" id="M183" style="vertical-align:-3.22282pt;width:69.099998px;" version="1.1" viewbox="0 0 69.099998 14.675" width="69.099998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.675)"> <g transform="translate(72,-60.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.402496" y="0"> ≃</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.442884" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.09568" y="0"> ∘</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.247398" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-21.66,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。整个过程中所描述的表<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/tab1/" target="_blank">1</一个>和图中所示<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig3/" target="_blank">3</一个>包括计算在不同的尺度上<年代vg height="13.6125" id="M184" style="vertical-align:-2.34499pt;width:63.974998px;" version="1.1" viewbox="0 0 63.974998 13.6125" width="63.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.530886" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.694386" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.945885" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.159637" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.911255" y="0"> ]</t年代p一个n></text> </g> </g> </svg>,从粗(<年代vg height="13.25" id="M185" style="vertical-align:-2.34499pt;width:35.912498px;" version="1.1" viewbox="0 0 35.912498 13.25" width="35.912498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.25)"> <g transform="translate(72,-61.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.367388" y="0"> </t年代p一个n></text> </g> </g> </svg>)罚款(<年代vg height="13.6125" id="M186" style="vertical-align:-2.34499pt;width:33.412498px;" version="1.1" viewbox="0 0 33.412498 13.6125" width="33.412498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.367388" y="0"> 0</t年代p一个n></text> </g> </g> </svg>)。每个规模相关联的子样品网格体素<年代vg height="19.0625" id="M187" style="vertical-align:-4.77652pt;width:64.025002px;" version="1.1" viewbox="0 0 64.025002 19.0625" width="64.025002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.0625)"> <g transform="translate(72,-56.75)"> <text transform="matrix(1,0,0,-1,-71.95,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.29,58.43)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.38,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-34.92,66.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-30.49,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,在那里<年代vg height="7.0124998" id="M188" style="vertical-align:-0.0pt;width:9.4125004px;" version="1.1" viewbox="0 0 9.4125004 7.0124998" width="9.4125004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是二次抽样的因素(例如,<年代vg height="20.4125" id="M189" style="vertical-align:-2.55817pt;width:51.112499px;" version="1.1" viewbox="0 0 51.112499 20.4125" width="51.112499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.4125)"> <g transform="translate(72,-55.67)"> <text transform="matrix(1,0,0,-1,-71.95,58.27)"> <tspan style="font-size: 12.50px; " x="22.940001" y="-0.69"> √</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.890113" y="0"> =</t年代p一个n></text> <g> <path d="m -37.41,70.71 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-37.41,58.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>在这项研究中)之间<年代vg height="12.675" id="M190" style="vertical-align:-2.34499pt;width:7.1374998px;" version="1.1" viewbox="0 0 7.1374998 12.675" width="7.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.675)"> <g transform="translate(72,-61.86)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和规模<年代vg height="13.6125" id="M191" style="vertical-align:-2.34499pt;width:31.674999px;" version="1.1" viewbox="0 0 31.674999 13.6125" width="31.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.979553" y="0"> 1</t年代p一个n></text> </g> </g> </svg>。的函数<年代vg height="13.4875" id="M192" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="9.9375" id="M193" style="vertical-align:-2.34499pt;width:8.4375px;" version="1.1" viewbox="0 0 8.4375 9.9375" width="8.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,定义在初始网格<年代vg height="17.8375" id="M194" style="vertical-align:-3.25793pt;width:188.5px;" version="1.1" viewbox="0 0 188.5 17.8375" width="188.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.8375)"> <g transform="translate(72,-57.73)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.12815" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.168539" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-37.11,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-28.76,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.029325" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.192825" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,0.32,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,5.19,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,17.28,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,22.15,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,34.24,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> <text transform="matrix(1,0,0,-1,39.11,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6268301" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> ℤ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,67.88,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> <text transform="matrix(1,0,0,-1,72.75,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</t年代p一个n></text> </g> </g> </svg>抗锯齿平滑后,downsampled()在任何规模<年代vg height="12.675" id="M195" style="vertical-align:-2.34499pt;width:7.1374998px;" version="1.1" viewbox="0 0 7.1374998 12.675" width="7.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.675)"> <g transform="translate(72,-61.86)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>的操作<年代p一个n年代tyle="font-family:monospace">下来</年代p一个n><我><年代ub>j</年代ub></i> <svg height="13.45" id="M196" style="vertical-align:-2.21957pt;width:10.5375px;" version="1.1" viewbox="0 0 10.5375 13.45" width="10.5375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> )</t年代p一个n></text> </g> </g> </svg>。一个upsampling运营商<年代p一个n年代tyle="font-family:monospace">向上</年代p一个n><年代vg height="13.45" id="M197" style="vertical-align:-2.21957pt;width:10.5375px;" version="1.1" viewbox="0 0 10.5375 13.45" width="10.5375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> )</t年代p一个n></text> </g> </g> </svg>实现为一个简单的线性插值,用来转移任何位移场网格上定义<年代vg height="16.8125" id="M198" style="vertical-align:-4.77652pt;width:30.049999px;" version="1.1" viewbox="0 0 30.049999 16.8125" width="30.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.8125)"> <g transform="translate(72,-58.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.29,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="0"> 1</t年代p一个n></text> </g> </g> </svg>到细网格<年代vg height="16.8125" id="M199" style="vertical-align:-4.77652pt;width:17.737499px;" version="1.1" viewbox="0 0 17.737499 16.8125" width="17.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.8125)"> <g transform="translate(72,-58.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.29,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>使用<年代vg height="7.0124998" id="M200" style="vertical-align:-0.0pt;width:9.4125004px;" version="1.1" viewbox="0 0 9.4125004 7.0124998" width="9.4125004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>作为upsampling因素。为每一个规模<年代vg height="13.6125" id="M201" style="vertical-align:-2.34499pt;width:63.974998px;" version="1.1" viewbox="0 0 63.974998 13.6125" width="63.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.530886" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.694386" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.945885" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.159637" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.911255" y="0"> ]</t年代p一个n></text> </g> </g> </svg>,累计位移场迭代更新,直到达到一个特定的停止准则<年代vg height="10.9875" id="M202" style="vertical-align:-0.1881pt;width:11.7375px;" version="1.1" viewbox="0 0 11.7375 10.9875" width="11.7375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9875)"> <g transform="translate(72,-63.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>(例如,收敛性的基础上<年代vg height="14.35" id="M203" style="vertical-align:-3.22282pt;width:18.5875px;" version="1.1" viewbox="0 0 18.5875 14.35" width="18.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.35)"> <g transform="translate(72,-60.52)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>或SSD,高精度的部分<一个href=”#sec5">5</一个>)。</p><d我v class="floats-partial-section partial-other-wrapper" data-section="tab1"> <div class="floats-partial-content fig-content-tab1"> <table class="table-group" id="tab1"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="1"> <hr></td> </tr> <tr> <td align="left"><b>输入参数:</gydF4y2Bab></td> </tr> <tr> <td align="left">(我)图片<年代vg height="13.4875" id="M204" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="7.1374998" id="M205" style="vertical-align:-0.10033pt" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>上定义<年代vg height="10.6875" id="M206" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 46.137501 10.6875" width="46.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.6875)"> <g transform="translate(72,-63.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2515001" y="0"> D</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.278666" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.530167" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.557331" y="0"> 2</t年代p一个n></text> </g> </g> </svg>。</td></tr><tr> <td align="left">(2)数量的尺度<年代vg height="10.5125" id="M207" style="vertical-align:-0.15048pt" version="1.1" viewbox="0 0 10.4375 10.5125" width="10.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5125)"> <g transform="translate(72,-63.59)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。</td></tr><tr> <td align="left">(3)停止准则<年代vg height="10.9875" id="M208" style="vertical-align:-0.1881pt" version="1.1" viewbox="0 0 11.7375 10.9875" width="11.7375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9875)"> <g transform="translate(72,-63.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。</td></tr><tr> <td align="left">内核(iv)高斯方差<年代vg height="19.200001" id="M209" style="vertical-align:-4.35121pt" version="1.1" viewbox="0 0 18.0875 19.200001" width="18.0875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.2)"> <g transform="translate(72,-56.64)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.61,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.3400002"> Ψ</t年代p一个n></text> </g> </g> </svg>的<年代vg height="10.9125" id="M210" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.7875 10.9125" width="11.7875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ψ</t年代p一个n></text> </g> </g> </svg>。</td></tr><tr> <td align="left"><b>输出:</gydF4y2Bab>的位移场<年代vg height="14.35" id="M211" style="vertical-align:-3.22282pt" version="1.1" viewbox="0 0 18.5875 14.35" width="18.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.35)"> <g transform="translate(72,-60.52)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。</td></tr><tr> <td align="left"><b>算法:</gydF4y2Bab></td> </tr> <tr> <td align="left">(<一个href=”#EEq1">4</一个>)<gydF4y2Ba我>初始化</我>:</td></tr><tr> <td align="left">集规模<年代vg height="13.25" id="M212" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 35.912498 13.25" width="35.912498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.25)"> <g transform="translate(72,-61.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.367388" y="0"> </t年代p一个n></text> </g> </g> </svg>并初始化<年代vg height="14.7125" id="M213" style="vertical-align:-3.22282pt" version="1.1" viewbox="0 0 45.787498 14.7125" width="45.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-53.71,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n></text> </g> </g> </svg>在<年代vg height="15.2125" id="M214" style="vertical-align:-3.49493pt" version="1.1" viewbox="0 0 31.700001 15.2125" width="31.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.2125)"> <g transform="translate(72,-59.83)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.29,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.7260799" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.7212" y="0"> 1</t年代p一个n></text> </g> </g> </svg>。</td></tr><tr> <td align="left">(<一个href=”#EEq2">5</一个>)<gydF4y2Ba我>在电网传输</我><年代vg height="16.8125" id="M215" style="vertical-align:-4.77652pt" version="1.1" viewbox="0 0 17.737499 16.8125" width="17.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.8125)"> <g transform="translate(72,-58.55)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.29,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>:</td></tr><tr> <td align="left">计算<年代vg height="12.975" id="M216" style="vertical-align:-4.77652pt" version="1.1" viewbox="0 0 16.75 12.975" width="16.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.975)"> <g transform="translate(72,-61.62)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg> <svg height="6.1624999" id="M217" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 10.825 6.1624999" width="10.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.1625)"> <g transform="translate(72,-67.07)"> <text transform="matrix(1,0,0,-1,-71.95,67.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n></text> </g> </g> </svg><span style="font-family:monospace">下来</年代p一个n><我><年代ub>j</年代ub></i> <svg height="13.45" id="M218" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 21.625 13.45" width="21.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.040629" y="0"> )</t年代p一个n></text> </g> </g> </svg>,<年代vg height="16.512501" id="M219" style="vertical-align:-4.77652pt" version="1.1" viewbox="0 0 29.375 16.512501" width="29.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5125)"> <g transform="translate(72,-58.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.11,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n></text> </g> </g> </svg><span style="font-family:monospace">下来</年代p一个n><我><年代ub>j</年代ub></i> <svg height="13.6125" id="M220" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 19.2125 13.6125" width="19.2125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> )</t年代p一个n></text> </g> </g> </svg>,</td></tr><tr> <td align="left">和分配<年代vg height="14.35" id="M221" style="vertical-align:-3.22282pt" version="1.1" viewbox="0 0 41.737499 14.35" width="41.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.35)"> <g transform="translate(72,-60.52)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-53.71,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ←</t年代p一个n></text> </g> </g> </svg><span style="font-family:monospace">向上</年代p一个n><年代vg height="14.7125" id="M222" style="vertical-align:-3.22282pt" version="1.1" viewbox="0 0 29 14.7125" width="29" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-53.02,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>。</td></tr><tr> <td align="left">(<一个href=”#EEq3">6</一个>),而<年代vg height="10.9875" id="M223" style="vertical-align:-0.1881pt" version="1.1" viewbox="0 0 11.7375 10.9875" width="11.7375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9875)"> <g transform="translate(72,-63.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是<年代p一个n年代tyle="font-family:monospace">假</年代p一个n>做:</td></tr><tr> <td align="left">(我)<我>扭曲</我>:<gydF4y2Ba年代vg height="16.612499" id="M224" style="vertical-align:-4.77652pt" version="1.1" viewbox="0 0 78.074997 16.612499" width="78.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6125)"> <g transform="translate(72,-58.71)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.153156" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.193544" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-37.87,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-30.67,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∘</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.1517162" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-14.48,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg></td> </tr> <tr> <td align="left">(2)<我>场计算</我>:<gydF4y2Ba年代vg height="16.637501" id="M225" style="vertical-align:-4.77652pt" version="1.1" viewbox="0 0 95.962502 16.637501" width="95.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-53.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ←</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.041109" y="0"> Θ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.068275" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.231773" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-18.77,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-14.34,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.891073" y="0"> )</t年代p一个n></text> </g> </g> </svg></td> </tr> <tr> <td align="left">(3)<我>积累</我>:<gydF4y2Ba年代vg height="14.7125" id="M226" style="vertical-align:-3.22282pt" version="1.1" viewbox="0 0 107.2 14.7125" width="107.2" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-53.71,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ←</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.041109" y="0"> Φ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.580898" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.744396" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-15.08,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-10.18,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,4.9,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,9.55,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg></td> </tr> <tr> <td align="left">(iv)<我>正则化</我>:<gydF4y2Ba年代vg height="14.925" id="M227" style="vertical-align:-3.22282pt" version="1.1" viewbox="0 0 82.275002 14.925" width="82.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.925)"> <g transform="translate(72,-60.06)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-53.71,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ←</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.041109" y="0"> Ψ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.368347" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.531845" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-15.29,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-10.4,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg></td> </tr> <tr> <td align="left">(<一个href=”#EEq4">7</一个>)如果<年代vg height="13.6125" id="M228" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 33.412498 13.6125" width="33.412498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.367388" y="0"> 0</t年代p一个n></text> </g> </g> </svg>,停止并返回<年代vg height="14.35" id="M229" style="vertical-align:-3.22282pt" version="1.1" viewbox="0 0 18.5875 14.35" width="18.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.35)"> <g transform="translate(72,-60.52)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,</td></tr><tr> <td align="left">其他的,<年代vg height="13.6125" id="M230" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 60.900002 13.6125" width="60.900002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> ←</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.38061" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.019943" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.360165" y="0"> 1</t年代p一个n></text> </g> </g> </svg>并返回步骤(<一个href=”#EEq2">5</一个>)。</td></tr><tr class="table-tr"> <td colspan="1"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表1</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/ijbi/2011/891585/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 多尺度非参数的过程。</d我v> </div> </div> <h4 id="diffeomorphic-morphons">4所示。Diffeomorphic Morphons</h4><p>gydF4y2Ba我们的论文适应全球注册方法在前一节中解释Morphons (<一个href=”#B26">26</一个>,<gydF4y2Ba一个href=”#B39">39</一个>照顾)的累积位移场的可逆性,即通过引入diffeomorphic领域积累。</p><p>gydF4y2Ba正如上面已经提到的,Morphons的特殊性,与其他非参数方法相比,是场计算(函数<年代vg height="10.9125" id="M231" style="vertical-align:-0.17555pt;width:11.4125px;" version="1.1" viewbox="0 0 11.4125 10.9125" width="11.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代p一个n></text> </g> </g> </svg>在(<一个href=”#EEq2">5</一个>)是基于当地的阶段而不是强度的差异。换句话说,知道周期信号之间的相位差相同的频率允许的估计它们之间的空间转移。因此,假设图像可以在当地被视为一种周期信号,计算当地的相位差的估计相当于本地图像之间的位移。这个过程是由多尺度稳定的部分中描述的方法<一个href=”#sec3.2">3.2</一个>。此外,Morphons结合位移向量的估计和衡量这些估计的信心,导致<我>确定地图</我>。因此,对于Morphons,给定两个图像<年代vg height="13.4875" id="M232" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="10.8" id="M233" style="vertical-align:-0.11285pt;width:66.425003px;" version="1.1" viewbox="0 0 66.425003 10.8" width="66.425003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8)"> <g transform="translate(72,-63.36)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.153156" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.193544" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.84634" y="0"> ∘</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.998058" y="0"> Δ</t年代p一个n></text> </g> </g> </svg>位移场估计<年代vg height="10.9125" id="M234" style="vertical-align:-0.17555pt;width:11.4125px;" version="1.1" viewbox="0 0 11.4125 10.9125" width="11.4125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代p一个n></text> </g> </g> </svg>实际上是分成两个数量吗<年代p一个ncl一个年代年代=”equation" id="eq4"> <svg height="41.349998" id="M235" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 41.349998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,41.35)"> <g transform="translate(72,-38.92)"> <text transform="matrix(1,0,0,-1,161.83,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,171.7,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,179.82,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⟵</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.155556" y="0"> Θ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,212,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,221.63,63.2)"> <tspan style="font-size: 12.50px; " x="-55.970001" y="20.48"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.303911" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.993736" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.245235" y="0"> ,</t年代p一个n></text> <text transform="matrix(1,0,0,-1,170.85,39.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,178.97,42.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⟵</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.143053" y="0"> Θ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,211.15,39.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,217.8,42.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.303911" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.993736" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.245235" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="256.32001" y="-9.6099997"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="260.48349" y="-9.6099997"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="266.73499" y="-9.6099997"> )</t年代p一个n></text> </g> </g> </svg></span>分别是一个更新的位移场以及地图更新的确定性。类似的分裂也进行后续操作<年代vg height="10.475" id="M236" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</t年代p一个n></text> </g> </g> </svg>和<年代vg height="10.9125" id="M237" style="vertical-align:-0.0pt;width:11.7875px;" version="1.1" viewbox="0 0 11.7875 10.9125" width="11.7875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ψ</t年代p一个n></text> </g> </g> </svg>。</p><p>gydF4y2Ba这是关于三个步骤的细节<年代vg height="13.7375" id="M238" style="vertical-align:-2.26974pt;width:63.025002px;" version="1.1" viewbox="0 0 63.025002 13.7375" width="63.025002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.7375)"> <g transform="translate(72,-61.01)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.00144" y="0"> Θ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.028606" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.229855" y="0"> Φ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.769644" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.983395" y="0"> Ψ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.310631" y="0"> }</t年代p一个n></text> </g> </g> </svg>管道的部分<一个href=”#sec3">3</一个>这个特定的注册,包括我们贡献领域积累的一步。</p><h5gydF4y2Baid="sec4.1">4.1。位移场的计算</h5><p>gydF4y2Ba在Morphons位移场估计由于当地之间的零相位化阶段的固定和移动图像。这地方阶段可以在一定探测频率和在某一特定方向上使用正交过滤器(<一个href=”#B40">40</一个>]。更准确地说,Morphons方法使用正交滤波器<年代vg height="16.7125" id="M239" style="vertical-align:-4.74141pt;width:15.2375px;" version="1.1" viewbox="0 0 15.2375 16.7125" width="15.2375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.7125)"> <g transform="translate(72,-58.63)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.74,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>的方向<年代vg height="16.637501" id="M240" style="vertical-align:-2.29482pt;width:45.099998px;" version="1.1" viewbox="0 0 45.099998 16.637501" width="45.099998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.7148314" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.75522" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-40.85,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> </g> </g> </svg>(也称为<我>loglet年代</gydF4y2Ba我>(<gydF4y2Ba一个href=”#B40">40</一个>])中定义的极性分离频率的函数<年代p一个ncl一个年代年代=”equation" id="eq5"> <svg height="23.9" id="M241" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 23.9" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,23.9)"> <g transform="translate(72,-52.88)"> <text transform="matrix(1,0,0,-1,114.36,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,125.28,55.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,132.24,58.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.678042" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.304873" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.345261" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,173.15,53.19)"> <tspan style="font-size: 6.25px; " x="0" y="0"> +</t年代p一个n></text> <text transform="matrix(1,0,0,-1,180.52,55.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,192.62,63.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,199.33,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.299999" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.5200005" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.446901" y="2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,227.89,63.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,235.35,58.5)"> <tspan style="font-size: 12.50px; " x="7.7600002" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-0.75018001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,248.96,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,253.84,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.327718" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.491217" y="0"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.030287" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.544828" y="0"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.171898" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.410896" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="220.28" y="-0.81"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="224.4435" y="-0.81"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="230.69499" y="-0.81"> )</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="14.1875" id="M242" style="vertical-align:-0.33858pt;width:47.924999px;" version="1.1" viewbox="0 0 47.924999 14.1875" width="47.924999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.1875)"> <g transform="translate(72,-60.65)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.977874" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.018263" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-38.58,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> </g> </g> </svg>是频率向量,<年代vg height="17.65" id="M243" style="vertical-align:-5.58662pt;width:63.5px;" version="1.1" viewbox="0 0 63.5 17.65" width="63.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.65)"> <g transform="translate(72,-57.88)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.39,58.18)"> <tspan style="font-size: 6.25px; " x="0" y="0"> +</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-58.11,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.927622" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.566956" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.594841" y="0"> 1</t年代p一个n></text> </g> </g> </svg>如果<年代vg height="11.0625" id="M244" style="vertical-align:-0.30096pt;width:35.787498px;" version="1.1" viewbox="0 0 35.787498 11.0625" width="35.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.227454" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.267843" y="0"> 0</t年代p一个n></text> </g> </g> </svg>和0,<年代vg height="17.15" id="M245" style="vertical-align:-2.37006pt;width:82.275002px;" version="1.1" viewbox="0 0 82.275002 17.15" width="82.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.15)"> <g transform="translate(72,-58.28)"> <text transform="matrix(1,0,0,-1,-71.95,60.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.5390692" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.053612" y="0"> 为</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-50.36,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-42.01,60.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-21.46,65.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-14.75,60.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="15.0625" id="M246" style="vertical-align:-2.37006pt;width:72.137497px;" version="1.1" viewbox="0 0 72.137497 15.0625" width="72.137497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.0625)"> <g transform="translate(72,-59.95)"> <text transform="matrix(1,0,0,-1,-71.19,62.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-0.75018001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.215191" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.255581" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.770123" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.245956" y="0"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.785027" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.299568" y="0"> 为</t年代p一个n></text> </g> </g> </svg>单位向量支持吗<年代vg height="7.1875" id="M247" style="vertical-align:-0.13794pt;width:10.7625px;" version="1.1" viewbox="0 0 10.7625 7.1875" width="10.7625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="10.325" id="M248" style="vertical-align:-0.0pt;width:11.6875px;" version="1.1" viewbox="0 0 11.6875 10.325" width="11.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是一个径向函数集中在吗<年代vg height="13.55" id="M249" style="vertical-align:-2.29482pt;width:35.174999px;" version="1.1" viewbox="0 0 35.174999 13.55" width="35.174999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.7398367" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.780226" y="0"> 0</t年代p一个n></text> </g> </g> </svg>和定义为<年代vg height="17.487499" id="M250" style="vertical-align:-2.72118pt;width:186.53751px;" version="1.1" viewbox="0 0 186.53751 17.487499" width="186.53751" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.4875)"> <g transform="translate(72,-58.01)"> <text transform="matrix(1,0,0,-1,-71.95,60.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.2522202" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.415719" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.516943" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.143772" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.184162" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.735493" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.986996" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.577995" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="68.741493" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="77.306046" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="80.781883" y="0"> n</t年代p一个n></text> <text transform="matrix(1,0,0,-1,19.25,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,24.13,60.78)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.2647228" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.740557" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.017063" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.180561" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.731894" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.207729" y="0"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.622726" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.874226" y="0"> ]</t年代p一个n></text> </g> </g> </svg>为<年代vg height="11.0625" id="M251" style="vertical-align:-0.30096pt;width:33.700001px;" version="1.1" viewbox="0 0 33.700001 11.0625" width="33.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0625)"> <g transform="translate(72,-63.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.5645552" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.604944" y="0"> 0</t年代p一个n></text> </g> </g> </svg>。</p><p>gydF4y2Ba因为他们支持对应体积的一半<年代vg height="16.637501" id="M252" style="vertical-align:-2.29482pt;width:133.64999px;" version="1.1" viewbox="0 0 133.64999 16.637501" width="133.64999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.00144" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.979315" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.019703" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-32.58,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-24.24,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∶</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8648672" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-8.12,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-1.41,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.977874" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.018263" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.269764" y="0"> }</t年代p一个n></text> </g> </g> </svg>由于<年代vg height="16.8375" id="M253" style="vertical-align:-2.29482pt;width:105.075px;" version="1.1" viewbox="0 0 105.075 16.8375" width="105.075" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.8375)"> <g transform="translate(72,-58.53)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.54,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.07,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-0.75018001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.7643628" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-42.14,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-33.8,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> c</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.579218" y="0"> o</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.830717" y="0"> 年代</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-0.93,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,3.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>(与<年代vg height="13.425" id="M254" style="vertical-align:-2.29482pt;width:10.2px;" version="1.1" viewbox="0 0 10.2 13.425" width="10.2" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>角分离<年代vg height="7.1875" id="M255" style="vertical-align:-0.13794pt;width:10.7625px;" version="1.1" viewbox="0 0 10.7625 7.1875" width="10.7625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="9.875" id="M256" style="vertical-align:-2.29482pt;width:7.9375px;" version="1.1" viewbox="0 0 7.9375 9.875" width="7.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>),loglets可以被视为分析同行的可操纵的过滤器由弗里曼和引入阿德尔森(<一个href=”#B41">41</一个>]。事实上,只有数量有限的方向<年代vg height="9.875" id="M257" style="vertical-align:-2.29482pt;width:7.9375px;" version="1.1" viewbox="0 0 7.9375 9.875" width="7.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是覆盖整个频率平面所必需的。通常,在2 d,作为这些方向<年代vg height="14.825" id="M258" style="vertical-align:-3.2316pt;width:133.5625px;" version="1.1" viewbox="0 0 133.5625 14.825" width="133.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.825)"> <g transform="translate(72,-60.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.7,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.98,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.191385" y="0"> c</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.742718" y="0"> o</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.994217" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.021381" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-11.88,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-6.64,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.064915" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.540749" y="0"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.955748" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,25.39,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,30.63,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>与<年代vg height="14.7125" id="M259" style="vertical-align:-3.2316pt;width:66.275002px;" version="1.1" viewbox="0 0 66.275002 14.7125" width="66.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.89,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.17,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.804512" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.406336" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.88217" y="0"> 4</t年代p一个n></text> </g> </g> </svg>为<年代vg height="12.3" id="M260" style="vertical-align:-1.29163pt;width:63px;" version="1.1" viewbox="0 0 63 12.3" width="63" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.3)"> <g transform="translate(72,-62.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.7148314" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.75522" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.007679" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.048069" y="0"> 3</t年代p一个n></text> </g> </g> </svg>,在3 d,<年代vg height="9.875" id="M261" style="vertical-align:-2.29482pt;width:7.9375px;" version="1.1" viewbox="0 0 7.9375 9.875" width="7.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>作为6法向量<年代vg height="14.9" id="M262" style="vertical-align:-3.2316pt;width:109.0375px;" version="1.1" viewbox="0 0 109.0375 14.9" width="109.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9)"> <g transform="translate(72,-60.08)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.00144" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.7,60.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-50.98,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∶</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8523636" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.579699" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.620087" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.860043" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.900433" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.151932" y="0"> }</t年代p一个n></text> </g> </g> </svg>的脸hemi-icosahedron [<一个href=”#B42">42</一个>,<gydF4y2Ba一个href=”#B43">43</一个>]。还要注意,每个过滤器<年代vg height="14.825" id="M263" style="vertical-align:-3.2316pt;width:34.700001px;" version="1.1" viewbox="0 0 34.700001 14.825" width="34.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.825)"> <g transform="translate(72,-60.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.74,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.49,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n></text> </g> </g> </svg>在空间域以原点为中心给出的一个典型的宽度<年代vg height="13.55" id="M264" style="vertical-align:-2.29482pt;width:20.125px;" version="1.1" viewbox="0 0 20.125 13.55" width="20.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2515001" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.727334" y="0"> </t年代p一个n></text> </g> </g> </svg>。</p><p>MorphonsgydF4y2Ba利用以下行为。给定一个图像<年代vg height="13.4875" id="M265" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,定义过滤<年代p一个ncl一个年代年代=”equation" id="eq6"> <svg height="19.6" id="M266" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.6" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.6)"> <g transform="translate(72,-56.32)"> <text transform="matrix(1,0,0,-1,142.73,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,148.46,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,156.94,61.14)"> <tspan style="font-size: 12.50px; " x="51.389999" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ;</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.603985" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.38061" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.183441" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.240002" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.954834" y="0.0099999998"> ∗</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="76.269569" y="0.0099999998"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,240.43,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,245.67,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9400001" y="-2.52"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.103499" y="-2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.980148" y="-2.52"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.219147" y="-2.52"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="222.2" y="-2.4200001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="226.36349" y="-2.4200001"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="232.61501" y="-2.4200001"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="238.8665" y="-2.4200001"> )</t年代p一个n></text> </g> </g> </svg></span>与<年代vg height="7.4875002" id="M267" style="vertical-align:-0.0pt;width:8.3000002px;" version="1.1" viewbox="0 0 8.3000002 7.4875002" width="8.3000002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.4875)"> <g transform="translate(72,-66.01)"> <text transform="matrix(1,0,0,-1,-71.95,66.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∗</t年代p一个n></text> </g> </g> </svg>常见的卷积运算和速记<年代vg height="17.525" id="M268" style="vertical-align:-5.39853pt;width:55.049999px;" version="1.1" viewbox="0 0 55.049999 17.525" width="55.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.525)"> <g transform="translate(72,-57.98)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.74,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.02,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-36.77,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-32.39,58.1)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,我们可以写<年代vg height="19.725" id="M269" style="vertical-align:-4.77652pt;width:168.95px;" version="1.1" viewbox="0 0 168.95 19.725" width="168.95" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.725)"> <g transform="translate(72,-56.22)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.22,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.82,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ;</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.59148" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.368107" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.007441" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.047829" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-7.8,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-1.4,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ;</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.59148" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.368107" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.531607" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,31.71,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,40.07,63.85)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,44.79,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="7.7280159" y="0"> ;</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.161072" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="14.904656" y="0"> )</t年代p一个n></text> </g> </g> </svg>自<年代vg height="16.637501" id="M270" style="vertical-align:-4.77652pt;width:45.700001px;" version="1.1" viewbox="0 0 45.700001 16.637501" width="45.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.22,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.34,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> ℂ</t年代p一个n></text> </g> </g> </svg>。因此,通过处理扭曲的形象<年代vg height="7.4499998" id="M271" style="vertical-align:-0.11285pt;width:12.2375px;" version="1.1" viewbox="0 0 12.2375 7.4499998" width="12.2375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.45)"> <g transform="translate(72,-66.04)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>同样的,当地的相位差可以计算<年代p一个ncl一个年代年代=”equation" id="eq7"> <svg height="19.6" id="M272" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.6" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.6)"> <g transform="translate(72,-56.32)"> <text transform="matrix(1,0,0,-1,119.05,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,136.14,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,143.47,61.14)"> <tspan style="font-size: 12.50px; " x="50.849998" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.700001" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.666979" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.707369" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.258701" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.422199" y="0"> g</t年代p一个n></text> <text transform="matrix(1,0,0,-1,205.89,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,214.38,61.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ;</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.603985" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.38061" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.619608" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,250.23,66.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-0.5" y="8.1300001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,259.1,61.14)"> <tspan style="font-size: 12.50px; " x="27.540001" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.48" y="0.0099999998"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ;</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.59148" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.368107" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="208.77" y="0.1"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="212.9335" y="0.1"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="219.185" y="0.1"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="225.43649" y="0.1"> )</t年代p一个n></text> </g> </g> </svg></span>与<年代vg height="14.5" id="M273" style="vertical-align:-2.21957pt;width:21.35px;" version="1.1" viewbox="0 0 21.35 14.5" width="21.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5)"> <g transform="translate(72,-60.4)"> <text transform="matrix(1,0,0,-1,-71.95,62.66)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.05,67.83)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∗</t年代p一个n></text> </g> </g> </svg>复杂的共轭和<年代vg height="16.637501" id="M274" style="vertical-align:-4.77652pt;width:190.21249px;" version="1.1" viewbox="0 0 190.21249 16.637501" width="190.21249" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.86,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-49.62,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.679482" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.707369" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-10.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-4.43,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ;</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.59148" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.368107" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.307272" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.647491" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,45.29,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,52.58,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ;</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.59148" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.368107" y="0"> )</t年代p一个n></text> </g> </g> </svg>当地的<我>移相</我>之间的<年代vg height="13.4875" id="M275" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="7.4499998" id="M276" style="vertical-align:-0.11285pt;width:12.2375px;" version="1.1" viewbox="0 0 12.2375 7.4499998" width="12.2375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.45)"> <g transform="translate(72,-66.04)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>方向<年代vg height="11.05" id="M277" style="vertical-align:-3.2316pt;width:14.4875px;" version="1.1" viewbox="0 0 14.4875 11.05" width="14.4875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.7,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。</p><p>gydF4y2Ba一个重要的观察是,非负价值<年代p一个ncl一个年代年代=”equation" id="eq8"> <svg height="44.075001" id="M278" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 44.075001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,44.075)"> <g transform="translate(72,-36.74)"> <text transform="matrix(1,0,0,-1,74.81,51.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,83.78,48.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,92.27,51.25)"> <tspan style="font-size: 12.50px; " x="43.049999" y="-1.59"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.049999" y="1.59"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.549999" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ;</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.59148" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.368107" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.007441" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.400002" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.11483" y="0.0099999998"> ∗</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.429565" y="0.0099999998"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,169.92,48.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,175.16,48.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.139999" y="-4.1100001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.139999" y="-0.93000001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.120001" y="-2.51"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.150002" y="-14.77"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.150002" y="-4.0999999"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.150002" y="6.5599999"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.150002" y="9.7299995"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.650002" y="5.1799998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9400001" y="-2.52"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.103499" y="-2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.980148" y="-2.52"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,224.56,39.75)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,231.1,43.2)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 3</t年代p一个n></text> <text transform="matrix(1,0,0,-1,237.31,51.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.52" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.370001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,260.56,56.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,264.03,48.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9400001" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,278.85,48.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 284.16,62.67 7.21,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,284.16,51.24)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,291.37,48.12)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,298.7,48.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,311.43,56.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,314.9,48.73)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.9400001" y="-2.51"> d</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.1915" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,335.96,56.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,339.44,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="10.67"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="21.33"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="24.5"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="128.42999" y="12.26"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="132.59351" y="12.26"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="138.845" y="12.26"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="145.0965" y="12.26"> )</t年代p一个n></text> </g> </g> </svg></span>也代表之间的关系<年代vg height="13.6375" id="M279" style="vertical-align:-2.34499pt;width:32.325001px;" version="1.1" viewbox="0 0 32.325001 13.6375" width="32.325001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6375)"> <g transform="translate(72,-61.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9391651" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.979315" y="0"> ′</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.592682" y="0"> )</t年代p一个n></text> </g> </g> </svg>和翻译后的过滤器<年代vg height="19.987499" id="M280" style="vertical-align:-3.2316pt;width:138.825px;" version="1.1" viewbox="0 0 138.825 19.987499" width="138.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.9875)"> <g transform="translate(72,-56.01)"> <text transform="matrix(1,0,0,-1,-71.95,59.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,56.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m -59.76,70.71 7.21,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-59.76,59.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.55,56.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-47.31,59.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-36.27,64.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-32.79,59.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6268301" y="0"> =</t年代p一个n></text> <g> <path d="m -13.12,70.71 7.22,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-13.12,59.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-5.9,56.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-0.66,59.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,10.38,64.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,16.63,59.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.216871" y="0"> )</t年代p一个n></text> </g> </g> </svg>;也就是说,过滤器<年代vg height="19.987499" id="M281" style="vertical-align:-3.2316pt;width:108.05px;" version="1.1" viewbox="0 0 108.05 19.987499" width="108.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.9875)"> <g transform="translate(72,-56.01)"> <g> <path d="m -71.95,70.71 7.21,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,59.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.74,56.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.49,59.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-48.45,64.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.98,59.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6268301" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-18.09,56.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-12.85,59.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.728054" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,6.76,64.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,10.23,59.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>翻译在<年代vg height="7.1624999" id="M282" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。如果图像<年代vg height="13.4875" id="M283" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>完全由后者,也就是说,如果我们在本地吗<年代vg height="16.5875" id="M284" style="vertical-align:-3.2316pt;width:123.1875px;" version="1.1" viewbox="0 0 123.1875 16.5875" width="123.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5875)"> <g transform="translate(72,-58.73)"> <text transform="matrix(1,0,0,-1,-71.95,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9391651" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-53.97,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-50.5,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.855965" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-18.42,58.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-13.18,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-2.14,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,4.11,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.216871" y="0"> )</t年代p一个n></text> </g> </g> </svg>对于任何<年代vg height="14.1875" id="M285" style="vertical-align:-0.33858pt;width:50.224998px;" version="1.1" viewbox="0 0 50.224998 14.1875" width="50.224998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.1875)"> <g transform="translate(72,-60.65)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-58.13,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-36.75,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> </g> </g> </svg>和一个常数<年代vg height="10.8875" id="M286" style="vertical-align:-0.33858pt;width:37.674999px;" version="1.1" viewbox="0 0 37.674999 10.8875" width="37.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8875)"> <g transform="translate(72,-63.29)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.6520758" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.692465" y="0"> ℝ</t年代p一个n></text> </g> </g> </svg>的位移<年代vg height="13.4875" id="M287" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>通过位移场<年代vg height="13.45" id="M288" style="vertical-align:-2.21957pt;width:31.475px;" version="1.1" viewbox="0 0 31.475 13.45" width="31.475" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8773699" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.040869" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.917519" y="0"> )</t年代p一个n></text> </g> </g> </svg>大约持续的支持<年代vg height="19.987499" id="M289" style="vertical-align:-3.2316pt;width:30.924999px;" version="1.1" viewbox="0 0 30.924999 19.987499" width="30.924999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.9875)"> <g transform="translate(72,-56.01)"> <text transform="matrix(1,0,0,-1,-71.95,59.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,56.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m -59.76,70.71 7.21,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-59.76,59.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.55,56.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>将诱导移相<年代vg height="18.825001" id="M290" style="vertical-align:-4.25465pt;width:121.8375px;" version="1.1" viewbox="0 0 121.8375 18.825001" width="121.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.825)"> <g transform="translate(72,-56.94)"> <text transform="matrix(1,0,0,-1,-71.95,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.86,58.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-49.62,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.679482" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.707369" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.983875" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-6.37,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,0.34,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8773699" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.040869" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.917519" y="0"> )</t年代p一个n></text> </g> </g> </svg>因为的频率向量<年代vg height="19.987499" id="M291" style="vertical-align:-3.2316pt;width:30.924999px;" version="1.1" viewbox="0 0 30.924999 19.987499" width="30.924999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.9875)"> <g transform="translate(72,-56.01)"> <text transform="matrix(1,0,0,-1,-71.95,59.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,56.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m -59.76,70.71 7.21,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-59.76,59.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.55,56.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是<年代vg height="11.05" id="M292" style="vertical-align:-3.2316pt;width:33.037498px;" version="1.1" viewbox="0 0 33.037498 11.05" width="33.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.5645552" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.841061" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-50.86,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。一个重要的隐式假设仍然是<年代vg height="18.825001" id="M293" style="vertical-align:-4.25465pt;width:90.675003px;" version="1.1" viewbox="0 0 90.675003 18.825001" width="90.675003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.825)"> <g transform="translate(72,-56.94)"> <text transform="matrix(1,0,0,-1,-71.95,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.7771063" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.92,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-50.21,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8773699" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.040869" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.917519" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.081018" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.044949" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.085339" y="0"> </t年代p一个n></text> </g> </g> </svg>由于移相是已知模<年代vg height="10.8875" id="M294" style="vertical-align:-0.16302pt;width:17.4375px;" version="1.1" viewbox="0 0 17.4375 10.8875" width="17.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8875)"> <g transform="translate(72,-63.29)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2515001" y="0"> </t年代p一个n></text> </g> </g> </svg>。此外,只有<年代vg height="18.825001" id="M295" style="vertical-align:-4.25465pt;width:28.9125px;" version="1.1" viewbox="0 0 28.9125 18.825001" width="28.9125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.825)"> <g transform="translate(72,-56.94)"> <text transform="matrix(1,0,0,-1,-71.95,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.7,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-58.99,61.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>而不是<年代vg height="10.325" id="M296" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>可以确定,空白的墙的另一个表现问题[<一个href=”#B44">44</一个>]。</p><p>gydF4y2Ba在实践中,对于大多数的<年代vg height="7.1624999" id="M297" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.6125" id="M298" style="vertical-align:-2.34499pt;width:27.799999px;" version="1.1" viewbox="0 0 27.799999 13.6125" width="27.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9391651" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.979315" y="0"> )</t年代p一个n></text> </g> </g> </svg>不完全由一个过滤器,但它们的线性组合振幅在哪里<年代vg height="16.637501" id="M299" style="vertical-align:-4.77652pt;width:53.762501px;" version="1.1" viewbox="0 0 53.762501 16.637501" width="53.762501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.99,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.58,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ;</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.59148" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.368107" y="0"> )</t年代p一个n></text> </g> </g> </svg>措施的充分性之间的配合<年代vg height="13.6125" id="M300" style="vertical-align:-2.34499pt;width:27.799999px;" version="1.1" viewbox="0 0 27.799999 13.6125" width="27.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9391651" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.979315" y="0"> )</t年代p一个n></text> </g> </g> </svg>和<年代vg height="19.987499" id="M301" style="vertical-align:-3.2316pt;width:30.924999px;" version="1.1" viewbox="0 0 30.924999 19.987499" width="30.924999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.9875)"> <g transform="translate(72,-56.01)"> <text transform="matrix(1,0,0,-1,-71.95,59.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,56.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m -59.76,70.71 7.21,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-59.76,59.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.55,56.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。因此,本地更新位移<年代vg height="14.7" id="M302" style="vertical-align:-3.21404pt;width:37.287498px;" version="1.1" viewbox="0 0 37.287498 14.7" width="37.287498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7)"> <g transform="translate(72,-60.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.43,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n></text> </g> </g> </svg>链接<年代vg height="13.6125" id="M303" style="vertical-align:-2.34499pt;width:27.799999px;" version="1.1" viewbox="0 0 27.799999 13.6125" width="27.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9391651" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.979315" y="0"> )</t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.7" id="M304" style="vertical-align:-3.21404pt;width:133.125px;" version="1.1" viewbox="0 0 133.125 14.7" width="133.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7)"> <g transform="translate(72,-60.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6898251" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.853324" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.729975" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.356804" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.397194" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.336357" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.499859" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.152172" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="72.492393" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,10.43,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,15.08,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.203648" y="0"> )</t年代p一个n></text> </g> </g> </svg>在每一个<年代vg height="14.1875" id="M305" style="vertical-align:-0.33858pt;width:45.875px;" version="1.1" viewbox="0 0 45.875 14.1875" width="45.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.1875)"> <g transform="translate(72,-60.65)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.339981" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.380369" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-40.22,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> </g> </g> </svg>估计通过求解加权最小二乘法优化<年代p一个ncl一个年代年代=”equation" id="EEq5"> <svg height="37.224998" id="M306" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 37.224998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,37.225)"> <g transform="translate(72,-42.22)"> <text transform="matrix(1,0,0,-1,94.18,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,103.21,55.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,112.84,58.51)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.303911" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.993736" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.633072" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.673458" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.224792" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.38829" y="0"> g</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.891289" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="77.618622" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="81.09446" y="0"> n</t年代p一个n></text> <text transform="matrix(1,0,0,-1,169.99,46.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.656064" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.651184" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,187.18,49.67)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 3</t年代p一个n></text> <text transform="matrix(1,0,0,-1,202.27,51.95)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,207.98,44.84)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,218.43,55.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.7800002" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,228.4,55.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,235.73,55.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.126506" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,254.11,63.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.1499996"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,260.82,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.4272623" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.767483" y="0"> Δ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.794649" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,298.69,55.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,303.93,55.99)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8514042" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,314.57,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,319.44,58.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="148.42999" y="4.52"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="152.59351" y="4.52"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="158.845" y="4.52"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="165.0965" y="4.52"> )</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="16.637501" id="M307" style="vertical-align:-4.77652pt;width:159.21249px;" version="1.1" viewbox="0 0 159.21249 16.637501" width="159.21249" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.76,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.52,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.666979" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.707369" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-21.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-15.43,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ;</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.59148" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.368107" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.531607" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,21.07,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,27.78,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ;</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.59148" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.368107" y="0"> )</t年代p一个n></text> </g> </g> </svg>是<我>确定地图</我>的过滤器<年代vg height="14.825" id="M308" style="vertical-align:-3.2316pt;width:15.7px;" version="1.1" viewbox="0 0 15.7 14.825" width="15.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.825)"> <g transform="translate(72,-60.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.74,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。正如上面介绍的那样,<年代vg height="11.05" id="M309" style="vertical-align:-3.2316pt;width:13.1625px;" version="1.1" viewbox="0 0 13.1625 11.05" width="13.1625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.76,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>反映了每个体素如何可靠的现场评估;也就是说,对比bandpass-filtered图像。</p><p>gydF4y2Ba数值优化(<一个href=”#EEq5">13</一个>)是一个标准的加权最小二乘法最小化;也就是说,它对应的能量的最小化<年代vg height="19.0375" id="M310" style="vertical-align:-3.88356pt;width:141.175px;" version="1.1" viewbox="0 0 141.175 19.0375" width="141.175" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.0375)"> <g transform="translate(72,-56.77)"> <text transform="matrix(1,0,0,-1,-71.95,60.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.9271421" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.090641" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.742237" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.369066" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.409454" y="0"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.948524" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.338039" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.501537" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.141586" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.568855" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="89.909073" y="0"> Γ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="97.248337" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="101.41183" y="0"> 为</t年代p一个n></text> <text transform="matrix(1,0,0,-1,36.01,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.21"> 2</t年代p一个n></text> </g> </g> </svg>,使用对角矩阵<年代vg height="14.8625" id="M311" style="vertical-align:-3.25793pt;width:128.95px;" version="1.1" viewbox="0 0 128.95 14.8625" width="128.95" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.852844" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.893232" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.144733" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.620567" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.171898" y="0"> g</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.586899" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.750397" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-13,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-8.13,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.006001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,22.07,60.28)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 6</t年代p一个n></text> <text transform="matrix(1,0,0,-1,26.94,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>,矩阵<年代vg height="17.7875" id="M312" style="vertical-align:-3.25793pt;width:110.6875px;" version="1.1" viewbox="0 0 110.6875 17.7875" width="110.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.7875)"> <g transform="translate(72,-57.77)"> <text transform="matrix(1,0,0,-1,-71.95,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.103384" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.143772" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.307272" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.38,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-30.51,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.006001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,0.75,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 6</t年代p一个n></text> <text transform="matrix(1,0,0,-1,5.62,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,9.79,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和向量<年代vg height="17.7875" id="M313" style="vertical-align:-3.25793pt;width:133.66251px;" version="1.1" viewbox="0 0 133.66251 17.7875" width="133.66251" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.7875)"> <g transform="translate(72,-57.77)"> <text transform="matrix(1,0,0,-1,-71.95,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Γ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.802592" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.842981" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.006479" y="0"> Δ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.033646" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-27.84,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-22.97,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.993498" y="0"> Δ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.020664" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,19.13,57.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 6</t年代p一个n></text> <text transform="matrix(1,0,0,-1,24,61.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,28.17,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。一个简单的计算表明,该解决方案(<一个href=”#EEq5">13</一个>),然后由Moore-Penrose伪逆<年代vg height="16.75" id="M314" style="vertical-align:-2.21957pt;width:175.675px;" version="1.1" viewbox="0 0 175.675 16.75" width="175.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.75)"> <g transform="translate(72,-58.6)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.553012" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.305832" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-43.47,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> __</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.12,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.191385" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-7.15,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-0.44,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,8.95,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,13.82,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.765323" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,29.75,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,40.62,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,52.39,65.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,59.1,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,也就是说,<年代p一个ncl一个年代年代=”equation" id="eq9"> <svg height="18.674999" id="M315" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 18.674999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.675)"> <g transform="translate(72,-57.06)"> <text transform="matrix(1,0,0,-1,150.1,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,159.13,57.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,168.76,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.303911" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.993736" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.633072" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.673458" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.83696" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.226471" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.991791" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,242.92,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> __</t年代p一个n></text> <text transform="matrix(1,0,0,-1,247.79,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.389513" y="0"> Γ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.728774" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="220.08" y="-0.54000002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="224.2435" y="-0.54000002"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="230.495" y="-0.54000002"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="236.74651" y="-0.54000002"> )</t年代p一个n></text> </g> </g> </svg></span>与<年代vg height="14.6" id="M316" style="vertical-align:-3.13504pt;width:58.549999px;" version="1.1" viewbox="0 0 58.549999 14.6" width="58.549999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.38,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.303911" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.993736" y="0"> )</t年代p一个n></text> </g> </g> </svg>任意设置为0时<年代vg height="16.5375" id="M317" style="vertical-align:-2.21957pt;width:64.762497px;" version="1.1" viewbox="0 0 64.762497 16.5375" width="64.762497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5375)"> <g transform="translate(72,-58.77)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.02,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-49.31,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-39.92,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.05,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.640053" y="0"> )</t年代p一个n></text> </g> </g> </svg>是不可逆的。</p><p>gydF4y2Ba联合估计(<一个href=”#EEq5">13</一个>),一个全球性的确定性地图相关的质量评估<年代vg height="14.6" id="M318" style="vertical-align:-3.13504pt;width:20.8375px;" version="1.1" viewbox="0 0 20.8375 14.6" width="20.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>被定义为(<一个href=”#B43">43</一个>]<gydF4y2Ba年代p一个ncl一个年代年代=”equation" id="eq10"> <svg height="35.650002" id="M319" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 35.650002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,35.65)"> <g transform="translate(72,-43.48)"> <text transform="matrix(1,0,0,-1,153.16,59.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,162.18,56.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,168.84,59.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.669998" y="6.5599999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.099165" y="0.0099999998"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.300413" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.990238" y="0.0099999998"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.62957" y="0.0099999998"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,220.22,46.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,230.67,59.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,235.86,56.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,243.18,59.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1599998" y="0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.03665" y="0.0099999998"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.288151" y="0.0099999998"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="224.69" y="5.1599998"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="228.8535" y="5.1599998"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="235.105" y="5.1599998"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="241.35651" y="5.1599998"> )</t年代p一个n></text> </g> </g> </svg></span>即每个正交滤波器确定措施的总和。这个更新的确定性地图必须要加上以前的迭代(见所积累的确定性计算的部分<一个href=”#sec4.2">4.2</一个>)。</p><p>gydF4y2Ba在部分描述的多尺度方法<一个href=”#sec3.2">3.2</一个>,使用相同的正交滤波器在减少<年代vg height="17.0625" id="M320" style="vertical-align:-5.39853pt;width:24.725px;" version="1.1" viewbox="0 0 24.725 17.0625" width="24.725" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.0625)"> <g transform="translate(72,-58.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.03,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.66,58.47)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>相当于估计bandpass-filtered形象的阶段截止频率增加,也就是说,<年代vg height="13.55" id="M321" style="vertical-align:-2.29482pt;width:46.787498px;" version="1.1" viewbox="0 0 46.787498 13.55" width="46.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.7398367" y="0"> ←</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.793449" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.044949" y="0"> </t年代p一个n></text> </g> </g> </svg>每一次<年代vg height="13.6125" id="M322" style="vertical-align:-2.34499pt;width:60.900002px;" version="1.1" viewbox="0 0 60.900002 13.6125" width="60.900002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> ←</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.38061" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.019943" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.360165" y="0"> 1</t年代p一个n></text> </g> </g> </svg>。这个支撑而且位移估计,计算<年代vg height="14.6" id="M323" style="vertical-align:-3.13504pt;width:20.8375px;" version="1.1" viewbox="0 0 20.8375 14.6" width="20.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.7125" id="M324" style="vertical-align:-3.2316pt;width:17.112499px;" version="1.1" viewbox="0 0 17.112499 14.7125" width="17.112499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>不同规模的乐队<年代vg height="16.512501" id="M325" style="vertical-align:-4.77652pt;width:14.3375px;" version="1.1" viewbox="0 0 14.3375 16.512501" width="14.3375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5125)"> <g transform="translate(72,-58.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="12.975" id="M326" style="vertical-align:-4.77652pt;width:16.75px;" version="1.1" viewbox="0 0 16.75 12.975" width="16.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.975)"> <g transform="translate(72,-61.62)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>的<年代vg height="13.4875" id="M327" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.4875)"> <g transform="translate(72,-61.21)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="7.1374998" id="M328" style="vertical-align:-0.10033pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。</p><p>gydF4y2Ba与正交旋转过滤器可以有效地实现在傅里叶域中由于FFT和卷积定理。然而,由于这些过滤器的空间范围很小,也可以使用有效的空间分布和截断内核,在这项研究。由于当地阶段是不变的地方强度定标,Morphons过程适用于注册图像各种对比增强。除此之外,一些研究表明,相位提取允许快速收敛和subvoxel精密位移估计(例如,看到<一个href=”#B39">39</一个>])。</p><h5gydF4y2Baid="sec4.2">4.2。领域积累</h5><p>gydF4y2Ba在原始Morphons方法,积累字段计算的加权和更新字段和之前的积累,用于阻尼优化方案。给出了权重的确定上更新字段(<年代vg height="11.025" id="M329" style="vertical-align:-3.21404pt;width:12.425px;" version="1.1" viewbox="0 0 12.425 11.025" width="12.425" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.025)"> <g transform="translate(72,-63.18)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.76,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,计算从<年代vg height="14.7125" id="M330" style="vertical-align:-3.2316pt;width:17.112499px;" version="1.1" viewbox="0 0 17.112499 14.7125" width="17.112499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Θ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>)和累积确定性地图(<年代vg height="11.0375" id="M331" style="vertical-align:-3.22282pt;width:12.725px;" version="1.1" viewbox="0 0 12.725 11.0375" width="12.725" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.76,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>)。确定性的地图还必须积累为了反映了信心,所有先前的位移计算,累积的一步<年代vg height="10.475" id="M332" style="vertical-align:-0.0pt;width:12.05px;" version="1.1" viewbox="0 0 12.05 10.475" width="12.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</t年代p一个n></text> </g> </g> </svg>必须分成两个操作<年代vg height="14.375" id="M333" style="vertical-align:-3.13504pt;width:21.475px;" version="1.1" viewbox="0 0 21.475 14.375" width="21.475" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.41,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>(字段积累)<年代vg height="14.5" id="M334" style="vertical-align:-3.2316pt;width:17.762501px;" version="1.1" viewbox="0 0 17.762501 14.5" width="17.762501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5)"> <g transform="translate(72,-60.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.41,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>(确定性积累):<年代p一个ncl一个年代年代=”equation" id="EEq6"> <svg height="84.837502" id="M335" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 84.837502" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,84.8375)"> <g transform="translate(72,-4.13)"> <text transform="matrix(1,0,0,-1,112.32,57.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,121.86,54.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,131.49,54.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,147.22,54.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,152.11,57.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,167.2,54.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,171.85,57.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,182.24,54.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,187.14,57.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,197.53,54.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,202.18,54.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3199997" y="-2.52"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.36039" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,233.42,54.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,241.09,57.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.639999" y="-9.2200003"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,270.92,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 253.63,60.34 34.04,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,253.63,48.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,258.82,45.34)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,266.49,48.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,283.02,45.34)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,288.86,57.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,298.74,54.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,303.39,57.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-148.75" y="41.080002"> Φ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="164.48" y="1.74"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="168.64349" y="1.74"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="174.895" y="1.74"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="181.1465" y="1.74"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,164.18,13.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,170.84,13.63)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,181.88,13.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,186.77,16.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,197.17,13.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,201.81,13.63)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3299999" y="-2.51"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.559999" y="-11.74"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,230.19,30.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-0.63" y="8.1300001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,237.84,25.37)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,254.99,30.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-0.62" y="8.1300001"> </t年代p一个n></text> <g> <path d="m 224.37,19.27 35.5,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,225.1,7.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,230.29,4.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,237.96,7.39)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,254.49,4.26)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,261.06,16.14)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="206.81" y="-0.95999998"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="210.9735" y="-0.95999998"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="217.22501" y="-0.95999998"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="223.4765" y="-0.95999998"> )</t年代p一个n></text> </g> </g> </svg></span>在最后一个公式,类似于领域积累,确定地图更新的确定性(<一个href=”#B43">43</一个>]。</p><p>gydF4y2Ba然而,解释之前,位移的增加字段不是真正适合积累空间转换,与构成。综合的积累也可以使用确定性阻尼作为权重因子<年代p一个ncl一个年代年代=”equation" id="eq11"> <svg height="33.5" id="M337" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 33.5" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,33.5)"> <g transform="translate(72,-45.2)"> <text transform="matrix(1,0,0,-1,110.3,57.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,119.84,54.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,129.47,54.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,145.2,54.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,150.09,57.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,165.18,54.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,169.82,57.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,180.22,54.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,185.11,57.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,195.51,54.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,200.16,54.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3199997" y="-2.52"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.347885" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,231.4,54.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,239.07,57.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.6" y="-9.2200003"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,270.86,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 253.57,60.34 34.04,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,253.57,48.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,258.76,45.34)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,266.43,48.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,282.96,45.34)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,288.8,57.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,298.68,54.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,303.33,57.22)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="164.53999" y="1.74"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="168.70351" y="1.74"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="174.955" y="1.74"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="181.2065" y="1.74"> )</t年代p一个n></text> </g> </g> </svg></span></p> <p>(SSD-based)恶魔登记是一种非参数算法执行优化之间的SSD图像。在[<一个href=”#B29">27</一个>),提出了一种diffeomorphic领域积累作为恶魔的改进方法。这个想法是使用优化方法的适应李群(<一个href=”#B45">45</一个>),以限制diffeomorphic转换的可能的解决方案。在实践中,这是通过取代了恶魔的积累一步积累使用diffeomorphic流<年代vg height="14.075" id="M338" style="vertical-align:-2.72118pt;width:38.3125px;" version="1.1" viewbox="0 0 38.3125 14.075" width="38.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.075)"> <g transform="translate(72,-60.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.217831" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.38133" y="0"> )</t年代p一个n></text> </g> </g> </svg>介绍了部分<一个href=”#sec2">2</一个>。这种积累阅读然后<年代p一个ncl一个年代年代=”equation" id="EEq8"> <svg height="19.35" id="M339" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 19.35" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.35)"> <g transform="translate(72,-56.52)"> <text transform="matrix(1,0,0,-1,106.52,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,116.06,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,125.68,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,141.41,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,146.3,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,161.39,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,166.04,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3199997" y="-2.51"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.347885" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,197.28,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,204.95,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.39" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.459999" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.310001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.24" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.791332" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.042831" y="0"> p</t年代p一个n></text> <text transform="matrix(1,0,0,-1,264.14,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,268.79,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.379999" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.6300001" y="-2.51"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.957718" y="-2.51"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.121218" y="-2.51"> d</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.32" y="-2.51"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="199.08" y="-2.51"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="203.2435" y="-2.51"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="209.495" y="-2.51"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="215.74651" y="-2.51"> )</t年代p一个n></text> </g> </g> </svg></span>领域的指数<年代vg height="14.7" id="M340" style="vertical-align:-3.21404pt;width:56.462502px;" version="1.1" viewbox="0 0 56.462502 14.7" width="56.462502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7)"> <g transform="translate(72,-60.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.217831" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.38133" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.69,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-31.04,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>可以使用少量的有效估计递归的成分<年代vg height="14.3375" id="M341" style="vertical-align:-3.21404pt;width:18.275px;" version="1.1" viewbox="0 0 18.275 14.3375" width="18.275" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>本身。因此,位移场<年代vg height="14.7125" id="M342" style="vertical-align:-3.22282pt;width:75.012497px;" version="1.1" viewbox="0 0 75.012497 14.7125" width="75.012497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.41,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.87,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-40.83,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.93,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-20.85,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-16.2,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>与变形操作吗<年代vg height="14.7125" id="M343" style="vertical-align:-3.22282pt;width:88.887497px;" version="1.1" viewbox="0 0 88.887497 14.7125" width="88.887497" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7125)"> <g transform="translate(72,-60.23)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.25,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∘</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.2272139" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.778546" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.030046" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.457548" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.621048" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-9.75,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-5.1,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>。</p><p>gydF4y2Ba对于Morphons,积累一步可以以同样的方式实现。这将产生平滑领域比传统的添加或组合。然而,积累一步Morphons方法涉及一个阻尼的基础上确定。因此,我们提出以下积累一步diffeomorphic Morphons:<年代p一个ncl一个年代年代=”equation" id="EEq9"> <svg height="38.575001" id="M344" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.575001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.575)"> <g transform="translate(72,-41.14)"> <text transform="matrix(1,0,0,-1,66.08,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,75.62,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,85.25,50.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,100.98,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,105.87,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,120.96,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,125.6,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,136,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,140.89,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,151.29,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,155.94,50.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3199997" y="-2.52"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.36039" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,187.18,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,194.85,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ⊕</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.39" y="7.3299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.990002" y="7.3299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.660004" y="-9.21"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.77" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.321333" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.57283" y="0"> p</t年代p一个n></text> <text transform="matrix(1,0,0,-1,269.7,59.54)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 252.41,56.57 34.04,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,252.41,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,257.6,41.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,265.27,44.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,281.8,41.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,287.64,53.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,297.52,50.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,302.17,46.12)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.91" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.15" y="-7.3299999"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.490221" y="-7.3299999"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.653721" y="-7.3299999"> d</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.369999" y="-7.3299999"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="165.7" y="-7.3299999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="169.86349" y="-7.3299999"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="176.11501" y="-7.3299999"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="182.3665" y="-7.3299999"> )</t年代p一个n></text> </g> </g> </svg></span>自<年代vg height="14.1875" id="M345" style="vertical-align:-2.72118pt;width:96.087502px;" version="1.1" viewbox="0 0 96.087502 14.1875" width="96.087502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.1875)"> <g transform="translate(72,-60.65)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.217831" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.38133" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.796329" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.673698" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.31303" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.353424" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.516922" y="0"> d</t年代p一个n></text> </g> </g> </svg>对于任何一个向量场<年代vg height="10.325" id="M346" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,积累逐渐消退<年代vg height="12.45" id="M347" style="vertical-align:-3.22282pt;width:48.287498px;" version="1.1" viewbox="0 0 48.287498 12.45" width="48.287498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.45)"> <g transform="translate(72,-62.04)"> <text transform="matrix(1,0,0,-1,-71.95,65.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.76,62.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-58.4,65.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≫</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.141133" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-38.07,62.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。确定地图依然如上所述的积累(<一个href=”#EEq6">17</一个>)。</p><p>gydF4y2Ba注意,因为这个领域是离散的网格体素,需要插值计算的构成两个解析。因此,由于连续插入错误可能会导致不可逆转的转换。然而,这样的问题没有观察到在实际的实验中使用合理的平滑。</p><h5我d=”年代ec4.3">4.3。场正则化</h5><p>gydF4y2Ba在位移估计步骤中,当地的相关性估计相位计算和使用作为积累的重量。这确定地图也可以用于智能位移场的正则化。正规化是使用来执行的<我>规范化卷积</我>(<gydF4y2Ba一个href=”#B46">46</一个>]的高斯核函数,考虑到确定地图为了高确定性的位置更重要。肯定也以同样的方式正规化位移场组件为了保持位移向量之间的对应关系及其相应的确定性。</p><p>gydF4y2Ba数学,因为一个积极的功能<年代vg height="10.95" id="M348" style="vertical-align:-0.1254pt;width:9.1374998px;" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代p一个n></text> </g> </g> </svg>和一个过滤器<年代vg height="9.9375" id="M349" style="vertical-align:-2.34499pt;width:8.4375px;" version="1.1" viewbox="0 0 8.4375 9.9375" width="8.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>(通常是一个高斯方差的内核<年代vg height="14.6" id="M350" style="vertical-align:-3.13504pt;width:45.287498px;" version="1.1" viewbox="0 0 45.287498 14.6" width="45.287498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.61,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> Ψ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.11,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n></text> </g> </g> </svg>),(标量)的规范化卷积函数<年代vg height="7.1875" id="M351" style="vertical-align:-0.13794pt;width:7px;" version="1.1" viewbox="0 0 7 7.1875" width="7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1875)"> <g transform="translate(72,-66.25)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>通过<年代vg height="9.9375" id="M352" style="vertical-align:-2.34499pt;width:8.4375px;" version="1.1" viewbox="0 0 8.4375 9.9375" width="8.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>所涉及的规范化<年代vg height="10.95" id="M353" style="vertical-align:-0.1254pt;width:9.1374998px;" version="1.1" viewbox="0 0 9.1374998 10.95" width="9.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.95)"> <g transform="translate(72,-63.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代p一个n></text> </g> </g> </svg>是<年代p一个ncl一个年代年代=”equation" id="eq12"> <svg height="35.099998" id="M354" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 35.099998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,35.1)"> <g transform="translate(72,-43.92)"> <text transform="matrix(1,0,0,-1,166.1,55.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.5013199" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,178.14,51.93)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,183.69,55.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6148071" y="0"> ≜</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.85" y="-8.3599997"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.013498" y="-8.3599997"> ℎ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.22773" y="-8.3599997"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.72905" y="-8.3599997"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.668217" y="-8.3599997"> ∗</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.982948" y="-8.3599997"> </t年代p一个n></text> <g> <path d="m 206.54,58.18 39.79,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,213.46,46.31)"> <tspan style="font-size: 12.50px; " x="34.07" y="-8.75"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ℎ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.9898968" y="0"> ∗</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.304632" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="254.41" y="-8.5200005"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="258.57349" y="-8.5200005"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="264.82501" y="-8.5200005"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="271.07651" y="-8.5200005"> )</t年代p一个n></text> </g> </g> </svg></span>这个操作不会增加的最大振幅过滤功能。的确,对于一个非负的内核<年代vg height="9.9375" id="M355" style="vertical-align:-2.34499pt;width:8.4375px;" version="1.1" viewbox="0 0 8.4375 9.9375" width="8.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.9375)"> <g transform="translate(72,-64.05)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,我们轻松地展示<年代vg height="14.925" id="M356" style="vertical-align:-3.22282pt;width:110.8875px;" version="1.1" viewbox="0 0 110.8875 14.925" width="110.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.925)"> <g transform="translate(72,-60.06)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.5390692" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-53.37,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ℎ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-47.82,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.6390929" y="0"> 为</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-34.63,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-22.56,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.579458" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.080778" y="0"> 为</t年代p一个n></text> <text transform="matrix(1,0,0,-1,8.06,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代p一个n></text> </g> </g> </svg>,<年代vg height="14.9125" id="M357" style="vertical-align:-3.21404pt;width:124.3875px;" version="1.1" viewbox="0 0 124.3875 14.9125" width="124.3875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.9125)"> <g transform="translate(72,-60.07)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.5390692" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> 为</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-53.37,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ∞</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-41.29,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.75522" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.306553" y="0"> x</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-3.56,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,1.75,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="2.5006001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0019197" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.165419" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.042068" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.205568" y="0"> |</t年代p一个n></text> </g> </g> </svg>。累积位移场<年代vg height="14.35" id="M358" style="vertical-align:-3.22282pt;width:18.5875px;" version="1.1" viewbox="0 0 18.5875 14.35" width="18.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.35)"> <g transform="translate(72,-60.52)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.07,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>随后确定地图因此正规化感谢这个操作使用规范化的确定性地图<年代vg height="11.0375" id="M359" style="vertical-align:-3.22282pt;width:12.725px;" version="1.1" viewbox="0 0 12.725 11.0375" width="12.725" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.0375)"> <g transform="translate(72,-63.17)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.76,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,也就是说,<年代p一个ncl一个年代年代=”equation" id="eq13"> <svg height="51.8125" id="M360" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 51.8125" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,51.8125)"> <g transform="translate(72,-30.55)"> <text transform="matrix(1,0,0,-1,151.09,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ψ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,160.41,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,170.04,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,185.77,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,190.66,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,201.06,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,205.95,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3299999" y="-2.51"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.357885" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,237.19,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,242.08,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,248.62,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,252.25,55.82)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,256.39,61.13)"> <tspan style="font-size: 12.50px; " x="-97.639999" y="25.15"> Ψ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.1514759" y="0"> ,</t年代p一个n></text> <text transform="matrix(1,0,0,-1,168.08,32.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,174.73,33.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,185.77,32.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,190.66,35.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,201.06,32.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,205.95,33.46)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3299999" y="-2.52"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.357885" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,232.5,32.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,237.39,35.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∗</t年代p一个n></text> <text transform="matrix(1,0,0,-1,243.93,32.85)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,247.57,30.66)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,251.7,35.98)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.1514759" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="216.17" y="-12.17"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="220.3335" y="-12.17"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="226.58499" y="-12.17"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="232.8365" y="-12.17"> )</t年代p一个n></text> </g> </g> </svg></span>注意,为计算<年代vg height="14.8125" id="M361" style="vertical-align:-3.13504pt;width:21.2125px;" version="1.1" viewbox="0 0 21.2125 14.8125" width="21.2125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8125)"> <g transform="translate(72,-60.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Ψ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.62,60.2)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>所有组件,分别执行规范化卷积的向量场。</p><p>gydF4y2Ba这个操作会传播的位移场确定性高的地区更明显的滤波器响应的地方。此外,通过设置为零卷外的确定性边界,规范化卷积取消填充策略的影响。这一步骤产生一个光滑的版本的积累的领域可能会减少产生的图像匹配精度位移估计步骤,因为它限制了可能的解决方案来平滑位移场。</p><p>gydF4y2Ba然而,如果迭代算法是收敛的,解决方案将定期和可逆的(除了大数值错误),由于积累和正则化约束,但它也将在本地(至少)最优的当地的相位差。事实上,阶段是单调和光滑,局部结构之间的不匹配会自动导致非零字段更新确定性高的值,这将会提高位移估计和符合结构联系在一起。</p><p>gydF4y2Ba位移场的雅可比矩阵可能被用作标准验证物理行为的变形。事实上,每个体素的雅可比矩阵为体素遇到在变形体积的变化。雅可比矩阵显示扩张大于1时,当它小于1和压缩。消极的雅可比矩阵意味着体素“倒”(得到一个负的体积),这是不符合mass-preservation原则。</p><p>gydF4y2Ba在下面,diffeomorphic版的恶魔和Morphons分别表示D-Demons D-Morphons。</p><h4gydF4y2Baid="experiments-and-results">5。实验和结果</h4><p>gydF4y2Ba首先比较了几个简单的方法2 d虚拟情况下为了证明兴趣选择准确的登记注册方法对图像。</p><p>gydF4y2Ba临床验证,Morphons D-Morphons首次验证注册在10-phase point-validated基于像素呼吸胸腔模型(POPI-model)<我>莱昂-癌症中心,法国里昂</我>(<gydF4y2Ba一个href=”#B4">4</一个>),为了比较D-Morphons Morphons,恶魔,D-Demons图像之间强度的保护。然后,它应用于肺图像用不同的对比度增强,为了说明的分阶段方法相比传统SSD-based注册方法的情况下图像之间的强度并不守恒的注册。</p><p>gydF4y2Ba所有模拟都是使用Linux,执行在一个处理器英特尔酷睿2 (2.4 GHz)。我们的MATLAB实现用于原型的方法也被用于仿真。注意,没有努力是实现良好的性能的计算成本和内存需求在本研究中使用的实现。估计是使用旋转执行当地的阶段<年代vg height="11.075" id="M362" style="vertical-align:-0.3135pt;width:57.462502px;" version="1.1" viewbox="0 0 57.462502 11.075" width="57.462502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.804752" y="0"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.831919" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.609505" y="0"> 9</t年代p一个n></text> </g> </g> </svg>正交过滤器。小于1 GB的RAM是需要注册的两卷<年代vg height="11.2625" id="M363" style="vertical-align:-0.3135pt;width:104.35px;" version="1.1" viewbox="0 0 104.35 11.2625" width="104.35" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.2625)"> <g transform="translate(72,-62.99)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2515001" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.503" y="0"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.530167" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.307751" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.559254" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.810753" y="0"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.837917" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.615501" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.867004" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="77.118507" y="0"> 0</t年代p一个n></text> </g> </g> </svg>体素使用所有注册。注册所需的时间这样的图像,使用以下给出的参数,是魔鬼,大约6分钟42 Morphons, 7为D-Morphons D-Demons 43。然而,初步结果基于Morphons的c++实现,它使用傅里叶域中的操作,而不是旋转(在我们的matlab实现)和四核CPU使用4线程,允许一个部门的计算时间,导致Morphons注册以一分钟为这样一个典型的图像大小。</p><h5我d=”年代ec5.1">5.1。说明虚拟实验</h5><p>gydF4y2Ba两个二维虚拟实验进行。第一个实验中,见图<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig4/" target="_blank">4</一个>之后,基于虚拟磁盘映像模糊。两张同一磁盘了,唯一的区别是强度的规模(乘以0.75)。这个实验展示了使用分阶段方法的兴趣(传统Morphons在本例中),而注册相同形状不同的对比,而灰度法(传统的恶魔)。</p><d我v class="floats-partial-section partial-carousel-wrapper" data-section="fig4"> <div class="floats-partial-content fig-content-fig4"> <div class="partial-carousel--single-image"> <img alt="" name="891585.fig.004a" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.004a.jpg"> <br> <strong></strong> </div> <div class="partial-carousel--single-image"> <img alt="" name="891585.fig.004b" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.004b.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig4"> <button class="partial-carousel-dot" aria-label=""><img alt="" name="891585.fig.004a" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.004a.jpg"><br><strong></strong></button> <button class="partial-carousel-dot" aria-label=""><img alt="" name="891585.fig.004b" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.004b.jpg"><br><strong></strong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig4"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图4</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/ijbi/2011/891585/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 结果登记2 identical-sized模糊磁盘之间不同的对比,使用恶魔和Morphons。黄色:磁盘的轮廓。红色:产生的向量场登记。造成的位移场Morphons非常接近于零。注意,SSD实际上是低于Morphons使用恶魔。然而,SSD并不反映形状的匹配,反对扭曲后的磁盘轮廓。</t一个ble> </div> </div> </div> <p>第二个虚拟实验是基于两个磁盘(参见图的图像<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig5/" target="_blank">5</一个>)。在固定的形象,一个磁盘的半径<年代vg height="12.575" id="M364" style="vertical-align:-3.13504pt;width:42.712502px;" version="1.1" viewbox="0 0 42.712502 12.575" width="42.712502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.575)"> <g transform="translate(72,-61.94)"> <text transform="matrix(1,0,0,-1,-71.95,65.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.85,61.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.2,65.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-42.75,61.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>创建,一个洞(磁盘半径<年代vg height="10.925" id="M365" style="vertical-align:-3.13504pt;width:12.6px;" version="1.1" viewbox="0 0 12.6 10.925" width="12.6" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.85,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>)被添加到它的中心。运动图像,一个磁盘的半径<年代vg height="10.925" id="M366" style="vertical-align:-3.13504pt;width:12.6px;" version="1.1" viewbox="0 0 12.6 10.925" width="12.6" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.85,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> </g> </g> </svg>创建具有相同强度比例的固定形象。这个例子说明了结构缺失的情况相比,一个图像,因为它在实践中可能发生的问题(例如,肠道气体在腹部CT图像)。这个实验说明了diffeomorphic Morphons算法的版本可以防止产生负面卷登记后,在不增加平滑通过使用一个更大的高斯正规化内核。</p><d我v class="floats-partial-section partial-carousel-wrapper" data-section="fig5"> <div class="floats-partial-content fig-content-fig5"> <div class="partial-carousel--single-image"> <img alt="" name="891585.fig.005a" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.005a.jpg"> <br> <strong></strong> </div> <div class="partial-carousel--single-image"> <img alt="" name="891585.fig.005b" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.005b.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig5"> <button class="partial-carousel-dot" aria-label=""><img alt="" name="891585.fig.005a" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.005a.jpg"><br><strong></strong></button> <button class="partial-carousel-dot" aria-label=""><img alt="" name="891585.fig.005b" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.005b.jpg"><br><strong></strong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig5"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图5</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/ijbi/2011/891585/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="13.45" id="M367" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 18.975 13.45" width="18.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.915119" y="0"> )</t年代p一个n></text> </g> </g> </svg> <table> 结果之间的登记2图像使用Morphons D-Morphons注册,结构(即说明了情况。,明亮的洞中心的固定形象)缺少运动图像。两种方法导致变形图片非常相似的固定形象除了中央明亮的部分(因为它不是出现在移动图像)。diffeomorphic方法产生很低,但仍积极的雅可比矩阵值(gydF4y2Ba接近0)中心的磁盘。考虑到像素网格的定义的字段是固定的形象,这就意味着中央明亮部分的表面移动的图像(消失)对应,正如预期的那样,几乎一个奇异点移动图像。然而,常规方法产生高度-雅克比中部,导致创建地区其他地区形象的“镜子”。</t一个ble> </div> </div> </div> <h5 id="sec5.2">5.2。胸腔呼吸模型精度评估</h5><p>gydF4y2Ba“模型(<一个href=”#B4">4</一个>)由10卷重建4 d respiration-correlated CT扫描(RCCT)胸腔,平均每个卷对应于一个特定阶段的呼吸循环。41地标被医学专家发现在每个10图像注册验证。</p><p>gydF4y2Ba传统Morphons D-Demons, D-Morphons应用参考相位和9人之间。对所有方法,天平将的数量<年代vg height="10.9125" id="M368" style="vertical-align:-0.17555pt;width:35.762501px;" version="1.1" viewbox="0 0 35.762501 10.9125" width="35.762501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.214951" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.255341" y="0"> 8</t年代p一个n></text> </g> </g> </svg>最终的解决办法<年代vg height="11.075" id="M369" style="vertical-align:-0.3135pt;width:138.2375px;" version="1.1" viewbox="0 0 138.2375 11.075" width="138.2375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3269978" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.054333" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.557331" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.34742" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.674419" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.401752" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.904755" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="82.694839" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="91.021843" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="100.74918" y="0"> 米</t年代p一个n></text> </g> </g> </svg>。高斯分布的方差内核用于正则化经验设置为两倍体素的大小(<年代vg height="19.200001" id="M370" style="vertical-align:-4.35121pt;width:45.287498px;" version="1.1" viewbox="0 0 45.287498 19.200001" width="45.287498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.2)"> <g transform="translate(72,-56.64)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.61,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.3400002"> Ψ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.11,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 2</t年代p一个n></text> </g> </g> </svg>体素)。对于这个实验,至少10,最高20使用迭代在每个规模。之间,迭代过程停止,如果变化,测量的SSD,低于0.01%。通常这样的收敛性判据是前20迭代,支持这一事实恶魔和Morphons像优化方法。</p><p>gydF4y2Ba结果相互比较,结果从传统的恶魔算法用于(<一个href=”#B4">4</一个>]。取得了比较的错误在具有里程碑意义的位置,SSD图像之间,谐波能量,雅可比矩阵和最小。<年代p一个ncl一个年代年代=”l是t”><span class="list-item"><span class="list-label">(我)</年代p一个n><年代p一个ncl一个年代s="list-content">具有里程碑意义的位置误差评估登记的能力找到的物理运动器官。</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(2)</年代p一个n><年代p一个ncl一个年代s="list-content">固定和变形之间的SSD图像的图像匹配的假设保护强度。它计算<年代vg height="18.7125" id="M371" style="vertical-align:-3.7908pt;width:98.675003px;" version="1.1" viewbox="0 0 98.675003 18.7125" width="98.675003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.7125)"> <g transform="translate(72,-57.03)"> <text transform="matrix(1,0,0,-1,-71.95,60.84)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∑</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.52,57.16)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.21,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.87833" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.218552" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.871346" y="0"> ∘</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.023064" y="0"> Δ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.050228" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,2.01,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>。</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(3)</年代p一个n><年代p一个ncl一个年代s="list-content">谐波的能量(<一个href=”#B27">29日</一个>,<gydF4y2Ba一个href=”#B31">32</一个>位移场的)<年代vg height="10.325" id="M372" style="vertical-align:-0.0pt;width:12.7px;" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>表明普通字段和计算<年代vg height="18.924999" id="M373" style="vertical-align:-3.7908pt;width:254.0625px;" version="1.1" viewbox="0 0 254.0625 18.924999" width="254.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.925)"> <g transform="translate(72,-56.86)"> <text transform="matrix(1,0,0,-1,-71.95,60.69)"> <tspan style="font-size: 12.50px; " x="24.309999" y="0.029999999"> ∑</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.414999" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.142332" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-36.22,56.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-30.9,60.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.702568" y="0"> ∇</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.84226" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-1.18,57.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,3.69,60.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代p一个n></text> <text transform="matrix(1,0,0,-1,10.23,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,17.88,60.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.87929" y="0"> ∇</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.018984" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,54.78,57.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,59.66,60.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代p一个n></text> <text transform="matrix(1,0,0,-1,66.19,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,73.85,60.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.327718" y="0"> 为</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.866787" y="0"> ∇</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.006479" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,110.75,57.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 3</t年代p一个n></text> <text transform="matrix(1,0,0,-1,115.62,60.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 为</t年代p一个n></text> <text transform="matrix(1,0,0,-1,122.16,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,127.03,60.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>。</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(iv)</年代p一个n><年代p一个ncl一个年代s="list-content">雅可比矩阵的表示各体素的体积变化。回想一下,负的雅可比矩阵对应倒卷,这是不能接受的一个物理的观点。雅可比矩阵计算<年代vg height="13.5625" id="M374" style="vertical-align:-2.21957pt;width:48.3125px;" version="1.1" viewbox="0 0 48.3125 13.5625" width="48.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.5625)"> <g transform="translate(72,-61.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2515001" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> t</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.192345" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.355844" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.383251" y="0"> )</t年代p一个n></text> </g> </g> </svg>,<年代vg height="16.637501" id="M375" style="vertical-align:-4.77652pt;width:191.375px;" version="1.1" viewbox="0 0 191.375 16.637501" width="191.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.92,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-51.3,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.41692" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-23.85,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-20.63,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8648672" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-3.88,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,4.02,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,22.34,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,32.27,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.729254" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,56.66,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,59.88,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8523636" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,76.62,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,在那里<年代vg height="16.512501" id="M376" style="vertical-align:-4.77652pt;width:16.924999px;" version="1.1" viewbox="0 0 16.924999 16.512501" width="16.924999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5125)"> <g transform="translate(72,-58.79)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.66,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> </g> </g> </svg>克罗内克的三角洲(<年代vg height="16.637501" id="M377" style="vertical-align:-4.77652pt;width:44.125px;" version="1.1" viewbox="0 0 44.125 16.637501" width="44.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.66,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.04,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代p一个n></text> </g> </g> </svg>如果<年代vg height="12.675" id="M378" style="vertical-align:-2.34499pt;width:31.387501px;" version="1.1" viewbox="0 0 31.387501 12.675" width="31.387501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.675)"> <g transform="translate(72,-61.86)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.3517642" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.392153" y="0"> </t年代p一个n></text> </g> </g> </svg>,0)和<年代vg height="14.5875" id="M379" style="vertical-align:-3.2316pt;width:12.4625px;" version="1.1" viewbox="0 0 12.4625 14.5875" width="12.4625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.3,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是<年代vg height="10.975" id="M380" style="vertical-align:-0.13794pt;width:17.275px;" version="1.1" viewbox="0 0 17.275 10.975" width="17.275" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.975)"> <g transform="translate(72,-63.22)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.888433" y="0"> t</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.4517879" y="0"> h</t年代p一个n></text> </g> </g> </svg>组件的位移场。在实践中,偏导数<年代vg height="16.637501" id="M381" style="vertical-align:-4.77652pt;width:46.912498px;" version="1.1" viewbox="0 0 46.912498 16.637501" width="46.912498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6375)"> <g transform="translate(72,-58.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.3765302" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-58.91,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.69,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8648672" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-38.95,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>可以使用集中有限差分近似计算。</年代p一个n></年代p一个n></span></p> <p>地标位置错误(表达的比较<年代vg height="7.3125" id="M382" style="vertical-align:-0.0pt;width:24.4375px;" version="1.1" viewbox="0 0 24.4375 7.3125" width="24.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.3125)"> <g transform="translate(72,-66.15)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.727334" y="0"> 米</t年代p一个n></text> </g> </g> </svg>)产生的不同的注册表中可以看到<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/tab2/" target="_blank">2</一个>从左到右,地标位置的误差(标准的区别)在注册之前,使用恶魔从“网站(值),Morphons D-Demons, D-Morphons。位置错误指出如下:的意思是/性病(max)。平均Morphons、D-Demons D-Morphons,地标位置的误差等于或不及1毫米,体素的大小的一半在最细尺度上的注册过程。</p><d我v class="floats-partial-section partial-other-wrapper" data-section="tab2"> <div class="floats-partial-content fig-content-tab2"> <table class="table-group" id="tab2"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="6"> <hr></td> </tr> <tr class="thead"> <td align="left">RCCT阶段</td><td一个l我gn="center">原始</td><td一个l我gn="center">恶魔(<一个href=”#B4">4</一个>]</td><tdgydF4y2Ba一个l我gn="center">Morphons</td><td一个l我gn="center">D-Demons</td><td一个l我gn="center">D-Morphons</td></tr><tr> <td class="thead-hr" colspan="6"> <hr></td> </tr> <tr> <td align="left">第一阶段</td><td一个l我gn="center">0.5/0.5 (2.4)</td><td一个l我gn="center">1.3/0.3 (1.8)</td><td一个l我gn="center">0.7/0.3 (1.6)</td><td一个l我gn="center">0.7/0.3 (1.6)</td><td一个l我gn="center">0.7/0.3 (1.6)</td></tr><tr> <td align="left">第二阶段</td><td一个l我gn="center">0.5/0.6 (2.6)</td><td一个l我gn="center">1.4/0.2 (2.1)</td><td一个l我gn="center">0.7/0.4 (2.1)</td><td一个l我gn="center">0.7/0.4 (1.6)</td><td一个l我gn="center">0.7/0.4 (2.1)</td></tr><tr> <td align="left">第三阶段</td><td一个l我gn="center">2.2/1.8 (6.6)</td><td一个l我gn="center">1.4/0.4 (2.3)</td><td一个l我gn="center">1.2/0.6 (2.5)</td><td一个l我gn="center">1.2/0.6 (2.5)</td><td一个l我gn="center">1.2/0.6 (2.4)</td></tr><tr> <td align="left">第四阶段</td><td一个l我gn="center">4.3/2.5 (10)</td><td一个l我gn="center">1.2/0.4 (2.3)</td><td一个l我gn="center">1.0/0.4 (2.2)</td><td一个l我gn="center">1.0/0.5 (2.5)</td><td一个l我gn="center">1.0/0.4 (2.2)</td></tr><tr> <td align="left">5级</td><td一个l我gn="center">5.8/2.6 (12)</td><td一个l我gn="center">1.3/0.5 (2.6)</td><td一个l我gn="center">1.1/0.5 (2.7)</td><td一个l我gn="center">1.1/0.5 (2.5)</td><td一个l我gn="center">1.1/0.5 (2.8)</td></tr><tr> <td align="left">6级</td><td一个l我gn="center">6.1/2.9 (14)</td><td一个l我gn="center">1.1/0.4 (2.0)</td><td一个l我gn="center">1.0/0.5 (2.1)</td><td一个l我gn="center">1.1/0.6 (2.8)</td><td一个l我gn="center">1.0/0.5 (2.1)</td></tr><tr> <td align="left">阶段7</td><td一个l我gn="center">5.0/2.3 (12)</td><td一个l我gn="center">1.3/0.5 (2.4)</td><td一个l我gn="center">1.1/0.6 (2.8)</td><td一个l我gn="center">1.2/0.6 (2.7)</td><td一个l我gn="center">1.1/0.6 (2.8)</td></tr><tr> <td align="left">阶段8</td><td一个l我gn="center">3.7/1.6 (6.2)</td><td一个l我gn="center">1.1/0.3 (1.7)</td><td一个l我gn="center">0.8/0.4 (1.9)</td><td一个l我gn="center">0.8/0.4 (1.8)</td><td一个l我gn="center">0.8/0.4 (1.8)</td></tr><tr> <td align="left">期9</td><td一个l我gn="center">2.1/1.1 (4.5)</td><td一个l我gn="center">1.1/0.3 (1.9)</td><td一个l我gn="center">0.8/0.4 (2.0)</td><td一个l我gn="center">0.8/0.4 (1.7)</td><td一个l我gn="center">0.8/0.4 (2.0)</td></tr><tr> <td align="center" colspan="6"> <hr></td> </tr> <tr> <td align="left">所有阶段</td><td一个l我gn="center">3.3/2.0 (14)</td><td一个l我gn="center">1.2/0.4 (2.6)</td><td一个l我gn="center">0.9/0.5 (2.8)</td><td一个l我gn="center">1.0/0.5 (2.8)</td><td一个l我gn="center">0.9/0.5 (2.8)</td></tr><tr class="table-tr"> <td colspan="6"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表2</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/ijbi/2011/891585/tab2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> “实验结果:错误具有里程碑意义的地位。</d我v> </div> </div> <p>结果表明,所有注册大大提高强度的匹配。固定和变形之间的SSD图像相似Morphons, D-Demons, D-Morphons(见图<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig6/" target="_blank">6</一个>)。从这些注册字段的谐波能量产生的也比较(见图<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig6/" target="_blank">6</一个>)。</p><d我v class="floats-partial-section partial-carousel-wrapper" data-section="fig6"> <div class="floats-partial-content fig-content-fig6"> <div class="partial-carousel--single-image"> <img alt="(一)”n一个米e=”891585。f我g.006a" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.006a.jpg"> <br> <strong>(一)</年代tr在g></d我v> <div class="partial-carousel--single-image"> <img alt="(b)”n一个米e=”891585。f我g.006b" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.006b.jpg"> <br> <strong>(b)</年代tr在g></d我v> <div class="partial-carousel--single-image"> <img alt="(c)”n一个米e=”891585。f我g.006c" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.006c.jpg"> <br> <strong>(c)</年代tr在g></d我v> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig6"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)”n一个米e=”891585。f我g.006a" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.006a.jpg"><br><strong>(一)</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)”n一个米e=”891585。f我g.006b" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.006b.jpg"><br><strong>(b)</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(c)"><img alt="(c)”n一个米e=”891585。f我g.006c" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.006c.jpg"><br><strong>(c)</年代tr在g></button> </div> <div class="partial-carousel-next-prev fig-nav-fig6"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图6</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/ijbi/2011/891585/fig6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 结果9“的注册阶段模型。(a)箱线图的SSD之前登记(黄色)和毕竟4注册。(b)箱线图变形的能量毕竟4注册。(c)箱线图的雅可比矩阵的最小毕竟4注册。从(a)到(c),这些注册恶魔(浅蓝色),Morphons(浅绿色),diffeomorphic恶魔(深蓝色)和diffeomorphic Morphons(深绿色)。对于每个盒子,中心水平线代表了中值,从下四分位数的盒子上四分位数,和垂直线代表最极端值在1.5四分位范围。十字架代表异常值。</t一个ble> </div> </div> </div> <p>匹配和谐波能量得到恶魔(作者提出的<一个href=”#B4">4</一个>]“网站)是3好略低于其他方法。然而,这最有可能是由于注册使用的参数(例如,数量的尺度,平滑的方差,等等)。特别是,非常相似的图像(RCCT的前两阶段),该算法无法找到一个光滑的位移场,减少了SSD。</p><p>gydF4y2Ba最低可比传统方法造成的位移场下来<年代vg height="11.1" id="M383" style="vertical-align:-0.17555pt;width:30.362499px;" version="1.1" viewbox="0 0 30.362499 11.1" width="30.362499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.5645552" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.816055" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.941805" y="0"> 5</t年代p一个n></text> </g> </g> </svg>恶魔和Morphons(见图<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig6/" target="_blank">6</一个>),67年和460年分别压倒了相应的相位在移动应用领域时图像(由近6百万像素点)。然而,当使用diffeomorphic积累,恶魔的最低雅可比矩阵提高到0.2和0.1 Morphons,表明diffeomorphic积累一步阻止该领域反相压。</p><h5gydF4y2Baid="sec5.3">5.3。应用程序的图像胸腔有或没有Lodine对比剂</h5><p>gydF4y2Ba肿瘤的breathing-correlated运动是肺癌的一个典型特征是处理放射治疗计划。肿瘤RCCT图像提供的信息在整个呼吸周期运动。从不同的呼吸阶段,一个适当的利润率在肿瘤(ITV,即。,the我ntern一个l Target Volume) can be estimated, integrating thus all tumor positions through the respiratory cycle [<一个href=”#B20">20.</一个>]。</p><p>gydF4y2Ba然而,对比度增强的缺乏,以及高噪音水平和构件描述4 d RCCT的存在,可能显著影响准确界定目标卷上这些图片。更特别,碘对比剂至关重要,帮助在区分肿瘤血管结构的区段集中位于肺肿瘤。在这种背景下,传统的超声造影CT (CE-CT)期间获得免费呼吸应考虑描述任务,而4 d RCCT用于估计肿瘤在呼吸的运动范围。自动化这个过程,描述肿瘤体积CE-CT可以变形的各种呼吸期图像使用非刚性的登记终于从4 d RCCT ITV,如在图所示<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig7/" target="_blank">7</一个>。</p><d我v class="floats-partial-section partial-carousel-wrapper" data-section="fig7"> <div class="floats-partial-content fig-content-fig7"> <div class="partial-carousel--single-image"> <img alt="" name="891585.fig.007" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.007.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图7</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/ijbi/2011/891585/fig7/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> ITV的示意图表示创建(只有4阶段)。CTV划定的参考图像对比度增强(左边)变形对每一阶段(中)使用位移字段估计登记,和他们的联盟被认为是ITV(右边)。</t一个ble> </div> </div> </div> <p>这个实验的目的是比较恶魔和Morphons算法(常规和diffeomorphic版本)注册图像之间没有对比度增强,同时保持相同的设置为“实验。</p><p>gydF4y2BaCE-CT扫描3肺癌患者以及收购4 d RCCT扫描在另一个时间点。第一次CT扫描是在使用碘对比剂自由呼吸。4 d RCCT扫描没有任何收购造影剂和重建为10阶段。直方图均衡化是无法正确的本地化CE-CT和RCCT阶段对比差异图像。3例,恶魔,Morphons D-Demons,和D-Morphons之间的10个RCCT图像和CE-CT,相同的注册参数的“模拟。</p><p>gydF4y2Ba这些注册产生的位移场相比而言,谐波能量和最低雅可比矩阵(见图<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig8/" target="_blank">8</一个>)。由此产生的图像比较的SSD和互信息。</p><d我v class="floats-partial-section partial-carousel-wrapper" data-section="fig8"> <div class="floats-partial-content fig-content-fig8"> <div class="partial-carousel--single-image"> <img alt="(一)”n一个米e=”891585。f我g.008a" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.008a.jpg"> <br> <strong>(一)</年代tr在g></d我v> <div class="partial-carousel--single-image"> <img alt="(b)”n一个米e=”891585。f我g.008b" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.008b.jpg"> <br> <strong>(b)</年代tr在g></d我v> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig8"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)”n一个米e=”891585。f我g.008a" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.008a.jpg"><br><strong>(一)</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)”n一个米e=”891585。f我g.008b" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.008b.jpg"><br><strong>(b)</年代tr在g></button> </div> <div class="partial-carousel-next-prev fig-nav-fig8"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图8</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/ijbi/2011/891585/fig8/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 结果变量对比实验阶段30日10个阶段每个患者(3)。(一)箱线图变形的能量毕竟4注册。(b)箱线图的雅可比矩阵的最小毕竟4注册。从(a) (b),这些注册恶魔(浅蓝色),Morphons(浅绿色),diffeomorphic恶魔(深蓝色)和diffeomorphic Morphons(深绿色)。对于每个盒子,中心水平线代表了中值,从下四分位数的盒子上四分位数,和垂直线代表最极端值在1.5内部四分位范围。十字架代表异常值。</t一个ble> </div> </div> </div> <p>恶魔的谐波能量产生的位移场和D-Demons很高于Morphons D-Morphons,和雅可比矩阵的最小位移场是积极注册使用diffeomorphic积累。压在最坏的情况下,7455年和1114年分别反向使用恶魔和Morphons diffeomorphic积累(5大型压)的形象。区域导致糟糕的转换的一个例子使用传统的方法(使用-雅克比)是描绘在图<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig9/" target="_blank">9</一个>。D-Morphons导致最顺利转换,用最小的雅可比矩阵值约为0.2。然而,这些值很低很零星的图像内的体积。</p><d我v class="floats-partial-section partial-carousel-wrapper" data-section="fig9"> <div class="floats-partial-content fig-content-fig9"> <div class="partial-carousel--single-image"> <img alt="" name="891585.fig.009" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.009.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图9</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/ijbi/2011/891585/fig9/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 说明造成负面的雅克比nondiffeomorphic注册。左:移动和固定的图像。右:字段造成注册(红色箭头)及其雅可比矩阵(灰度图像)。消极的雅克比用黄色区域是波状外形的。</t一个ble> </div> </div> </div> <p>我们注意到,与“模拟的结果不同,产生的SSD Morphons和D-Morphons有点高于恶魔和D-Demons所带来的SSD。然而,如下图的例子<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig4/" target="_blank">4</一个>,SSD并不反映出变量的匹配对比区域。另一方面,无显著差异的图像之间的互信息观察造成不同的注册。这可能是由于非常低的对比在相应区域内的41图像对比度增强组织的其他形象而位移场方面的主要区别是位于这些区域,如图<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig10/" target="_blank">10</一个>。</p><d我v class="floats-partial-section partial-carousel-wrapper" data-section="fig10"> <div class="floats-partial-content fig-content-fig10"> <div class="partial-carousel--single-image"> <img alt="(一)”n一个米e=”891585。f我g.0010a" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.0010a.jpg"> <br> <strong>(一)</年代tr在g></d我v> <div class="partial-carousel--single-image"> <img alt="(b)”n一个米e=”891585。f我g.0010b" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.0010b.jpg"> <br> <strong>(b)</年代tr在g></d我v> <div class="partial-carousel--single-image"> <img alt="(c)”n一个米e=”891585。f我g.0010c" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.0010c.jpg"> <br> <strong>(c)</年代tr在g></d我v> <div class="partial-carousel--single-image"> <img alt="(d)”n一个米e=”891585。f我g.0010d" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.0010d.jpg"> <br> <strong>(d)</年代tr在g></d我v> <div class="partial-carousel--single-image"> <img alt="(e)”n一个米e=”891585。f我g.0010e" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.0010e.jpg"> <br> <strong>(e)</年代tr在g></d我v> <div class="partial-carousel--single-image"> <img alt="(f)”n一个米e=”891585。f我g.0010f" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.0010f.jpg"> <br> <strong>(f)</年代tr在g></d我v> <div class="partial-carousel--single-image"> <img alt="(g)”n一个米e=”891585。f我g.0010g" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.0010g.jpg"> <br> <strong>(g)</年代tr在g></d我v> <div class="partial-carousel--single-image"> <img alt="(h)”n一个米e=”891585。f我g.0010h" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.0010h.jpg"> <br> <strong>(h)</年代tr在g></d我v> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig10"> <button class="partial-carousel-dot" aria-label="(a)"><img alt="(一)”n一个米e=”891585。f我g.0010a" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.0010a.jpg"><br><strong>(一)</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(b)"><img alt="(b)”n一个米e=”891585。f我g.0010b" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.0010b.jpg"><br><strong>(b)</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(c)"><img alt="(c)”n一个米e=”891585。f我g.0010c" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.0010c.jpg"><br><strong>(c)</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(d)"><img alt="(d)”n一个米e=”891585。f我g.0010d" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.0010d.jpg"><br><strong>(d)</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(e)"><img alt="(e)”n一个米e=”891585。f我g.0010e" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.0010e.jpg"><br><strong>(e)</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(f)"><img alt="(f)”n一个米e=”891585。f我g.0010f" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.0010f.jpg"><br><strong>(f)</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(g)"><img alt="(g)”n一个米e=”891585。f我g.0010g" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.0010g.jpg"><br><strong>(g)</年代tr在g></button> <button class="partial-carousel-dot" aria-label="(h)"><img alt="(h)”n一个米e=”891585。f我g.0010h" src="https://static-01.hindawi.com/articles/ijbi/volume-2011/891585/figures/891585.fig.0010h.jpg"><br><strong>(h)</年代tr在g></button> </div> <div class="partial-carousel-next-prev fig-nav-fig10"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图10</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/ijbi/2011/891585/fig10/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 对比实验说明结果的变量。(a)和(b):固定图像(左)和移动图像(右)。(c)和(d):变形图像变形轮廓和位移场造成D-Demons(左)和从D-Morphons(右)。(e)和(f):两个注册产生的位移场的雅可比矩阵,使用相同的颜色来表示。(g)和(h):谐波产生的位移场的能量都注册,使用相同的颜色来表示。</t一个ble> </div> </div> </div> <p>为了说明注册对比度增强组织的影响,一个阶段的RCCT扫描的3例被选为例。对这个病人,肿瘤是靠近对比组织。肿瘤和血管被医生描述,对比增强扫描和RCCT扫描的一个阶段。阶段上的描绘图像变形根据产生的领域不同注册。结果见图<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig10/" target="_blank">10</一个>。</p><p>gydF4y2Ba由于扭曲是计算体积的变化,以及谐波能量在划定汉斯和肿瘤的质心之间的区别有或没有注册。</p><p>gydF4y2Ba体积的变化非常小在使用分阶段场计算船舶(约0%)和肿瘤品(约1%),而血管和23%上升到6%的肿瘤在使用恶魔。同样,谐波能量和错误的质心肿瘤为分阶段登记方法小得多。这些结果总结表<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/tab3/" target="_blank">3</一个>。人能注意到diffeomorphic Morphons积累的字段并没有改变结果的谐波能量和体积变化相比传统Morphons。这是由于这样的事实,认为器官的位移很小,光滑。</p><d我v class="floats-partial-section partial-other-wrapper" data-section="tab3"> <div class="floats-partial-content fig-content-tab3"> <table class="table-group" id="tab3"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="6"> <hr></td> </tr> <tr class="thead"> <td align="left"></td> <td align="center">原始</td><td一个l我gn="center">恶魔</td><td一个l我gn="center">Morphons</td><td一个l我gn="center">D-Demons</td><td一个l我gn="center">D-Morphons</td></tr><tr> <td class="thead-hr" colspan="6"> <hr></td> </tr> <tr> <td align="left">体积变化(血管)(%)</td><td一个l我gn="center"></td> <td align="center">23</td><td一个l我gn="center">0</td><td一个l我gn="center">21</td><td一个l我gn="center">0</td></tr><tr> <td align="left">体积变化(肿瘤)(%)</td><td一个l我gn="center"></td> <td align="center">6</td><td一个l我gn="center">1</td><td一个l我gn="center">6</td><td一个l我gn="center">1</td></tr><tr> <td align="left">谐波能量(血管)<年代vg height="14.375" id="M384" style="vertical-align:-0.3135pt" version="1.1" viewbox="0 0 39.337502 14.375" width="39.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0019197" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.25342" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-51.45,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 3</t年代p一个n></text> </g> </g> </svg>]</td><td一个l我gn="center"></td> <td align="center">89年</td><td一个l我gn="center">8</td><td一个l我gn="center">69年</td><td一个l我gn="center">8</td></tr><tr> <td align="left">谐波能量(肿瘤)<年代vg height="14.375" id="M385" style="vertical-align:-0.3135pt" version="1.1" viewbox="0 0 39.337502 14.375" width="39.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0019197" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.25342" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-51.45,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 3</t年代p一个n></text> </g> </g> </svg>]</td><td一个l我gn="center"></td> <td align="center">39</td><td一个l我gn="center">4</td><td一个l我gn="center">34</td><td一个l我gn="center">4</td></tr><tr> <td align="left">在COM(肿瘤)(在错误<年代vg height="7.3125" id="M386" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 24.4375 7.3125" width="24.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.3125)"> <g transform="translate(72,-66.15)"> <text transform="matrix(1,0,0,-1,-71.95,66.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.727334" y="0"> 米</t年代p一个n></text> </g> </g> </svg>]</td><td一个l我gn="center">2.1</td><td一个l我gn="center">1。5</td><td一个l我gn="center">1。1</td><td一个l我gn="center">1。5</td><td一个l我gn="center">1。1</td></tr><tr class="table-tr"> <td colspan="6"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表3</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/ijbi/2011/891585/tab3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 比较的体积变化,谐波能量,和错误的质心之间的血管和肿瘤在一个阶段。</d我v> </div> </div> <h4 id="discussion">6。讨论</h4><p>gydF4y2Ba第一医学实验表明D-Morphons D-Demons导致相似匹配的图像强度和解剖标志。这表明monomodal登记的肺部CT扫描,相位差的效率与SSD的效率指标。此外,D-Morphons产生位移场可以同D-Demons一样光滑。反对传统的恶魔和Morphons diffeomporphic方法产生可逆的位移场的物理意义。</p><p>gydF4y2Ba注册第二医学实验说明了限制级别不同的图像对比度增强的恶魔的方法。事实上,造成强度匹配恶魔从Morphons比这更好,但显然是错误的,作为恶魔的结果在全球对比组织的萎缩(动脉),并不能反映一个适当的解剖的行为,但这是由于恶魔登记是基于最小化的SSD,产生一个广义位移估计的强度相同的组织是不同的固定和移动图像。注册的解剖结构之间的不匹配图上清晰可见<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig10/" target="_blank">10</一个>。如下图的例子<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig4/" target="_blank">4</一个>,恶魔试图产生的场匹配相同的结构强度,不对应于相同的解剖结构,因为对比剂浓度的差异。因此,该领域带来恶魔(见图左边的领域的一部分<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig10/" target="_blank">10</一个>)光滑远低于它应该和可能导致错误的变形估计示例(见表所示<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/tab3/" target="_blank">3</一个>)。在这种情况下,强度图像之间的差异和不对比度增强导致重要的血管和肿瘤体积变化通过使用恶魔或D-Demons,而几乎没有体积的变化被观察到这些组织在使用分阶段方法。除此之外,这些组织内的谐波能量显示字段是使用分阶段注册更光滑。重要的是要注意,这些影响主要是有限的正规化位移场在恶魔和D-Demons注册,他们仍将是更糟糕的是如果使用更少的正规化(较小的方差的高斯内核用于平滑位移场)。情况不是这样的字段由Morphons和diffeomorphic Morphons,更为顺畅和保持解剖拓扑即使对比差异图像(见图<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/fig10/" target="_blank">10</一个>)。注意减少最小的细分,可以观察到在Morphons结果主要是由于interslices运动,所确认的雅可比矩阵这个地区接近1,表明没有重要的体积变化在这个分割区域。最后,一个可以看到可逆性位移场的观察与diffeomorphic注册。</p><p>gydF4y2Ba这些结果可以总结为分类不同的注册策略根据平滑(谐波能量)和可逆性(最低雅可比矩阵)的位移(见表字段<一个href=”http年代://www.newsama.com/journals/ijbi/2011/891585/tab4/" target="_blank">4</一个>)为变量的对比实验。</p><d我v class="floats-partial-section partial-other-wrapper" data-section="tab4"> <div class="floats-partial-content fig-content-tab4"> <table class="table-group" id="tab4"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="3"> <hr></td> </tr> <tr class="thead"> <td align="left"></td> <td align="center">低谐波能量</td><td一个l我gn="center">高谐波能量</td></tr><tr> <td class="thead-hr" colspan="3"> <hr></td> </tr> <tr> <td align="left">可逆的(<年代vg height="14.6" id="M387" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 57.0625 14.6" width="57.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.2,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.8090558" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.2421122" y="0"> n</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.69,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n></text> </g> </g> </svg>)</td><td一个l我gn="center">D-Morphons</td><td一个l我gn="center">D-Demons</td></tr><tr> <td align="left">不可逆转(<年代vg height="14.6" id="M388" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 57.0625 14.6" width="57.0625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.2,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.8090558" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.2421122" y="0"> n</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.69,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n></text> </g> </g> </svg>)</td><td一个l我gn="center">Morphons</td><td一个l我gn="center">恶魔</td></tr><tr class="table-tr"> <td colspan="3"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表4</年代p一个n><一个一个r我一个-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/ijbi/2011/891585/tab4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 注册分类变量对比度增强算法。</d我v> </div> </div> <p>人能注意到D-Morphons算法结合优势:是可逆的和光滑的,这表明它可能是一个更好的估计是光滑的真正转变。</p><h4gydF4y2Baid="conclusion">7所示。结论</h4><p>DgydF4y2Ba-Morphons是注册多分辨率算法计算一个diffeomorphic基于最小化位移场的局部强度阶段。管理的方法来估计呼吸胸腔变形,具有准确度D-Demons的准确性,并导致相同的可逆性的必需的属性字段。此外,D-Morphons设法准确地估计图像之间的变形与变量的对比,而常规SSD-based方法导致错位的解剖结构对比变化的影响。</p><h4我d=”一个cknowledgments">确认</h4><p>gydF4y2Ba作者感谢林雪平大学医学信息学实验室Morphons分享他们的实现。和j·g·詹森o . de Xivry由一个FRIA格兰特。l·雅克是一个比利时FRS-FNRS资助的博士后研究员。</p></d我v> <div class="xml-content"> <h4 class="references" id="references">引用</h4><ol><l我我d="B1">j·b·A . 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Borga" target="_blank">谷歌学术搜索</一个></年代p一个n></li> </ol> </div> <div class="xml-content"> <h4 class="copyright" id="copyright">版权</h4><p>gydF4y2Ba版权©2011 Guillaume詹森等。这是一个开放访问分布在条<一个rel=”l我cen年代e”href="http://creativecommons.org/licenses/by/3.0/">知识共享归属许可</一个>,它允许无限制的使用、分配和复制在任何媒介,提供最初的工作是正确引用。</p></d我v> </div> </article> </div> </div> </div> <div class="biblio__Wrapper-sc-1nou1lz-0 eyHfWh journal_article__BiblioIntegratorWidget-sc-12fk6zy-5 dbAANp article_widget biblioWrapper hide"> <hr> <h4 class="biblio__H4-sc-1nou1lz-2 kgAKHb hrTitleRef">更多相关文章</h4><d我v id="biblio_widget" class="biblio__BiblioWrapper-sc-1nou1lz-1 dDdJpQ"></div> </div> </div> </div> <div class="threeColumn__RightWrapper-sc-1bf4078-2 jzTMLK rightWrapper" id="rightSectionMenu"> <div> <div class="journal_article__ArticleStickyTopToolbar-sc-12fk6zy-0 gbrQxi article_sticky_top_toolbar"> <div class="sc-eTpRJs DEpmD article_top_toolbar"> <div class="sc-dxZgTM bNaYih article_toolbar_views"> 2254年<gydF4y2Ba!-- --> 的观点<gydF4y2Ba!-- -->|<gydF4y2Ba!-- --> 857年<gydF4y2Ba!-- --> 下载<gydF4y2Ba!-- --> |<gydF4y2Ba!-- -->47<gydF4y2Ba!-- --> 引用</d我v> <a class="sc-htpNat bUhGXt link sc-bnXvFD hgeknQ sc-iomxrj fOYLEe pdf_desktop button__group" href="//www.newsama.com/downloads/journals/ijbi/2011/891585.pdf" aria-label="" target="_blank" id="toolbar__dcNavSmall"><span><img alt="" class="sc-EHOje jOLhQl sc-gFaPwZ fzHUvS" title="" role="presentation" src="https://static-01.hindawi.com/next_assets/dMW3d4HZTf9_66ywKW4Jh/_next/static/node_modules/hindawi-ui/src/icon/svg/pdf.svg" height="24"><span class="text">PDF</年代p一个n></年代p一个n><span class="sc-htoDjs bqeMOy sc-fhYwyz iBoHeM fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> <a class="sc-htpNat bUhGXt link sc-bnXvFD hgeknQ sc-dvCyap hTIXhE ref_desktop" href="//www.newsama.com/journals/ijbi/2011/891585.ris" aria-label="" target="" id="toolbar__dcNavLarge"><span><img alt="" class="sc-EHOje jOLhQl sc-gFaPwZ fzHUvS" 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src="data:image/svg+xml;base64,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" height="24"><span class="text">下载引用</年代p一个n></年代p一个n><span class="sc-htoDjs bqeMOy sc-fhYwyz iBoHeM fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> <a class="sc-htpNat bUhGXt link sc-bnXvFD hgeknQ sc-iFMziU bGHCWJ ref_desktop" href="//www.newsama.com/journals/ijbi/2011/891585.ris" aria-label="" target="" id="toolbar__dcNavSmall"><span><img alt="" class="sc-EHOje jOLhQl sc-gFaPwZ fzHUvS" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="text">引用</年代p一个n></年代p一个n><span class="sc-htoDjs bqeMOy sc-fhYwyz iBoHeM fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> </div> </div> <div class="journal_article__ArticleStickyBottomToolbar-sc-12fk6zy-1 isgRZA article_sticky_bottom_toolbar"> <div class="sc-cBdUnI dwpJFe article_bottom_toolbar"> <div class="sc-exkUMo lkBlhM accordion" property="background-color" color="#D8D8D8" id="toolbar__dofNav"> <span><img alt="" class="sc-EHOje jOLhQl sc-cqpYsc kDQNGn" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="sc-dyGzUR jTZjyd">下载其他格式</年代p一个n><年代p一个ncl一个年代s="sc-drKuOJ fgdSqC">更多的</年代p一个n></年代p一个n> <span class="sc-htoDjs bMdQcY sc-hBbWxd eeglal icon-colored _1CwL9R82TPl2HxDleeYGDR icon-themeable" title="" font-size="11"></span> </div> <div class="sc-kcDeIU lkBwlY"> <a class="sc-htpNat bUhGXt link sc-BngTV jWvDXH open_panel" href="//www.newsama.com/downloads/journals/ijbi/2011/891585.xml" aria-label="XML" property="background-color" color="#D8D8D8"> <div class="sc-bFADNz dBLFTk"> XML</d我v><img alt="" class="sc-EHOje jOLhQl sc-cqpYsc kDQNGn" title="" role="presentation" src="data:image/svg+xml;base64,PD94bWwgdmVyc2lvbj0iMS4wIiBlbmNvZGluZz0iVVRGLTgiPz4KPHN2ZyB3aWR0aD0iMjBweCIgaGVpZ2h0PSIyMnB4IiB2aWV3Qm94PSIwIDAgMjAgMjIiIHZlcnNpb249IjEuMSIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIiB4bWxuczp4bGluaz0iaHR0cDovL3d3dy53My5vcmcvMTk5OS94bGluayI+CiAgICA8IS0tIEdlbmVyYXRvcjogU2tldGNoIDUzLjIgKDcyNjQzKSAtIGh0dHBzOi8vc2tldGNoYXBwLmNvbSAtLT4KICAgIDx0aXRsZT5jaGV2cm9uLWRvd24gY29weSAzPC90aXRsZT4KICAgIDxkZXNjPkNyZWF0ZWQgd2l0aCBTa2V0Y2guPC9kZXNjPgogICAgPGRlZnM+CiAgICAgICAgPHBhdGggZD0iTTExLDEzLjU4NTc4NjQgTDExLDIgQzExLDEuNDQ3NzE1MjUgMTEuNDQ3NzE1MywxIDEyLDEgQzEyLjU1MjI4NDcsMSAxMywxLjQ0NzcxNTI1IDEzLDIgTDEzLDEzLjU4NTc4NjQgTDE1LjI5Mjg5MzIsMTEuMjkyODkzMiBDMTUuNjgzNDE3NSwxMC45MDIzNjg5IDE2LjMxNjU4MjUsMTAuOTAyMzY4OSAxNi43MDcxMDY4LDExLjI5Mjg5MzIgQzE3LjA5NzYzMTEsMTEuNjgzNDE3NSAxNy4wOTc2MzExLDEyLjMxNjU4MjUgMTYuNzA3MTA2OCwxMi43MDcxMDY4IEwxMi43MDcxMDY4LDE2LjcwNzEwNjggQzEyLjMxNjU4MjUsMTcuMDk3NjMxMSAxMS42ODM0MTc1LDE3LjA5NzYzMTEgMTEuMjkyODkzMiwxNi43MDcxMDY4IEw3LjI5Mjg5MzIyLDEyLjcwNzEwNjggQzYuOTAyMzY4OTMsMTIuMzE2NTgyNSA2LjkwMjM2ODkzLDExLjY4MzQxNzUgNy4yOTI4OTMyMiwxMS4yOTI4OTMyIEM3LjY4MzQxNzUxLDEwLjkwMjM2ODkgOC4zMTY1ODI0OSwxMC45MDIzNjg5IDguNzA3MTA2NzgsMTEuMjkyODkzMiBMMTEsMTMuNTg1Nzg2NCBaIE0yLDE3IEMyLDE2LjQ0NzcxNTMgMi40NDc3MTUyNSwxNiAzLDE2IEMzLjU1MjI4NDc1LDE2IDQsMTYuNDQ3NzE1MyA0LDE3IEw0LDIwIEM0LDIwLjU1MjI4NDcgNC40NDc3MTUyNSwyMSA1LDIxIEwxOSwyMSBDMTkuNTUyMjg0NywyMSAyMCwyMC41NTIyODQ3IDIwLDIwIEwyMCwxNyBDMjAsMTYuNDQ3NzE1MyAyMC40NDc3MTUzLDE2IDIxLDE2IEMyMS41NTIyODQ3LDE2IDIyLDE2LjQ0NzcxNTMgMjIsMTcgTDIyLDIwIEMyMiwyMS42NTY4NTQyIDIwLjY1Njg1NDIsMjMgMTksMjMgTDUsMjMgQzMuMzQzMTQ1NzUsMjMgMiwyMS42NTY4NTQyIDIsMjAgTDIsMTcgWiIgaWQ9InBhdGgtMSI+PC9wYXRoPgogICAgPC9kZWZzPgogICAgPGcgaWQ9IlN5bWJvbHMiIHN0cm9rZT0ibm9uZSIgc3Ryb2tlLXdpZHRoPSIxIiBmaWxsPSJub25lIiBmaWxsLXJ1bGU9ImV2ZW5vZGQiPgogICAgICAgIDxnIGlkPSJTaWRlYmFycy9EZXNrdG9wL0FydGljbGUtU2lkZWJhciIgdHJhbnNmb3JtPSJ0cmFuc2xhdGUoLTI5MS4wMDAwMDAsIC0xMzQuMDAwMDAwKSI+CiAgICAgICAgICAgIDxnIGlkPSJEb3dubG9hZC1yZWZlcmVuY2UiIHRyYW5zZm9ybT0idHJhbnNsYXRlKDAuMDAwMDAwLCAxMTIuMDAwMDAwKSI+CiAgICAgICAgICAgICAgICA8ZyBpZD0iVHlwZS1hbmQtaWNvbnMiIHRyYW5zZm9ybT0idHJhbnNsYXRlKDIwLjAwMDAwMCwgMjEuMDAwMDAwKSI+CiAgICAgICAgICAgICAgICAgICAgPGcgaWQ9Ikljb25zL0Rvd25sb2FkIiB0cmFuc2Zvcm09InRyYW5zbGF0ZSgyNjkuMDAwMDAwLCAwLjAwMDAwMCkiPgogICAgICAgICAgICAgICAgICAgICAgICA8ZyBpZD0iZG93bmxvYWQiPgogICAgICAgICAgICAgICAgICAgICAgICAgICAgPG1hc2sgaWQ9Im1hc2stMiIgZmlsbD0id2hpdGUiPgogICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgIDx1c2UgeGxpbms6aHJlZj0iI3BhdGgtMSI+PC91c2U+CiAgICAgICAgICAgICAgICAgICAgICAgICAgICA8L21hc2s+CiAgICAgICAgICAgICAgICAgICAgICAgICAgICA8dXNlIGlkPSJDb21iaW5lZC1TaGFwZSIgZmlsbD0iIzAwMDAwMCIgZmlsbC1ydWxlPSJub256ZXJvIiB4bGluazpocmVmPSIjcGF0aC0xIj48L3VzZT4KICAgICAgICAgICAgICAgICAgICAgICAgICAgIDxnIGlkPSJDT0xPUi8tUHJpbWFyeS1HcmVlbiIgbWFzaz0idXJsKCNtYXNrLTIpIiBmaWxsPSIjNkJBNDM5IiBmaWxsLXJ1bGU9ImV2ZW5vZGQiPgogICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgIDxyZWN0IGlkPSJSZWN0YW5nbGUiIHg9IjAiIHk9IjAiIHdpZHRoPSIyNCIgaGVpZ2h0PSIyNCI+PC9yZWN0PgogICAgICAgICAgICAgICAgICAgICAgICAgICAgPC9nPgogICAgICAgICAgICAgICAgICAgICAgICA8L2c+CiAgICAgICAgICAgICAgICAgICAgPC9nPgogICAgICAgICAgICAgICAgPC9nPgogICAgICAgICAgICA8L2c+CiAgICAgICAgPC9nPgogICAgPC9nPgo8L3N2Zz4=" 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