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<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/625d92c892dc900e627b2cb9/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/625d92c892dc900e627b2cb9/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">医学图像分割方法综述 </div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls1 ws0">林瑶，田捷</div><div class="t m0 x3 h4 y3 ff1 fs2 fc0 sc0 ls2 ws0">1</div><div class="t m0 x4 h5 y4 ff1 fs3 fc0 sc1 ls2 ws0">北京<span class="ff2">,</span>中国科学院自动化研究所人工智能实验室<span class="ff2 ls3">,100080 </span></div><div class="t m0 x5 h5 y5 ff1 fs3 fc0 sc0 ls2 ws0">摘要<span class="ff2 sc1 ls4">: <span class="_"> </span></span><span class="sc1">图像分割是一个经典难题，<span class="_ _0"></span>随着影像医学的发展，<span class="_ _0"></span>图像分割在医学应用中具有特</span></div><div class="t m0 x5 h5 y6 ff1 fs3 fc0 sc1 ls5 ws0">殊的重要意义。本文从<span class="_ _1"></span>医学应用的角度出发，<span class="_ _1"></span>对医学图像分割方法，<span class="_ _1"></span>特别是近几年来</div><div class="t m0 x5 h5 y7 ff1 fs3 fc0 sc1 ls5 ws0">图像分割领域中出现的<span class="_ _1"></span>新思路、新方法或对原<span class="_ _1"></span>有方法的新的改进给出<span class="_ _1"></span>了一个比较全面</div><div class="t m0 x5 h5 y8 ff1 fs3 fc0 sc1 ls2 ws0">的综述，最后总结了医学图像分割方法的研究特点。<span class="ff2"> </span></div><div class="t m0 x6 h5 y9 ff2 fs3 fc0 sc1 ls6 ws0"> <span class="ff1 ls2">关键词：医学图像分割</span> <span class="ff1 ls2">综述</span> </div><div class="t m0 x6 h6 ya ff2 fs3 fc0 sc1 ls2 ws0"> </div><div class="t m0 x6 h6 yb ff2 fs3 fc0 sc1 ls2 ws0"> </div><div class="t m0 x7 h7 yc ff3 fs1 fc0 sc1 ls2 ws0">1<span class="ff1 sc0 ls1">．背景介绍</span> </div><div class="t m0 x8 h5 yd ff1 fs3 fc0 sc1 ls7 ws0">医学图像包括<span class="_ _2"> </span><span class="ff2 ls8">CT</span><span class="ls5">、正电子放射<span class="_ _1"></span>层析成像技术（<span class="ff2 ls9">PET<span class="_ _1"></span></span><span class="ls2">）<span class="_ _3"></span><span class="ls5">、单光子辐射断层摄像<span class="_ _1"></span>（<span class="ff2 ls2">SPECT<span class="ff1">）<span class="_ _3"></span>、</span></span></span></span></span></div><div class="t m0 x6 h5 ye ff2 fs3 fc0 sc1 lsa ws0">MRI<span class="ff1 ls2">（磁共振成像技术）<span class="_ _3"></span>、<span class="ff2 lsb">Ultrasou<span class="_ _4"></span>nd<span class="ff1 ls2">（超声）及其它医学影像设备所获得的图像。随着影像医</span></span></span></div><div class="t m0 x6 h5 yf ff1 fs3 fc0 sc1 ls2 ws0">学在临床医学的成功应用，<span class="_ _5"></span>图像分割在影像医学中发挥着越来越大的作用<span class="ff2 lsc">[1]</span>。<span class="_ _5"></span>图像分割是提取</div><div class="t m0 x6 h5 y10 ff1 fs3 fc0 sc1 lsd ws0">影像图像中特殊组织的定量信息的不可缺少的<span class="_ _4"></span>手段，同时也是可视化实现的预处理步骤和前</div><div class="t m0 x6 h5 y11 ff1 fs3 fc0 sc1 ls2 ws0">提。<span class="_ _5"></span>分割后的图像正被广泛应用于各种场合，<span class="_ _5"></span>如组织容积的定量分析，<span class="_ _5"></span>诊断，<span class="_ _6"></span>病变组织的定位，</div><div class="t m0 x6 h5 y12 ff1 fs3 fc0 sc1 ls2 ws0">解剖结构的学习，治疗规划，功能成像数据的局部体效应校正和计算机指导手术<span class="ff2 lse">[2]</span>。<span class="ff2"> </span></div><div class="t m0 x8 h5 y13 ff1 fs3 fc0 sc1 lsd ws0">所谓图像分割是指将图像中具有特殊涵义的不同区域区分开来，这些区域是互相不交叉</div><div class="t m0 x6 h5 y14 ff1 fs3 fc0 sc1 ls2 ws0">的，每一个区域都满足特定区域的一致性。<span class="ff2"> </span></div><div class="t m0 x8 h8 y15 ff1 fs3 fc0 sc0 ls2 ws0">定义<span class="ff3 sc1"> <span class="_"> </span><span class="ff1">将一幅图像<span class="_ _7"> </span><span class="lsf">，其<span class="_ _8"> </span>中</span></span></span></div><div class="t m0 x4 h9 y16 ff4 fs4 fc0 sc1 ls10 ws0">gxy<span class="_ _9"></span><span class="ff2 ls11">(,<span class="_ _a"></span>)<span class="_ _b"> </span><span class="ls2">0</span></span></div><div class="c x9 y17 w2 ha"><div class="t m0 x0 hb y18 ff5 fs4 fc0 sc1 ls2 ws0">≤</div></div><div class="c xa y17 w2 ha"><div class="t m0 x0 hb y18 ff5 fs4 fc0 sc1 ls2 ws0">≤</div></div><div class="t m0 xb h9 y16 ff4 fs4 fc0 sc1 ls12 ws0">xM<span class="_ _c"></span>a<span class="_ _c"></span>x<span class="_ _d"></span>x<span class="_ _e"></span><span class="ff2 ls2">_</span></div><div class="t m0 xc h6 y15 ff2 fs3 fc0 sc1 ls2 ws0">,</div><div class="t m0 xd hc y16 ff2 fs4 fc0 sc1 ls2 ws0">0</div><div class="c xe y17 w2 ha"><div class="t m0 x0 hb y18 ff5 fs4 fc0 sc1 ls2 ws0">≤</div></div><div class="c xf y17 w2 ha"><div class="t m0 x0 hb y18 ff5 fs4 fc0 sc1 ls2 ws0">≤</div></div><div class="t m0 x10 h9 y16 ff4 fs4 fc0 sc1 ls12 ws0">yM<span class="_ _c"></span>a<span class="_ _c"></span>x<span class="_ _d"></span>y<span class="_ _e"></span><span class="ff2 ls2">_</span></div><div class="t m0 x11 h5 y15 ff1 fs3 fc0 sc1 ls2 ws0">，<span class="_ _6"></span>进行分割就是将图像划分为</div><div class="t m0 x6 h5 y19 ff1 fs3 fc0 sc1 ls2 ws0">满足如下条件的子区域<span class="_ _f"> </span><span class="ff2 ls13">...</span>：<span class="ff2"> </span></div><div class="t m0 x12 hd y1a ff4 fs5 fc0 sc1 ls2 ws0">g</div><div class="t m0 x13 he y1b ff2 fs6 fc0 sc1 ls2 ws0">1</div><div class="t m0 x14 hd y1a ff4 fs5 fc0 sc1 ls2 ws0">g</div><div class="t m0 x15 he y1b ff2 fs6 fc0 sc1 ls2 ws0">2</div><div class="t m0 x16 hd y1a ff4 fs5 fc0 sc1 ls2 ws0">g</div><div class="t m0 x17 he y1b ff2 fs6 fc0 sc1 ls2 ws0">3</div><div class="t m0 x6 h5 y1c ff2 fs3 fc0 sc1 ls6 ws0"> (<span class="_ _10"></span>a<span class="_ _10"></span>)<span class="_ _10"></span> <span class="_ _4"></span> <span class="ff1 ls2">，即所有子区域组成了整幅图像。<span class="ff2"> </span></span></div><div class="t m0 x6 h5 y1d ff2 fs3 fc0 sc1 ls14 ws1"> (b) <span class="_ _11"> </span><span class="ff1 ls2 ws0">是连通的区域。<span class="ff2"> </span></span></div><div class="t m0 x18 hd y1e ff4 fs5 fc0 sc1 ls2 ws0">g</div><div class="t m0 x19 hf y1f ff4 fs6 fc0 sc1 ls2 ws0">k</div><div class="t m0 x6 h5 y20 ff2 fs3 fc0 sc1 ls6 ws0"> (<span class="_ _10"></span>c<span class="_ _10"></span>)<span class="_ _10"></span> <span class="_ _4"></span> <span class="ff1 ls2">，即任意两个子区域不存在公共元素。<span class="ff2"> </span></span></div><div class="t m0 x1a h5 y21 ff2 fs3 fc0 sc1 ls14 ws0">(d) <span class="_"> </span><span class="ff1 ls2">区域<span class="_ _11"> </span>满足一定的均一性条件。<span class="_ _12"></span>均一性<span class="_ _12"></span>（或相似性）<span class="_ _13"></span>一般指同一区域内的像素点之间</span></div><div class="t m0 x6 h5 y22 ff1 fs3 fc0 sc1 ls2 ws0">的灰度值差异较小或灰度值的变化较缓慢。<span class="ff2"> </span></div><div class="t m0 x1b hd y23 ff4 fs5 fc0 sc1 ls2 ws0">g</div><div class="t m0 x1c hf y24 ff4 fs6 fc0 sc1 ls2 ws0">k</div><div class="t m0 x1a h5 y25 ff1 fs3 fc0 sc1 ls15 ws0">如果连通性的约束被取消，那么对像素集的划分就称为分类（pixel classi<span class="ls16">fication），</span></div><div class="t m0 x6 h5 y26 ff1 fs3 fc0 sc1 ls7 ws0">每一个像素集称为类（c<span class="_ _4"></span>la<span class="_ _4"></span>ss）。在下面的叙述<span class="_ _4"></span>中，为了简单，我们将经典的分<span class="_ _4"></span>割和像素分类</div><div class="t m0 x6 h5 y27 ff1 fs3 fc0 sc1 ls2 ws0">通称为分割。<span class="ff2"> </span></div><div class="t m0 x8 h5 y28 ff1 fs3 fc0 sc1 ls2 ws0">医学图像分割到今天仍然没有获得解决，一个重要的原因是医学图像的复杂性和多样性。</div><div class="t m0 x6 h5 y29 ff1 fs3 fc0 sc1 ls2 ws0">由于医学图像的成像原理和组织本身的特性差异，<span class="_ _12"></span>图像的形成受到诸如噪音、<span class="_ _4"></span>场偏移效应、<span class="_ _12"></span>局</div><div class="t m0 x6 h5 y2a ff1 fs3 fc0 sc1 ls2 ws0">部体效应和组织运动等的影响，<span class="_ _12"></span>医学图像与普通图像比较，<span class="_ _4"></span>不可避免的具有模糊、<span class="_ _12"></span>不均匀性等</div><div class="t m0 x6 h5 y2b ff1 fs3 fc0 sc1 ls2 ws0">特点。<span class="_ _4"></span>另外，<span class="_ _4"></span>人体的解剖组织结构和形状复杂，<span class="_ _12"></span>而且人与人之间有相当大的差别。这些都给医</div><div class="t m0 x6 h5 y2c ff1 fs3 fc0 sc1 ls2 ws0">学图像分割的分割带来了困难。<span class="_ _14"></span>传统的分割技术或者完全失败，<span class="_ _14"></span>或者需要一些特殊的处理技术。</div><div class="t m0 x6 h5 y2d ff1 fs3 fc0 sc1 ls2 ws0">因此，我们有必要针对医学应用这个领域，对图像分割方法进行研究。 </div><div class="t m0 x8 h5 y2e ff1 fs3 fc0 sc1 ls2 ws0">为了解决医学图像的分割问题，<span class="_ _12"></span>近几年来，<span class="_ _4"></span>很多研究人员做了大量的工作，<span class="_ _12"></span>提出了很多实</div><div class="t m0 x6 h5 y2f ff1 fs3 fc0 sc1 ls7 ws0">用的分割算法<span class="ff2 ls17">[2][3][4]</span>，随着统计学理论、模<span class="_ _4"></span>糊集理论、神经网络、形<span class="_ _4"></span>态学理论、小波理论等</div><div class="t m0 x6 h5 y30 ff1 fs3 fc0 sc1 ls2 ws0">在图像分割中的应用日渐广泛，<span class="_ _4"></span>遗传算法、<span class="_ _4"></span>尺度空间、<span class="_ _12"></span>多分辨率方法、非线性扩散方程等近期</div><div class="t m0 x6 h5 y31 ff1 fs3 fc0 sc1 ls2 ws0">涌现的新方法和新思想也不断被用于解决分割问题，<span class="_ _5"></span>国内外学者提出了不少有针对性的好分割</div><div class="t m0 x6 h5 y32 ff1 fs3 fc0 sc1 ls2 ws0">方法。<span class="_ _12"></span>本文将主要介绍近几年这一领域中研究人员提出的新方法或对原有方法的新改进。<span class="_ _13"></span>需要</div><div class="t m0 x6 h5 y33 ff1 fs3 fc0 sc1 ls2 ws0">指出的是，<span class="_ _14"></span>由于从不同的角度将得到不同的分类结果，<span class="_ _14"></span>本文中所涉及方法的分类并不是绝对的，</div><div class="t m0 x6 h5 y34 ff1 fs3 fc0 sc1 ls2 ws0">而且许多分割方法还是多种简单方法的综合体，<span class="_ _5"></span>我们只能大致将它们分为属于最能反映其特点</div><div class="t m0 x6 h6 y35 ff2 fs3 fc0 sc1 ls2 ws0"> <span class="_ _15"></span> </div><div class="t m0 x1d h6 y36 ff2 fs3 fc0 sc1 ls2 ws0"> </div><div class="t m0 x1e h10 y37 ff2 fs2 fc0 sc1 ls2 ws0">1</div><div class="t m0 x1f hd y38 ff4 fs5 fc0 sc1 ls2 ws0">x<span class="_ _16"></span>x<span class="_ _17"></span>g</div><div class="t m0 x20 h11 y39 ff4 fs2 fc0 sc1 ls2 ws0">N</div><div class="t m0 x21 h11 y37 ff4 fs2 fc0 sc1 ls2 ws0">k</div><div class="t m0 x22 h11 y3a ff4 fs2 fc0 sc1 ls2 ws0">k</div><div class="t m0 x23 h12 y37 ff5 fs2 fc0 sc1 ls2 ws0">=</div><div class="t m0 x24 hd y38 ff2 fs5 fc0 sc1 ls2 ws0">)<span class="_ _18"></span>,<span class="_ _c"></span>(<span class="_ _e"></span>)<span class="_ _18"></span>,<span class="_ _c"></span>(<span class="_ _19"> </span><span class="ff4">y<span class="_ _1a"></span>g<span class="_ _1b"></span>y<span class="_ _1c"> </span><span class="ff5">=</span></span></div><div class="t m0 x25 h13 y3b ff6 fs7 fc0 sc1 ls2 ws0">∪</div><div class="c x26 y3c w3 h14"><div class="t m1 x0 h15 y3d ff5 fs8 fc0 sc1 ls2 ws0">φ</div></div><div class="t m0 x27 h16 y3e ff5 fs9 fc0 sc1 ls2 ws0">=<span class="_ _1d"></span><span class="ff2">(<span class="_ _1e"> </span><span class="ff4">y<span class="_ _1f"></span>y<span class="_ _20"></span>g</span></span></div><div class="t m0 x28 h17 y3f ff4 fsa fc0 sc1 ls2 ws0">j<span class="_ _21"></span>k</div><div class="t m0 x29 h16 y3e ff6 fs9 fc0 sc1 ls2 ws0">∩<span class="_ _22"> </span><span class="ff2">)<span class="_ _18"></span>,<span class="_ _c"></span>(<span class="_ _23"></span>)<span class="_ _18"></span>,<span class="_ _24"> </span><span class="ff4">x<span class="_ _17"></span>g<span class="_ _25"></span>x</span></span></div><div class="t m0 x6 h10 y40 ff2 fs2 fc0 sc1 ls2 ws0">1</div><div class="t m0 x2a h18 y41 ff2 fsb fc0 sc1 ls2 ws0"> <span class="_"> </span><span class="ff1">联系人：田捷</span><span class="ls18"> </span><span class="ff1">电话：</span><span class="ls19 ws2">82618465 E-mail:tian@doctor<span class="_ _12"></span>.com </span></div><div class="t m0 x2b h19 y42 ff2 fsb fc0 sc1 ls2 ws0">1 </div><a class="l" rel='nofollow' onclick='return false;'><div class="d m2"></div></a></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div> </body> </html>

<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/625d92c892dc900e627b2cb9/bg2.jpg"><div class="t m0 x6 h5 y43 ff1 fs3 fc0 sc1 ls2 ws0">的某一类。<span class="sc0"> </span></div><div class="t m0 x2c h7 y44 ff1 fs1 fc0 sc0 ls1a ws0">2．基于区域的分割方法<span class="ff3 sc1 ls2"> </span></div><div class="t m0 x8 h5 y45 ff1 fs3 fc0 sc1 ls2 ws0">图像分割通常会用到不同对象间特征的不连续性和同一对象内部的特征相似性。<span class="_ _5"></span>基于区域</div><div class="t m0 x6 h5 y46 ff1 fs3 fc0 sc1 ls2 ws0">的算</div><div class="t m0 x6 h8 y47 ff3 fs3 fc0 sc1 ls1b ws0">2.1 <span class="_ _26"> </span><span class="ff1 sc0 ls5">法</span><span class="ls2"> </span></div><div class="t m0 x2d h5 y48 ff1 fs3 fc0 sc1 ls2 ws0">是最常见的并行的直接检测区域的分割方法<span class="ff2 lsc">[5]</span>。<span class="_ _27"></span>如果只用选取一个阈值称为单阈</div><div class="t m0 x6 h5 y49 ff1 fs3 fc0 sc1 ls2 ws0">值分</div><div class="t m0 x2e h5 y4a ff1 fs3 fc0 sc1 ls2 ws0">同类的物体灰度值或其他特征值相差很大时，<span class="_ _5"></span>它能很</div><div class="t m0 x6 h5 y4b ff1 fs3 fc0 sc1 ls2 ws0">有效</div><div class="t m0 x2f h5 y4c ff1 fs3 fc0 sc1 ls2 ws0">大的图像，<span class="_ _10"></span>对于图像中不存在明显</div><div class="t m0 x6 h5 y4d ff1 fs3 fc0 sc1 ls2 ws0">的灰</div><div class="t m0 x30 h5 y4e ff1 fs3 fc0 sc1 ls2 ws0">的困难所在。<span class="_ _5"></span>至今</div><div class="t m0 x6 h5 y4f ff1 fs3 fc0 sc1 ls2 ws0">仍有</div><div class="t m0 x31 h8 y50 ff3 fs3 fc0 sc1 ls1b ws0">.2 <span class="_"> </span><span class="ff1 sc0 ls2">区域生长和分裂合并</span><span class="ls2"> </span></div><div class="t m0 x32 h5 y51 ff1 fs3 fc0 sc1 ls2 ws0">两种典型的串行区域分割方法。<span class="_ _5"></span>其特点是将分割过程分解为顺序的</div><div class="t m0 x6 h5 y52 ff1 fs3 fc0 sc1 ls2 ws0">多个</div><div class="t m0 x33 h5 y53 ff1 fs3 fc0 sc1 ls2 ws0">，该方法需要先选取一个</div><div class="t m0 x34 h5 y54 ff1 fs3 fc0 sc1 ls2 ws0">种子</div><div class="t m0 x35 h5 y55 ff1 fs3 fc0 sc1 ls2 ws0">用者必须在每个需要抽取出的区</div><div class="t m0 x34 h5 y56 ff1 fs3 fc0 sc1 ls2 ws0">域中</div><div class="t m0 x8 h5 y57 ff1 fs3 fc0 sc1 ls2 ws0">法测重于利用区域内特征的相似性。 </div><div class="t m0 x8 h6 y58 ff2 fs3 fc0 sc1 ls2 ws0"> </div><div class="t m0 x5 h5 y59 ff1 fs3 fc0 sc0 ls5 ws0">阈值</div><div class="t m0 x8 h5 y5a ff1 fs3 fc0 sc1 ls2 ws0">阈值分割</div><div class="t m0 x8 h5 y5b ff1 fs3 fc0 sc1 ls2 ws0">割，<span class="_ _13"></span>它将图像分为目标和背景两大类；<span class="_ _13"></span>如果用多个阈值分割称为多阈值方法，<span class="_ _13"></span>图像将被分</div><div class="t m0 x6 h5 y5c ff1 fs3 fc0 sc1 ls2 ws0">割为多个目标区域和背景，<span class="_ _13"></span>为区分目标，<span class="_ _13"></span>还需要对各个区域进行标记。<span class="_ _13"></span>阈值分割方法基于对灰</div><div class="t m0 x6 h5 y5d ff1 fs3 fc0 sc1 ls2 ws0">度图像的一种假设：<span class="_ _5"></span>目标或背景内的相邻像素间的灰度值是相似的，<span class="_ _13"></span>但不同目标或背景的像素</div><div class="t m0 x6 h5 y5e ff1 fs3 fc0 sc1 ls2 ws0">在灰度上有差异，<span class="_ _13"></span>反映在图像直方图上，<span class="_ _13"></span>不同目标和背景则对应不同的峰。<span class="_ _13"></span>选取的阈值应位于</div><div class="t m0 x6 h5 y5f ff1 fs3 fc0 sc1 ls2 ws0">两个峰之间的谷，从而将各个峰分开。<span class="ff2"> </span></div><div class="t m0 x8 h5 y60 ff1 fs3 fc0 sc1 ls2 ws0">阈值分割的优点是实现简单，<span class="_ _5"></span>对于不</div><div class="t m0 x8 h5 y61 ff1 fs3 fc0 sc1 ls2 ws0">的对图像进行分割。<span class="_ _5"></span>阈值分割通常作为医学图像的预处理，<span class="_ _13"></span>然后应用其他一系列分割方法</div><div class="t m0 x6 h5 y62 ff1 fs3 fc0 sc1 ls2 ws0">进行后处理。它也常被用于<span class="ff2 ls8">CT</span>图像中皮肤、骨骼的分割。<span class="ff2"> </span></div><div class="t m0 x8 h5 y63 ff1 fs3 fc0 sc1 ls2 ws0">阈值分割的缺点是不适用于多通道图像和特征值相差不</div><div class="t m0 x8 h5 y64 ff1 fs3 fc0 sc1 ls2 ws0">度差异或各物体的灰度值范围有较大重叠的图像分割问题难以得到准确的结果。<span class="_ _5"></span>另外，<span class="_ _13"></span>由</div><div class="t m0 x6 h5 y65 ff1 fs3 fc0 sc1 ls2 ws0">于它仅仅考虑了图像的灰度信息而不考虑图像的空间信息，<span class="_ _10"></span>阈值分割对噪声和灰度不均匀很敏</div><div class="t m0 x6 h5 y66 ff1 fs3 fc0 sc1 ls2 ws0">感。<span class="_ _13"></span>针对阈值分割方法的缺点，<span class="_ _28"></span>不少学者提出了许多改进方法，<span class="_ _28"></span>如基于过渡区的方法<span class="ff2 lsc">[6]</span><span class="ls1c">，还<span class="_ _a"></span>有</span></div><div class="t m0 x6 h5 y67 ff1 fs3 fc0 sc1 ls2 ws0">利用像素点空间位置信息的变化阈值法<span class="ff2 lsc">[7]</span>，结合连通信息<span class="ff2 lse">[8]</span>的阈值方法。<span class="ff2"> </span></div><div class="t m0 x8 h5 y68 ff1 fs3 fc0 sc1 ls2 ws0">对于多目标的图像来讲，<span class="_ _5"></span>如何选取合适的阈值实在是基于阈值分割方法</div><div class="t m0 x8 h5 y69 ff1 fs3 fc0 sc1 ls2 ws0">不少学者针对该问题进行深入的研究，<span class="_ _5"></span>提出了许多新方法。<span class="_ _28"></span>在近年来的自动选取阈值方法</div><div class="t m0 x6 h5 y6a ff1 fs3 fc0 sc1 ls5 ws0">中，基于最大熵原则选择阈值是最重要的方法之一，由<span class="ff2 ls1d">T.<span class="_ _15"></span>P<span class="_ _a"></span>u<span class="_ _15"></span>n<span class="_ _29"></span></span>首先在<span class="ff2 lsc">[9]</span>中提出。这种方法的目</div><div class="t m0 x6 h5 y6b ff1 fs3 fc0 sc1 ls2 ws0">的在于将图像的灰度直方图分成两个或多个独立的类，<span class="_ _5"></span>使得各类熵的总值最大，<span class="_ _28"></span>从信息论角度</div><div class="t m0 x6 h5 y6c ff1 fs3 fc0 sc1 ls1e ws0">来说就是使这样选择阈值获得的信息量最大。<span class="ff2 ls15">J.N.Kapur<span class="_ _15"></span></span>等人进一步发展了这种方法<span class="ff2 lsc">[10]<span class="_ _15"></span></span><span class="ls2">，</span></div><div class="t m0 x6 h5 y6d ff1 fs3 fc0 sc1 ls1f ws0">P.Sahoo等人提出了用Renyi熵代替常规熵的最大熵原则<span class="ls20">[11]。Jui-Cheng Yen等人提出用最大</span></div><div class="t m0 x6 h5 y6e ff1 fs3 fc0 sc1 ls2 ws0">相关性原则选择阈值[12]，<span class="_ _10"></span>这种方法其实只是用他们定义的一个最大相关性原则取代了一般用</div><div class="t m0 x6 h5 y6f ff1 fs3 fc0 sc1 ls2 ws0">的最大熵原则。<span class="ff2"> </span></div><div class="t m0 x6 h8 y70 ff3 fs3 fc0 sc1 ls2 ws0"> </div><div class="t m0 x6 h8 y71 ff3 fs3 fc0 sc1 ls1b ws0">2</div><div class="t m0 x8 h5 y72 ff1 fs3 fc0 sc1 ls2 ws0">区域生长和分裂合并是</div><div class="t m0 x8 h5 y73 ff1 fs3 fc0 sc1 ls2 ws0">步骤，其中后续步骤要根据前面步骤的结果进行判断而确定。<span class="ff2"> </span></div><div class="t m0 x36 h5 y74 ff1 fs3 fc0 sc1 ls2 ws0">区域生长的基本思想是将具有相似性质的像素<span class="_ _1"></span>集合起来构成区域</div><div class="t m0 x36 h5 y75 ff1 fs3 fc0 sc1 ls2 ws0">点，然后依次将种子像素周围的相似像素<span class="_ _1"></span>合并到种子像素所在的区域中。区域生长算法<span class="_ _1"></span>的</div><div class="t m0 x34 h5 y76 ff1 fs3 fc0 sc1 ls2 ws0">研究重点一是特征度量和区域增长规则的设计<span class="_ _1"></span>，二是算法的高效性和准确性。区域增长方式<span class="_ _1"></span>的</div><div class="t m0 x34 h5 y77 ff1 fs3 fc0 sc1 ls2 ws0">优点是计算简单。与阈值分割类似，区域增长<span class="_ _1"></span>也很少单独使用，往往是与其他分割方法一起<span class="_ _1"></span>使</div><div class="t m0 x34 h5 y78 ff1 fs3 fc0 sc1 ls2 ws0">用，特别适用于分割小的结构如肿瘤和伤疤<span class="ff2 lsc">[13]</span>。<span class="ff2"> </span></div><div class="t m0 x36 h5 y79 ff1 fs3 fc0 sc1 ls2 ws0">区域生长的缺点是它需要人工交互以获得种子<span class="_ _1"></span>点，这样使</div><div class="t m0 x36 h5 y7a ff1 fs3 fc0 sc1 ls2 ws0">植入一个种子点。同时，区域增长方式也<span class="_ _1"></span>对噪声敏感，导致抽取出的区域有空洞或者在<span class="_ _1"></span>局</div><div class="t m0 x34 h5 y7b ff1 fs3 fc0 sc1 ls2 ws0">部体效应的情况下将分开的区域连接起来。<span class="_ _13"></span>为解决这些问题，<span class="_ _13"></span><span class="ff2 ls19 ws3">J.F<span class="_ _13"></span>. Mangin <span class="_"> </span><span class="ff1 ls2 ws0">等提出了一种同伦的</span></span></div><div class="t m0 x34 h5 y7c ff1 fs3 fc0 sc1 ls2 ws0">（<span class="ff2 ls21">homotopic</span>）<span class="_ _2a"></span>区域生长方式<span class="ff2 lsc">[14]</span>，<span class="_ _2a"></span>以保证初始区域和最终抽取出的区域的拓扑结构相同。<span class="_ _3"></span><span class="ff2 ls19">Shu-Yen </span></div><div class="t m0 x34 h5 y7d ff2 fs3 fc0 sc1 ls22 ws0">Wan<span class="_ _2"> </span><span class="ff1 ls2">等提出的对称区域增长算法</span><span class="lsc">[15]<span class="ff1 ls2">有效地弥补了原算法对种子点敏感和占用内存多的弱点，</span></span></div><div class="t m0 x34 h5 y7e ff1 fs3 fc0 sc1 ls2 ws0">而且对<span class="_ _2b"> </span><span class="ff2 ls23">3D<span class="_ _2b"> </span></span>连接对象标记和删除空洞的算法效率较高。另外，模糊连接度方法与区域增长相结</div><div class="t m0 x34 h5 y7f ff1 fs3 fc0 sc1 ls2 ws0">合也是一个发展方向<span class="ff2 lsc">[16]</span>。<span class="ff2"> </span></div><div class="t m0 x2b h19 y42 ff2 fsb fc0 sc1 ls2 ws0">2 </div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>

<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/625d92c892dc900e627b2cb9/bg3.jpg"><div class="t m0 x8 h5 y43 ff1 fs3 fc0 sc1 ls2 ws0">在区域生长或合并方法中，<span class="_ _12"></span>输入图像往往被分为多个相似的区域。<span class="_ _13"></span>然后类似的相邻区域根</div><div class="t m0 x6 h5 y80 ff1 fs3 fc0 sc1 ls2 ws0">据某种判断准则迭代地进行合并。<span class="_ _12"></span>在分裂技术中，<span class="_ _4"></span>整个图像先被看成一个区域，<span class="_ _12"></span>然后区域不断</div><div class="t m0 x6 h5 y81 ff1 fs3 fc0 sc1 ls5 ws0">被分裂为四个矩形区域，直到每个区域内部都<span class="_ _4"></span>是相似的。分裂合并方法中<span class="ff2 ls24">[17]</span>，区域从整幅图</div><div class="t m0 x6 h5 y82 ff1 fs3 fc0 sc1 ls2 ws0">像进行分裂，<span class="_ _12"></span>然后将相邻的区域进行合并。<span class="_ _4"></span>分裂合并方法不需要预先指定种子点，<span class="_ _12"></span>它的研究重</div><div class="t m0 x6 h5 y83 ff1 fs3 fc0 sc1 ls2 ws0">点是分裂和合并规则的设计。但是，分裂技术可能会使分割区域的边界被破坏。<span class="ff2"> </span></div><div class="t m0 x6 h6 y84 ff2 fs3 fc0 sc1 ls2 ws0"> </div><div class="t m0 x6 h8 y85 ff3 fs3 fc0 sc1 ls1b ws0">2.3<span class="ff1 sc0 ls2">分类器和聚类</span><span class="ls2"> </span></div><div class="t m0 x8 h5 y86 ff1 fs3 fc0 sc1 ls2 ws0">分类是模式识别领域中一种基本的统计分析方法。<span class="_ _5"></span>分类的目的利用已知的训练样本集在图</div><div class="t m0 x6 h5 y87 ff1 fs3 fc0 sc1 ls2 ws0">像的特征空间找到点<span class="_ _4"></span>（<span class="ff2 ls23">1D</span>）<span class="_ _2a"></span><span class="ls25">、曲<span class="_ _1"></span>线（<span class="_ _15"></span><span class="ff2 ls23">2D</span><span class="ls2">）<span class="_ _2a"></span><span class="ls25">、曲<span class="_ _1"></span>面（<span class="_ _15"></span><span class="ff2 ls23">3D</span><span class="ls2">）<span class="_ _12"></span>或超曲面（高维）<span class="_ _2a"></span>，<span class="_ _12"></span>从而实现对图像的划</span></span></span></span></div><div class="t m0 x6 h5 y88 ff1 fs3 fc0 sc1 ls2 ws0">分。<span class="_ _5"></span>用分类器<span class="ff2 lsc">[2]</span>进行分割是一种有监督的统计方法，<span class="_ _6"></span>它需要手工分割得到的样本集作为对新的</div><div class="t m0 x6 h5 y89 ff1 fs3 fc0 sc1 ls26 ws0">图像进行自动分割的参考。分类器又分为两种<span class="_ _4"></span>：非参数（<span class="ff2 lsb">nonparametric<span class="_ _15"></span></span>）分类器和参数</div><div class="t m0 x6 h5 y8a ff1 fs3 fc0 sc1 ls2 ws0">（<span class="ff2 ls27">parametric</span>）分类器。<span class="_ _4"></span>典型的非参数分类器包括<span class="_ _2c"> </span><span class="ff2">K<span class="_"> </span></span>近邻（<span class="ff2 ls28">KNN</span><span class="ls29">）以及<span class="_ _2c"> </span><span class="ff2 ls2a">Parzen<span class="_"> </span></span></span>窗（一种投票分</div><div class="t m0 x6 h5 y8b ff1 fs3 fc0 sc1 ls2 ws0">类器）<span class="_ _2a"></span>。它们对图像数据的统计结构没有要求。参数分类器的代表是<span class="_ _2d"> </span><span class="ff2 ls19">Bayes<span class="_ _2d"> </span></span>分类器<span class="ff2">,</span>它假定图像</div><div class="t m0 x6 h5 y8c ff1 fs3 fc0 sc1 ls5 ws0">的密度函数符合高斯独立分布。分类器的有两<span class="_ _4"></span>个优点：<span class="ff2 ls14">(1) <span class="_"> </span></span>不需要迭代运算，因此计算量相对</div><div class="t m0 x6 h5 y8d ff1 fs3 fc0 sc1 ls5 ws0">较小。<span class="ff2 ls14">(2) <span class="_"> </span></span>能应用于多通道图像。但是分类器同样没有考虑空间信息，<span class="_ _4"></span>因此对灰度不均匀的图</div><div class="t m0 x6 h5 y8e ff1 fs3 fc0 sc1 ls2 ws0">像分割效果不好。<span class="_ _4"></span>分类器还要求由手工分类生成训练集，<span class="_ _4"></span>而手工分类的工作量很大。<span class="_ _12"></span>同时，用</div><div class="t m0 x6 h5 y8f ff1 fs3 fc0 sc1 ls2 ws0">小量的训练集训练的分类器对大量的样本空间进行分类时会产生误差，<span class="_ _5"></span>因为它没有考虑到人体</div><div class="t m0 x6 h5 y90 ff1 fs3 fc0 sc1 ls2 ws0">的解剖机构的个体差异。<span class="ff2"> </span></div><div class="t m0 x8 h5 y91 ff1 fs3 fc0 sc1 ls2b ws0">聚类算法与分类器算法极为类似，只是它不需要训练样本，因此聚类是一种无监督的</div><div class="t m0 x6 h5 y92 ff2 fs3 fc0 sc1 ls2c ws0">(unsupervised) <span class="_ _2e"> </span><span class="ff1 ls7">统计方法。因为没有训练样本集，聚类算法迭代的执行<span class="_ _1"></span>对图像分类和提取各类</span></div><div class="t m0 x6 h5 y93 ff1 fs3 fc0 sc1 ls2 ws0">的特征值。从某种意义上说，聚类是一种自我训练的分类。<span class="_ _4"></span>其中，<span class="ff2">K<span class="_"> </span></span>均值、<span class="_ _4"></span>模糊<span class="_ _2c"> </span><span class="ff2">C<span class="_"> </span></span>均值<span class="ff2 ls2d">(Fuzzy </span></div><div class="t m0 x6 h5 y94 ff2 fs3 fc0 sc1 ls22 ws0">C-Means)<span class="ff1 ls2">、<span class="_ _6"></span><span class="ff2 ls13">EM(Expectation-Maximization)<span class="_ _4"></span><span class="ff1 ls2">和分层聚类方法<span class="ff2 ls17">[18][19]</span>是常用的聚类算法。<span class="_ _6"></span><span class="ff2">K<span class="_"> </span><span class="ff1">均值算</span></span></span></span></span></div><div class="t m0 x6 h5 y95 ff1 fs3 fc0 sc1 ls2 ws0">法先对当前的每一类求均值，<span class="_ _3"></span>然后按新生成的均值对像素进行重新分类<span class="ff2">(</span>将像素归入均值最近的</div><div class="t m0 x6 h5 y96 ff1 fs3 fc0 sc1 ls2 ws0">类<span class="ff2">)</span>，对新生成的类再迭代执行前面的步骤。模糊<span class="_ _2e"> </span><span class="ff2">C<span class="_ _2e"> </span></span>均值算法从模糊集合理论的角度对<span class="_ _2e"> </span><span class="ff2">K<span class="_ _2c"> </span></span>均值</div><div class="t m0 x6 h5 y97 ff1 fs3 fc0 sc1 ls2 ws0">进行了推广。<span class="_ _4"></span><span class="ff2 ls19">EM<span class="_"> </span><span class="ff1 ls2">算法把图像中每一个像素的灰度值看作是几个概率分布<span class="_ _4"></span>（一般用<span class="_ _2c"> </span><span class="ff2 ls14">Gaussian<span class="_"> </span></span>分</span></span></div><div class="t m0 x6 h5 y98 ff1 fs3 fc0 sc1 ls2 ws0">布）<span class="_ _12"></span>按一定比例的混合，<span class="_ _13"></span>通过优化基于最大后验概率的目标函数来估计这几个概率分布的参数</div><div class="t m0 x6 h5 y99 ff1 fs3 fc0 sc1 ls2 ws0">和它们之间的混合比例。<span class="_ _12"></span>分层聚类方法通过一系列类别的连续合并和分裂完成，<span class="_ _13"></span>聚类过程可以</div><div class="t m0 x6 h5 y9a ff1 fs3 fc0 sc1 ls2 ws0">用一个类似树的结构来表示。<span class="_ _14"></span>聚类分析不需要训练集，<span class="_ _14"></span>但是需要有一个初始分割提供初始参数，</div><div class="t m0 x6 h5 y9b ff1 fs3 fc0 sc1 ls2 ws0">初始参数对最终分类结果影响较大。<span class="_ _12"></span>另一方面，<span class="_ _4"></span>聚类也没有考虑空间关联信息，<span class="_ _12"></span>因此也对噪声</div><div class="t m0 x6 h5 y9c ff1 fs3 fc0 sc1 ls2 ws0">和灰度不均匀敏感<span class="ff2 lsc">[2]</span>。<span class="ff2"> </span></div><div class="t m0 x8 h5 y9d ff1 fs3 fc0 sc1 ls2 ws0">八十年代以来，<span class="_ _12"></span>聚类方法开始被用于核磁图像多参数特性空间的分类，<span class="_ _13"></span>如脑白质和灰质的</div><div class="t m0 x6 h5 y9e ff1 fs3 fc0 sc1 ls2 ws0">分割。<span class="_ _12"></span>随着近十年来像数据保真度的提高，<span class="_ _4"></span>这类方法逐渐发展成熟起来，<span class="_ _12"></span>出现了一系列方法来</div><div class="t m0 x6 h5 y9f ff1 fs3 fc0 sc1 ls2 ws0">提高聚类算法对图像灰度不均匀和噪声的鲁棒性，<span class="_ _5"></span>并在磁共振图像上取得了成功<span class="ff2 lsc">[1]</span>。<span class="_ _6"></span>不均匀的</div><div class="t m0 x6 h5 ya0 ff1 fs3 fc0 sc1 ls2 ws0">医学图像可以先用校正算法消除偏场效应，再<span class="_ _1"></span>运用标准的分割算法<span class="ff2 ls3 ws4">[20] [21]</span>。还有一些方法在</div><div class="t m0 x6 h5 ya1 ff1 fs3 fc0 sc1 ls2e ws0">分类的同时补偿偏场效应<span class="ff2 ls2f">[22][23][24<span class="_ _4"></span>]<span class="ff1 ls2e">，其中最有<span class="_ _1"></span>名的方法是<span class="_"> </span></span><span class="ls1b">W<span class="_ _13"></span>ells<span class="_ _2f"> </span><span class="ff1 ls2e">等提出的自适应分割方法</span></span></span></div><div class="t m0 x6 h5 ya2 ff2 fs3 fc0 sc1 lsc ws0">[25]<span class="ff1 ls2">，在分类同时采用<span class="_ _2d"> </span></span><span class="ls19">EM<span class="_ _2d"> </span><span class="ff1 ls2">算法估计图像偏场。用此方法能够得到基于后验概率的模糊分割，</span></span></div><div class="t m0 x6 h5 ya3 ff1 fs3 fc0 sc1 ls2 ws0">但对大多数数据集仍需要一些人工交互提供训练数据。<span class="_ _12"></span>当然，<span class="_ _13"></span>并非所有人承认该方法是最好的</div><div class="t m0 x6 h5 ya4 ff1 fs3 fc0 sc1 ls2 ws0">解决方案，不少学者仍在继续研究其他解决方法。<span class="ff2 ls6"> </span></div><div class="t m0 x6 h8 ya5 ff3 fs3 fc0 sc1 ls2 ws0"> </div><div class="t m0 x6 h8 ya6 ff3 fs3 fc0 sc1 ls1b ws0">2.4<span class="_"> </span><span class="ff1 sc0 ls2">基于随机场的方法</span><span class="ls2"> </span></div><div class="t m0 x8 h5 ya7 ff1 fs3 fc0 sc1 ls7 ws0">统计学方法中最常用的<span class="_ _4"></span>一种是将图像看作一个马尔科夫<span class="_ _4"></span>随机场MR<span class="_ _4"></span>F。统计学方法的实质是</div><div class="t m0 x6 h5 ya8 ff1 fs3 fc0 sc1 ls2 ws0">从统计学的角度出发对数字图像进行建模，<span class="_ _5"></span>把图像中各个像素点的灰度值看作是具有一定概率</div><div class="t m0 x6 h5 ya9 ff1 fs3 fc0 sc1 ls2 ws0">分布的随机变量。<span class="_ _5"></span>从观察到的图像中恢复实际物体或正确分割观察到的图像从统计学的角度看</div><div class="t m0 x6 h5 yaa ff1 fs3 fc0 sc1 ls2 ws0">就是要找出最有可能即以最大的概率得到该图像的物体组合来。<span class="_ _12"></span>从贝叶斯定理的角度看，<span class="_ _13"></span>就是</div><div class="t m0 x6 h5 yab ff1 fs3 fc0 sc1 ls2 ws0">要求出具有最大后验概率的分布。<span class="ff2"> </span></div><div class="t m0 x8 h5 yac ff2 fs3 fc0 sc1 ls27 ws5">MRF(Markov random<span class="_ _4"></span> field)<span class="ff1 ls2 ws0">本身是一个条件概率模型，其中每个像素的概率只与相邻<span class="_ _1"></span>点相</span></div><div class="t m0 x6 h5 yad ff1 fs3 fc0 sc1 ls30 ws0">关。直观的理<span class="_ _4"></span>解是，在<span class="ff2 lsa">MRF<span class="_ _8"> </span></span>假设下，大多数像素和<span class="_ _4"></span>其邻近的像素属于同<span class="_ _4"></span>一类。以</div><div class="t m0 x6 h1a yae ff2 fs3 fc0 sc1 ls19 ws0">L={(<span class="ff4 ls2">i<span class="ff2">,</span>j</span><span class="ls31">):1<span class="ff7 ls2">≤<span class="ff4">i</span>≤</span><span class="ls32">N1,1<span class="ff7 ls2">≤<span class="ff4">j</span>≤</span><span class="ls28">N2}<span class="ff1 ls2">表示一个</span>N1<span class="_ _1"></span><span class="ff1 ls2">×</span>N2<span class="ff1 ls2">的图像网格。<span class="_ _4"></span>以<span class="ff2"> <span class="_"> </span><span class="ff4">X</span><span class="ls33">={</span><span class="ff4">X</span></span></span></span></span></span></div><div class="t m0 x37 h1b yaf ff4 fsc fc0 sc1 ls34 ws0">ij</div><div class="t m0 x38 h5 yb0 ff2 fs3 fc0 sc1 ls2 ws0">}<span class="ff1">表示一个离散取值的随机场，</span></div><div class="t m0 x6 h1a yb1 ff1 fs3 fc0 sc1 ls2 ws0">随机变量<span class="ff2">Xij</span>可取图像可能的灰度值集合<span class="ff2 ls13">G={g1,g2,...gM}</span>中的一个，以<span class="ff4">x</span></div><div class="t m0 x39 h1b yb2 ff4 fsc fc0 sc1 ls34 ws0">ij</div><div class="t m0 x3a h1a yb3 ff1 fs3 fc0 sc1 ls2 ws0">表示<span class="ff4">X</span></div><div class="t m0 x3b h1b yb2 ff4 fsc fc0 sc1 ls34 ws0">ij</div><div class="t m0 x3c h5 yb3 ff1 fs3 fc0 sc1 ls2 ws0">的一个特定值。</div><div class="t m0 x2b h19 y42 ff2 fsb fc0 sc1 ls2 ws0">3 </div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>