计算机视觉_计算机视觉_图像处理_其他

<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/626e691615314c70c3957c53/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/626e691615314c70c3957c53/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0"> 130</div><div class="t m0 x2 h3 y2 ff2 fs1 fc0 sc1 ls0 ws1">第七章 <span class="_"> </span>运动视觉<span class="ff3 sc0"> </span></div><div class="t m0 x1 h4 y3 ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x1 h5 y4 ff1 fs2 fc0 sc0 ls1 ws1">7.1 <span class="ff2 ls0">概述<span class="ff1"> </span></span></div><div class="t m0 x1 h5 y5 ff1 fs2 fc0 sc0 ls1 ws1">7.2 <span class="ff2 ls0">视觉运动的检测和测量<span class="ff1"> </span></span></div><div class="t m0 x1 h5 y6 ff1 fs2 fc0 sc0 ls2 ws1">7.2.1 <span class="ff2 ls0">以灰度为基础的方法<span class="ff1"> </span></span></div><div class="t m0 x1 h5 y7 ff1 fs2 fc0 sc0 ls3 ws1">(1) <span class="ff2 ls0">速度场和光流<span class="ff1"> </span></span></div><div class="t m0 x1 h5 y8 ff1 fs2 fc0 sc0 ls3 ws1">(2) <span class="ff2 ls0">光流<span class="ff1"> </span></span></div><div class="t m0 x1 h5 y9 ff1 fs2 fc0 sc0 ls3 ws1">(3) <span class="ff2 ls0">光流的估算<span class="ff1"> </span></span></div><div class="t m0 x1 h5 ya ff1 fs2 fc0 sc0 ls2 ws1">7.2.2 <span class="ff2 ls0">基于过零点的方法<span class="ff1"> </span></span></div><div class="t m0 x1 h5 yb ff1 fs2 fc0 sc0 ls1 ws1">7.2.3<span class="_ _0"> </span><span class="ff2 ls0">基于特征的运动检测方法<span class="ff1"> </span></span></div><div class="t m0 x1 h5 yc ff1 fs2 fc0 sc0 ls1 ws1">7.3 <span class="ff2 ls0">运动理解<span class="ff1"> </span></span></div><div class="t m0 x1 h5 yd ff1 fs2 fc0 sc0 ls1 ws1">7.3.1<span class="_ _0"> </span><span class="ff2 ls0">基于光流的运动理解<span class="ff1"> </span></span></div><div class="t m0 x1 h5 ye ff1 fs2 fc0 sc0 ls1 ws1">7.3.2<span class="_ _0"> </span><span class="ff2 ls0">基于特征的运动理解<span class="ff1"> </span></span></div><div class="t m0 x1 h5 yf ff1 fs2 fc0 sc0 ls1 ws1">7.3.3<span class="_ _0"> </span><span class="ff2 ls0">根据图象流动力学恢复表面结构和三维运动<span class="ff1"> </span></span></div><div class="t m0 x1 h5 y10 ff1 fs2 fc0 sc0 ls2 ws1">7.3.4 <span class="ff2 ls0">基于光流的代数法恢复运动参数和景物深度</span></div><div class="t m0 x3 h6 y11 ff1 fs3 fc0 sc0 ls4 ws2">[Tek 96]</div><div class="t m0 x4 h4 y12 ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x1 h7 y13 ff3 fs4 fc0 sc0 ls0 ws1">7.1 <span class="ff2 sc1">概述</span></div><div class="t m0 x5 h8 y14 ff3 fs5 fc0 sc0 ls5 ws3">[Ull 79]</div><div class="t m0 x6 h9 y13 ff3 fs4 fc0 sc0 ls0 ws1"> </div><div class="t m0 x1 h5 y15 ff2 fs2 fc0 sc0 ls6 ws1"> <span class="_ _1"> </span> <span class="_ _1"> </span>对运动的分析在生理系统中<span class="_ _2"></span>占中心位置。甚至在简单<span class="_ _2"></span>的动物身上都存在着复杂的观</div><div class="t m0 x1 h5 y16 ff2 fs2 fc0 sc0 ls7 ws1">察、跟踪和利用运动的功能。<span class="_ _3"></span>例如，青蛙可以有效地探测<span class="_ _3"></span>小飞虫。这样的动物可有选择<span class="_ _3"></span>地</div><div class="t m0 x1 h5 y17 ff2 fs2 fc0 sc0 ls7 ws1">对在视场中运动着的小的、深<span class="_ _3"></span>色的物体进行跟踪。家蝇可<span class="_ _3"></span>以跟踪运动物体和发现目标跟<span class="_ _3"></span>背</div><div class="t m0 x1 h5 y18 ff2 fs2 fc0 sc0 ls7 ws1">景之间的相对运动，甚至当物<span class="_ _3"></span>体与背景在纹理上相同，因<span class="_ _3"></span>此如果没有相对运动是区分不<span class="_ _3"></span>开</div><div class="t m0 x1 h5 y19 ff2 fs2 fc0 sc0 ls0 ws1">的情况下也是这样的。<span class="ff1"> </span></div><div class="t m0 x1 h5 y1a ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _1"> </span>在高等<span class="_ _3"></span>动物包括灵长目动物中，运动<span class="_ _3"></span>的分析从早期视觉处理阶段<span class="_ _3"></span>开始就渗透到视觉系</div><div class="t m0 x1 h5 y1b ff2 fs2 fc0 sc0 ls7 ws1">统中。某些生物，例如鸽子和<span class="_ _3"></span>免子在视网膜的水平上完成<span class="_ _3"></span>基本运动分析。在其他动物，<span class="_ _3"></span>包</div><div class="t m0 x1 h5 y1c ff2 fs2 fc0 sc0 ls7 ws1">括猫和灵长目动物，视觉皮层<span class="_ _3"></span>中从眼睛接受输入的第一个<span class="_ _3"></span>神经里已经涉及到运动的分析<span class="_ _3"></span>：</div><div class="t m0 x1 h5 y1d ff2 fs2 fc0 sc0 ls7 ws1">这些神经对沿某一方向运动的<span class="_ _3"></span>刺激反应很灵敏，但对沿相<span class="_ _3"></span>反方向的运动却反应很小，或<span class="_ _3"></span>根</div><div class="t m0 x1 h5 y1e ff2 fs2 fc0 sc0 ls0 ws1">本不反应。<span class="ff1"> </span></div><div class="t m0 x1 h5 y1f ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _1"> </span>运动视<span class="_ _3"></span>觉在生理系统中占主要地位不<span class="_ _3"></span>令人奇怪的，因为运动揭示<span class="_ _3"></span>了关于环境的有价值</div><div class="t m0 x1 h5 y20 ff2 fs2 fc0 sc0 ls7 ws1">的信息。本章的研究任务是根<span class="_ _3"></span>据运动发现结构和解释由运<span class="_ _3"></span>动所产生的光流场。对生理系<span class="_ _3"></span>统</div><div class="t m0 x1 h5 y21 ff2 fs2 fc0 sc0 ls0 ws1">运动视觉的研究将有助于时变图象的计算机分析算法的研究。<span class="ff1"> </span></div><div class="t m0 x1 h5 y22 ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _1"> </span>反之，<span class="_ _3"></span>对时变图象解释的研究可以深<span class="_ _3"></span>化对一般原理的理解，这些<span class="_ _3"></span>理解可增进我们对生</div><div class="t m0 x1 h5 y23 ff2 fs2 fc0 sc0 ls7 ws1">理视觉系统的理解。时变图象<span class="_ _3"></span>分析的基本计算问题可分成<span class="_ _3"></span>两大类：运动的检测和测量，<span class="_ _3"></span>以</div><div class="t m0 x1 h5 y24 ff2 fs2 fc0 sc0 ls0 ws1">及视觉运动的解释。<span class="ff1"> </span></div><div class="t m0 x1 ha y25 ff3 fs6 fc0 sc0 ls8 ws1">7.1.1 <span class="ff2 sc1 ls0">运动探测和测量</span><span class="ls0"> </span></div><div class="t m0 x1 h5 y26 ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _1"> </span>图象中<span class="_ _3"></span>基元和区域的运动不是直接给<span class="_ _3"></span>出的，而是必须根据基本量<span class="_ _3"></span>测来计算得到。由眼</div><div class="t m0 x1 h5 y27 ff2 fs2 fc0 sc0 ls9 ws1">睛或由电子成象系统记录的时<span class="_ _3"></span>变图象可描述为随时间变化<span class="_ _3"></span>的亮度值</div><div class="t m1 x7 hb y28 ff4 fs7 fc0 sc0 lsa ws1">()</div><div class="t m0 x8 h5 y29 ff5 fs8 fc0 sc0 lsb ws1">Ex<span class="_ _4"> </span>y<span class="_ _5"></span>t<span class="_ _6"></span><span class="ff1 lsc">,,<span class="_ _7"> </span><span class="ff2 fs2 lsd">的二维阵</span></span></div><div class="t m0 x1 h5 y2a ff2 fs2 fc0 sc0 lse ws1">列。图象中的运动可用速度场</div><div class="t m2 x9 hc y2b ff4 fs9 fc0 sc0 lsf ws1">()</div><div class="t m0 xa h5 y2c ff5 fsa fc0 sc0 ls10 ws1">Vx<span class="_ _5"></span>yt<span class="_ _8"></span><span class="ff1 ls11">,,<span class="_ _9"> </span><span class="ff2 fs2 lse">来表示。</span></span></div><div class="c xb y2d w2 hd"><div class="t m3 x0 hc y2e ff4 fs9 fc0 sc0 ls0 ws1">(</div></div><div class="t m3 xc hc y2b ff4 fs9 fc0 sc0 ls0 ws1">)</div><div class="t m0 xd h5 y2c ff5 fsa fc0 sc0 ls12 ws1">Vx<span class="_ _a"></span>yt<span class="_ _8"></span><span class="ff1 ls13">,,<span class="_ _4"> </span><span class="ff2 fs2 lse">给出某一时刻<span class="_ _0"> </span><span class="ff5 fsb ls0">t<span class="_ _b"> </span></span>，在图象中</span></span></div><div class="t m4 xe hc y2f ff4 fs9 fc0 sc0 ls14 ws1">()</div><div class="t m0 xf h5 y30 ff5 fsa fc0 sc0 ls15 ws1">xy<span class="_ _c"></span><span class="ff1 ls0">,<span class="_ _d"> </span><span class="ff2 fs2 ls16">处点的运动速度和方向。</span></span></div><div class="c x10 y31 w3 hd"><div class="t m5 x0 hc y2e ff4 fs9 fc0 sc0 ls0 ws1">(</div></div><div class="t m5 x11 hc y2f ff4 fs9 fc0 sc0 ls0 ws1">)</div><div class="t m0 x12 h5 y30 ff5 fsa fc0 sc0 ls17 ws1">Ex<span class="_ _4"> </span>y<span class="_ _5"></span>t<span class="_ _6"></span><span class="ff1 ls11">,,<span class="_ _e"> </span><span class="ff2 fs2 ls16">是由原始的测量直接得到的，而</span></span></div><div class="t m4 x13 hc y2f ff4 fs9 fc0 sc0 ls18 ws1">()</div><div class="t m0 x14 h5 y30 ff5 fsa fc0 sc0 ls10 ws1">Vx<span class="_ _5"></span>yt<span class="_ _8"></span><span class="ff1 ls11">,,<span class="_ _4"> </span><span class="ff2 fs2 ls16">不是</span></span></div><div class="t m0 x1 h5 y32 ff2 fs2 fc0 sc0 ls16 ws1">这样。因此，分析运动中的第一个问题是根据</div><div class="c x15 y33 w2 hd"><div class="t m6 x0 hb y2e ff4 fs7 fc0 sc0 ls0 ws1">(</div></div><div class="t m6 x16 hb y34 ff4 fs7 fc0 sc0 ls0 ws1">)</div><div class="t m0 x17 h5 y35 ff5 fsa fc0 sc0 ls17 ws1">Ex<span class="_ _4"> </span>y<span class="_ _5"></span>t<span class="_ _6"></span><span class="ff1 ls11">,,<span class="_ _9"> </span><span class="ff2 fs2 ls16">计算</span></span></div><div class="c x18 y33 w2 hd"><div class="t m7 x0 hb y2e ff4 fs7 fc0 sc0 ls0 ws1">(</div></div><div class="t m7 x19 hb y34 ff4 fs7 fc0 sc0 ls0 ws1">)</div><div class="t m0 x1a h5 y35 ff5 fsa fc0 sc0 ls12 ws1">Vx<span class="_ _a"></span>yt<span class="_ _8"></span><span class="ff1 ls13">,,<span class="_ _0"> </span><span class="ff2 fs2 ls16">。这些计算是视觉</span></span></div><div class="t m0 x1 h5 y36 ff2 fs2 fc0 sc0 ls0 ws1">运动的量测。<span class="ff1"> </span></div><div class="t m0 x1 h5 y37 ff2 fs2 fc0 sc0 ls19 ws1"> <span class="_ _1"> </span> <span class="_ _1"> </span>在某些情况下，只要检测<span class="_ _3"></span>速度场</div><div class="c x1b y38 w2 hd"><div class="t m7 x0 hb y39 ff4 fs7 fc0 sc0 ls0 ws1">(</div></div><div class="t m7 x1c hb y3a ff4 fs7 fc0 sc0 ls0 ws1">)</div><div class="t m0 x1d he y3b ff5 fsa fc0 sc0 ls12 ws1">Vx<span class="_ _a"></span>yt<span class="_ _8"></span><span class="ff1 ls13">,,</span></div><div class="t m0 x1e h5 y3c ff2 fs2 fc0 sc0 ls19 ws1">的某些特性就足够了，而不<span class="_ _3"></span>要完全和精确</div><div class="t m0 x1 h5 y3d ff2 fs2 fc0 sc0 ls7 ws1">的量测。例如，当希望迅速地<span class="_ _3"></span>对运动物体作出响应时，在<span class="_ _3"></span>这种情况下必须检测运动，但<span class="_ _3"></span>不</div><div class="t m0 x1 h5 y3e ff2 fs2 fc0 sc0 ls0 ws1">需要测量。<span class="ff1"> </span></div><div class="t m0 x1 h5 y3f ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _1"> </span>但是，<span class="_ _3"></span>从这里讨论问题的分类来说这<span class="_ _3"></span>两个问题都重要。当研究深<span class="_ _3"></span>入时，这些问题将被</div><div class="t m0 x1 h5 y40 ff2 fs2 fc0 sc0 ls7 ws1">证明比原来所预计的更为困难<span class="_ _3"></span>。因此，对有效和可靠的测<span class="_ _3"></span>量方法的研究是对时变图象分<span class="_ _3"></span>析</div><div class="t m0 x1 h5 y41 ff2 fs2 fc0 sc0 ls0 ws1">方面的重要研究邻域。<span class="ff1"> </span></div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div> 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<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/626e691615314c70c3957c53/bg2.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0"> 131</div><div class="t m0 x1 hf y42 ff3 fsc fc0 sc0 ls1a ws1">1. <span class="ff6 sc1 ls1b">离散和连续运动</span><span class="ls0"> </span></div><div class="t m0 x1 h5 y43 ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _1"> </span>对由人<span class="_ _3"></span>类视觉系统进行的运动检测和<span class="_ _3"></span>测量的心理学研究确定了两<span class="_ _3"></span>种类型的运动：离散</div><div class="t m0 x1 h5 y44 ff2 fs2 fc0 sc0 ls7 ws1">的和连续的。对感觉运动的观<span class="_ _3"></span>察者来说，刺激物不一定要<span class="_ _3"></span>连续地移过视场。选择合适的<span class="_ _3"></span>空</div><div class="t m0 x1 h5 y45 ff2 fs2 fc0 sc0 ls7 ws1">间和时间显示参数，可以给出<span class="_ _3"></span>对顺序刺激的平滑、不中断<span class="_ _3"></span>运动的印象。视觉系统可以填<span class="_ _3"></span>补</div><div class="t m0 x1 h5 y46 ff2 fs2 fc0 sc0 ls1c ws1">离散显示之间的间隙，甚至当刺激物相隔几度视觉角，和<span class="_ _2"></span>长的时间间隔（<span class="ff1 ls1d">400ms</span><span class="ls19">）也是这</span></div><div class="t m0 x1 h10 y47 ff2 fs2 fc0 sc0 ls7 ws1">样。所得到的运动，叫做表观的（<span class="ff1 ls1e">appera<span class="_ _3"></span>nt<span class="ff2 ls7">）或<span class="ff4 ls0">β<span class="_ _2"></span></span>运动，从感觉来说跟连续运动无法区分。</span></span></div><div class="t m0 x1 h5 y48 ff2 fs2 fc0 sc0 ls7 ws1">此外填入的位置可为以后的处<span class="_ _3"></span>理，例如立体视觉所利用。<span class="_ _3"></span>表观运动机理在人类和低等运<span class="_ _3"></span>动</div><div class="t m0 x1 h5 y49 ff2 fs2 fc0 sc0 ls0 ws1">物中都是天生的。<span class="ff1"> </span></div><div class="t m0 x1 h5 y4a ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _1"> </span>表观运<span class="_ _3"></span>动现象引起了离散和连续运动<span class="_ _3"></span>是由相同的还是由分别的机<span class="_ _3"></span>理所记录的问题。视</div><div class="t m0 x1 h5 y4b ff2 fs2 fc0 sc0 ls7 ws1">觉系统可以记录两种类型运动<span class="_ _3"></span>的事实不一定意味着分别的<span class="_ _3"></span>实现机理，因为从原理上来说<span class="_ _3"></span>一</div><div class="t m0 x1 h5 y4c ff2 fs2 fc0 sc0 ls7 ws1">个记录离散运动的系统可以记<span class="_ _3"></span>录连续运动。最近的心理物<span class="_ _3"></span>理学方面的证据支持存在两种<span class="_ _3"></span>机</div><div class="t m0 x1 h5 y4d ff2 fs2 fc0 sc0 ls1f ws1">理。<span class="ff1 ls20">Braddick</span></div><div class="t m0 x1f h6 y4e ff1 fs3 fc0 sc0 ls21 ws4">[Bra 74]</div><div class="t m0 x20 h5 y4d ff2 fs2 fc0 sc0 ls1f ws1">提出把这两种机理叫做短范围和长范围（<span class="ff1 ls22 ws5">s<span class="_ _3"></span>hort range and long ran<span class="_ _3"></span>ge<span class="ff2 ls1f ws1">）。</span></span></div><div class="t m0 x1 h5 y4f ff2 fs2 fc0 sc0 ls0 ws1">短范围机理测量连续运动或大约<span class="_ _7"> </span><span class="ff1 ls1d">15<span class="_ _4"> </span></span>弧分（在视场中心）（<span class="ff1 ls23 ws6">minute of are<span class="_ _3"></span><span class="ff2 ls0 ws1">）和小于大约<span class="_ _7"> </span><span class="ff1 ls1d">60</span>～</span></span></div><div class="t m0 x1 h5 y50 ff1 fs2 fc0 sc0 ls24 ws7">100 msec<span class="_ _b"> </span><span class="ff2 ls16 ws1">时间间隔的离散运动。长范围机理处理比较大的位移和时间间隔。这样的术语比</span></div><div class="t m0 x1 h5 y51 ff2 fs2 fc0 sc0 ls0 ws1">用离散／连续这样的分类法更好些，因为大到<span class="_ _7"> </span><span class="ff1 ls25">15<span class="_ _0"> </span></span>分的视觉弧度跳变的离散显示是由短范围</div><div class="t m0 x1 h5 y52 ff2 fs2 fc0 sc0 ls0 ws1">机理来处理的。<span class="ff1"> </span></div><div class="t m0 x1 h5 y53 ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _1"> </span>这样的<span class="_ _3"></span>两个系统之间存在着比它们的<span class="_ _3"></span>范围差别更为基本的差别。<span class="_ _3"></span>它们似乎是根据不同</div><div class="t m0 x1 h5 y54 ff2 fs2 fc0 sc0 ls7 ws1">的运动基元，在不同处理阶段<span class="_ _3"></span>进行各自的运动量测。在量<span class="_ _3"></span>测运动中，对这两种主要的处<span class="_ _3"></span>理</div><div class="t m0 x1 h5 y55 ff2 fs2 fc0 sc0 ls7 ws1">方案进行区别是有益的。在最<span class="_ _3"></span>低层，运动量测是直接以灰<span class="_ _3"></span>度值的局部变化为基础，这称<span class="_ _3"></span>为</div><div class="t m0 x1 h5 y56 ff2 fs2 fc0 sc0 ls6 ws1">以灰度为基础的方案。另外还有<span class="_ _2"></span>一种可能是首先识别象边<span class="_ _2"></span>缘、线、斑点或区域这样的特</div><div class="t m0 x1 h5 y57 ff2 fs2 fc0 sc0 ls7 ws1">征，然后通过在时间和位置的<span class="_ _3"></span>变化范围内匹配这些特征来<span class="_ _3"></span>进行检测，这种类型的方案被<span class="_ _3"></span>称</div><div class="t m0 x1 h5 y58 ff2 fs2 fc0 sc0 ls7 ws1">为标记匹配方案（<span class="ff1 ls26 ws8">token-m<span class="_ _3"></span>atching schemes<span class="ff2 ls7 ws1">）。在人类视觉系统中，似乎短范围过程是以灰</span></span></div><div class="t m0 x1 h5 y59 ff2 fs2 fc0 sc0 ls0 ws1">度为基础的方案，长范围过程是标记匹配方案。<span class="ff1"> </span></div><div class="t m0 x1 h5 y5a ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _1"> </span>这两种<span class="_ _3"></span>运动检测和测量方式将产生不<span class="_ _3"></span>同的计算问题，并且随之在<span class="_ _3"></span>生理系统和计算机视</div><div class="t m0 x1 h5 y5b ff2 fs2 fc0 sc0 ls0 ws1">觉系统中产生不同种类的过程。<span class="ff1"> </span></div><div class="t m0 x1 hf y5c ff3 fsc fc0 sc0 ls1a ws1">2. <span class="ff6 sc1 ls27">以灰度为基础的方案</span><span class="ls0"> </span></div><div class="t m0 x1 h5 y5d ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _1"> </span>已经提<span class="_ _3"></span>出了几种在生理系统中的以灰<span class="_ _3"></span>度为基础的运动测量方案。<span class="_ _3"></span>这些方案可分成两个</div><div class="t m0 x1 h5 y5e ff2 fs2 fc0 sc0 ls0 ws1">主要类型：相关技术和梯度方法。<span class="ff1"> </span></div><div class="t m0 x1 h5 y5f ff2 fs2 fc0 sc0 ls28 ws1"> <span class="ff1 ls3">(1) </span><span class="ls0">相关方案<span class="ff1"> </span></span></div><div class="t m0 x1 h5 y60 ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _1"> </span>通过把<span class="_ _3"></span>在两个相邻位置处光增量检测<span class="_ _3"></span>器的输出作比较可构成简单<span class="_ _3"></span>的运动检测器。在位</div><div class="t m0 x1 h5 y61 ff2 fs2 fc0 sc0 ls0 ws1">置<span class="_ _7"> </span><span class="ff5 fsd">p</span></div><div class="t m0 x21 h11 y62 ff1 fse fc0 sc0 ls0 ws1">1</div><div class="t m0 x22 h5 y61 ff2 fs2 fc0 sc0 lsd ws1">和时间<span class="_ _f"> </span><span class="ff5 fsd ls0">t</span></div><div class="t m0 x5 h11 y62 ff1 fse fc0 sc0 ls0 ws1">1</div><div class="t m0 x23 h5 y61 ff2 fs2 fc0 sc0 lsd ws1">的输出跟位置<span class="_ _e"> </span><span class="ff5 fsd ls0">p</span></div><div class="t m0 x24 h11 y62 ff1 fse fc0 sc0 ls0 ws1">2</div><div class="t m0 x25 h5 y61 ff2 fs2 fc0 sc0 lsd ws1">在时间<span class="_ _f"> </span><span class="ff5 fsd ls29">tt</span></div><div class="c x26 y63 w4 h12"><div class="t m0 x0 h13 y64 ff4 fsd fc0 sc0 ls0 ws1">−</div></div><div class="c x27 y63 w5 h12"><div class="t m8 x0 h14 y64 ff4 fsf fc0 sc0 ls0 ws1">δ</div></div><div class="t m0 x28 h5 y61 ff2 fs2 fc0 sc0 lsd ws1">的输出相比较。这种方法称为延迟比较方</div><div class="t m0 x1 h5 y65 ff2 fs2 fc0 sc0 ls7 ws1">案，该方案的两种变种已经提<span class="_ _3"></span>出来作为生理系统的模型。<span class="_ _3"></span>按第一种模型，生理系统把两<span class="_ _3"></span>个</div><div class="t m0 x1 h5 y66 ff2 fs2 fc0 sc0 ls0 ws1">值相乘，也即</div><div class="t m9 x29 hc y67 ff4 fs9 fc0 sc0 ls2a ws1">()<span class="_ _10"></span>(<span class="_ _11"> </span>)</div><div class="t m0 x2a h15 y68 ff5 fsa fc0 sc0 ls2b ws1">Dp<span class="_ _7"> </span>t<span class="_ _12"> </span>Dp<span class="_ _13"> </span>t<span class="_ _14"> </span>t</div><div class="t m0 x2b h16 y69 ff1 fs10 fc0 sc0 ls2c ws1">12</div><div class="t m0 x2c h17 y68 ff1 fsa fc0 sc0 ls2d ws1">,,<span class="_ _15"></span><span class="ff4 ls2e">⋅−</span></div><div class="t ma x2d h18 y68 ff4 fs11 fc0 sc0 ls0 ws1">δ</div><div class="t m0 x2e h5 y68 ff2 fs2 fc0 sc0 ls0 ws1">，其中<span class="_ _4"> </span><span class="ff5 fs12">D<span class="_ _f"> </span></span>表示为单元（<span class="ff1 ls1">subunit</span>）的输出（图<span class="_ _7"> </span><span class="ff1 ls1d">7.1</span><span class="ls2f">）。</span></div><div class="t m0 x1 h5 y6a ff2 fs2 fc0 sc0 ls1f ws1">如果一个光点由</div><div class="t m0 x2f h19 y6b ff5 fsd fc0 sc0 ls0 ws1">p</div><div class="t m0 x30 h11 y6c ff1 fse fc0 sc0 ls0 ws1">2</div><div class="t m0 x2c h5 y6d ff2 fs2 fc0 sc0 ls1f ws1">点在时间</div><div class="c x31 y6e w5 h12"><div class="t m8 x0 h14 y6f ff4 fsf fc0 sc0 ls0 ws1">δ</div></div><div class="t m0 x32 h19 y6b ff5 fsd fc0 sc0 ls0 ws1">t</div><div class="t m0 x33 h5 y6d ff2 fs2 fc0 sc0 ls1f ws1">内移到</div><div class="t m0 x1b h19 y6b ff5 fsd fc0 sc0 ls0 ws1">p</div><div class="t m0 x34 h11 y6c ff1 fse fc0 sc0 ls0 ws1">1</div><div class="t m0 x35 h5 y6d ff2 fs2 fc0 sc0 ls1f ws1">，这样在</div><div class="t m0 x36 h19 y6b ff5 fsd fc0 sc0 ls0 ws1">p</div><div class="t m0 x37 h11 y6c ff1 fse fc0 sc0 ls0 ws1">2</div><div class="t m0 x38 h5 y6d ff2 fs2 fc0 sc0 ls1f ws1">点处造成光线增加的</div><div class="c x39 y6e w5 h12"><div class="t m8 x0 h14 y6f ff4 fsf fc0 sc0 ls0 ws1">δ</div></div><div class="t m0 x3a h19 y6b ff5 fsd fc0 sc0 ls0 ws1">t</div><div class="t m0 x3b h5 y6d ff2 fs2 fc0 sc0 ls1f ws1">时间后，造</div><div class="t m0 x1 h5 y70 ff2 fs2 fc0 sc0 ls16 ws1">成了</div><div class="t m0 x3c h1a y71 ff5 fs13 fc0 sc0 ls0 ws1">p</div><div class="t m0 x3d h1b y72 ff1 fs14 fc0 sc0 ls0 ws1">1</div><div class="t m0 x3e h5 y71 ff2 fs2 fc0 sc0 ls16 ws1">点处光线的增加。因此，上述乘积是正的。在这样的检测器阵列中，平均输出本质</div><div class="t m0 x1 h5 y73 ff2 fs2 fc0 sc0 ls19 ws1">上等于输入的交叉相关（<span class="ff1 ls30">cross-corre<span class="_ _3"></span>lation<span class="ff2 ls19">）。这种模型可成功地描述各种昆虫对在<span class="_ _3"></span>它们视</span></span></div><div class="t m0 x1 h5 y74 ff2 fs2 fc0 sc0 ls0 ws1">场中的运动所作的反应。<span class="ff1"> </span></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/626e691615314c70c3957c53/bg3.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0"> 132</div><div class="t m0 x3f h1c y75 ff5 fs15 fc0 sc0 ls0 ws1">p</div><div class="t m0 x40 h1d y76 ff1 fs16 fc0 sc0 ls0 ws1">1</div><div class="t m0 x41 h1c y77 ff5 fs15 fc0 sc0 ls0 ws1">p</div><div class="t m0 x42 h1d y78 ff1 fs16 fc0 sc0 ls0 ws1">1</div><div class="t m0 x43 h1c y79 ff5 fs15 fc0 sc0 ls0 ws1">p</div><div class="t m0 x44 h1d y7a ff1 fs16 fc0 sc0 ls0 ws1">2</div><div class="t m0 x45 h1c y7b ff5 fs15 fc0 sc0 ls0 ws1">p</div><div class="t m0 x46 h1d y7c ff1 fs16 fc0 sc0 ls0 ws1">2</div><div class="t m0 x37 h1e y7d ff1 fs17 fc0 sc0 ls31 ws1">(b)<span class="_ _16"></span><span class="ls32">(a)</span></div><div class="t m0 x47 h1e y7e ff1 fs17 fc0 sc0 ls0 ws1">X</div><div class="t m0 x48 h1e y7f ff1 fs17 fc0 sc0 ls33 ws1">AND</div><div class="c x16 y80 w6 h1f"><div class="t m0 x0 h1e y81 ff1 fs17 fc0 sc0 ls0 ws1">N</div></div><div class="t m0 x49 h1e y82 ff1 fs17 fc0 sc0 ls0 ws1">o</div><div class="t m0 x4a h1e y83 ff1 fs17 fc0 sc0 ls34 ws1">delay</div><div class="t m0 x9 h1e y84 ff1 fs17 fc0 sc0 ls34 ws1">delay</div><div class="t m0 x4b h20 y85 ff2 fs18 fc0 sc0 ls0 ws1">图<span class="_ _4"> </span>7.1<span class="_ _9"> </span>　延迟比较运动检测方案</div><div class="t mb x4c h21 y86 ff2 fs19 fc0 sc0 ls0 ws1">P</div><div class="t m0 x4d h22 y87 ff2 fs1a fc0 sc0 ls0 ws1">1</div><div class="t m0 x4e h20 y86 ff2 fs18 fc0 sc0 ls0 ws1">和</div><div class="t mb x4f h21 y86 ff2 fs19 fc0 sc0 ls0 ws1">P</div><div class="t m0 x50 h22 y87 ff2 fs1a fc0 sc0 ls0 ws1">2</div><div class="t m0 x12 h20 y86 ff2 fs18 fc0 sc0 ls0 ws1">是对光点瞬时作出响应的检测器</div><div class="t m0 x5 h20 y88 ff1 fs18 fc0 sc0 ls35 ws1">(a) <span class="_"> </span><span class="ff2 ls0">对以合适的速度向左移动的光点，<span class="_ _b"> </span><span class="ff5">P</span></span></div><div class="t m0 x51 h23 y89 ff1 fs1b fc0 sc0 ls0 ws1">1</div><div class="t m0 x52 h20 y8a ff2 fs18 fc0 sc0 ls0 ws1">和<span class="_ _b"> </span><span class="ff5">P</span></div><div class="t m0 x53 h23 y89 ff1 fs1b fc0 sc0 ls0 ws1">2</div><div class="t m0 x1a h20 y8a ff2 fs18 fc0 sc0 ls0 ws1">的响应相重合，</div><div class="t m0 x5 h20 y8b ff2 fs18 fc0 sc0 ls0 ws1">在组合单元处产生正的输出；<span class="_ _3"></span><span class="ff1 ls36">(b) <span class="_"> </span><span class="ff2 ls0">禁止方案，<span class="_ _17"></span>对从<span class="_ _4"> </span><span class="ff5">P</span></span></span></div><div class="t m0 x54 h23 y8c ff1 fs1b fc0 sc0 ls0 ws1">2</div><div class="t m0 x55 h20 y8d ff2 fs18 fc0 sc0 ls0 ws1">和<span class="_ _4"> </span><span class="ff5">P</span></div><div class="t m0 x19 h23 y8c ff1 fs1b fc0 sc0 ls0 ws1">1</div><div class="t m0 x56 h20 y8d ff2 fs18 fc0 sc0 ls0 ws1">的运</div><div class="t m0 x5 h20 y8e ff2 fs18 fc0 sc0 ls0 ws1">动不产生响应，因为<span class="_ _4"> </span><span class="ff5">P</span></div><div class="t m0 x44 h23 y8f ff1 fs1b fc0 sc0 ls0 ws1">2</div><div class="t m0 x1d h20 y90 ff2 fs18 fc0 sc0 ls0 ws1">从的延迟响应抵消了来自<span class="_ _4"> </span><span class="ff5">P</span></div><div class="t m0 x57 h23 y8f ff1 fs1b fc0 sc0 ls0 ws1">1</div><div class="t m0 x58 h20 y90 ff2 fs18 fc0 sc0 ls0 ws1">的响应。</div><div class="t m0 x59 h4 y91 ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x1 h5 y92 ff2 fs2 fc0 sc0 ls0 ws1"> <span class="_"> </span> <span class="_"> </span>另一种比较简单的方法是<span class="_ _18"> </span><span class="ff1 ls23">And-Not<span class="_ _7"> </span></span>方法，这<span class="_ _3"></span>是由<span class="_ _18"> </span><span class="ff1 ls22">Barlow<span class="_ _e"> </span></span>和<span class="_ _18"> </span><span class="ff1">Levick<span class="_ _7"> </span></span>针对在兔子视觉皮</div><div class="t m0 x1 h5 y93 ff2 fs2 fc0 sc0 ls0 ws1">层中有方向选择性单元所提出的模型，这也是<span class="_ _7"> </span><span class="ff1 ls37">Em<span class="_ _17"></span>erso<span class="_"> </span><span class="ff2 ls0">和<span class="_ _e"> </span></span><span class="ls38">Gerstein<span class="_"> </span><span class="ff2 ls0">针对猫的视觉皮层提出的</span></span></span></div><div class="t m0 x1 h5 y94 ff2 fs2 fc0 sc0 ls7 ws1">模型。这些单元被称为方向选<span class="_ _3"></span>择性，因为这些单元对沿所<span class="_ _3"></span>谓的优先方向运动的刺激物的<span class="_ _3"></span>反</div><div class="t m0 x1 h5 y95 ff2 fs2 fc0 sc0 ls0 ws1">应要比对沿相反方向运动的刺激物的反应强烈得多。因为<span class="_ _19"> </span><span class="ff1 ls22">Barlow<span class="_ _b"> </span></span>和<span class="_"> </span><span class="ff1 ls39">Le<span class="_ _2"></span>vick<span class="_ _18"> </span></span>发现了方向选</div><div class="t m0 x1 h5 y96 ff2 fs2 fc0 sc0 ls6 ws1">择性机理之间固有的相互影响的<span class="_ _2"></span>证据，他们提出一种模型<span class="_ _2"></span>，按这种模型运动检测器计算</div><div class="t mc x5a h24 y97 ff4 fs1c fc0 sc0 ls3a ws1">()</div><div class="t m0 x22 h25 y98 ff5 fs1d fc0 sc0 ls0 ws1">t<span class="_ _1a"></span>p<span class="_ _1b"></span>D<span class="_ _1c"> </span><span class="ff1">,</span></div><div class="t m0 x5b h26 y99 ff1 fs1e fc0 sc0 ls0 ws1">1</div><div class="t m0 x5c h5 y98 ff2 fs2 fc0 sc0 ls0 ws1">和</div><div class="t md x5d h24 y97 ff4 fs1c fc0 sc0 ls3b ws1">()</div><div class="t m0 x5e h27 y98 ff5 fs1d fc0 sc0 ls0 ws1">t<span class="_ _1d"></span>t<span class="_ _1e"></span>p<span class="_ _1b"></span>D<span class="_ _1f"> </span><span class="ff4">δ<span class="_ _20"></span>−<span class="_ _21"></span><span class="ff1">,</span></span></div><div class="t m0 x5f h26 y99 ff1 fs1e fc0 sc0 ls0 ws1">2</div><div class="t m0 x60 h5 y98 ff2 fs2 fc0 sc0 ls0 ws1">“<span class="ff1 ls3c">Not</span>”<span class="ff1"> <span class="_ _f"> </span></span>的“<span class="ff1 ls3c">And</span>”（图<span class="_ _19"> </span><span class="ff1 ls3d">7.1(b)</span>）。按这种方案，从<span class="_ _e"> </span><span class="ff5 fs13">p</span></div><div class="t m0 x61 h26 y9a ff1 fs1e fc0 sc0 ls0 ws1">2</div><div class="t m0 x62 h5 y98 ff2 fs2 fc0 sc0 ls0 ws1">到<span class="_ _e"> </span><span class="ff5 fs13">p</span></div><div class="t m0 x63 h26 y9a ff1 fs1e fc0 sc0 ls0 ws1">1</div><div class="t m0 x64 h5 y98 ff2 fs2 fc0 sc0 ls0 ws1">的运动由</div><div class="t m0 x1 h5 y9b ff2 fs2 fc0 sc0 ls0 ws1">于来自<span class="_ _e"> </span><span class="ff5 fsd">p</span></div><div class="t m0 x65 h11 y9c ff1 fse fc0 sc0 ls0 ws1">2</div><div class="t m0 x66 h5 y9b ff2 fs2 fc0 sc0 ls0 ws1">的响应被延迟而被禁止，而从<span class="_ _e"> </span><span class="ff5 fsd">p</span></div><div class="t m0 x11 h11 y9c ff1 fse fc0 sc0 ls0 ws1">1</div><div class="t m0 x67 h5 y9b ff2 fs2 fc0 sc0 ls0 ws1">到<span class="_ _e"> </span><span class="ff5 fsd">p</span></div><div class="t m0 x28 h11 y9c ff1 fse fc0 sc0 ls0 ws1">2</div><div class="t m0 x68 h5 y9b ff2 fs2 fc0 sc0 ls0 ws1">的运动产生一个正的响应。<span class="ff1"> </span></div><div class="t m0 x1 h5 y9d ff2 fs2 fc0 sc0 ls3e ws1"> <span class="ff1 ls3f">Torre<span class="_ _22"> </span></span><span class="ls0">和<span class="_"> </span><span class="ff1 ls26">Reichardt<span class="_ _b"> </span></span><span class="ls16">对家蝇的视觉系统提出一种相似的方案，按这种方案，用低通时间</span></span></div><div class="t m0 x1 h5 y9e ff2 fs2 fc0 sc0 ls40 ws1">滤波代替延迟。<span class="ff1 ls3f">Torre<span class="_ _13"> </span></span><span class="ls0">和<span class="_ _12"> </span><span class="ff1 ls1d">poggio<span class="_ _1"> </span></span></span>描述了一种实现这种计算的很巧妙<span class="_ _3"></span>的触突（<span class="ff1 ls41">synaptie </span></div><div class="t m0 x1 h5 y9f ff1 fs2 fc0 sc0 ls42 ws1">mechanism<span class="ff2 ls0">）机理。<span class="ff1"> </span></span></div><div class="t m0 x1 h5 ya0 ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _13"> </span>延迟比较的某些通用特性值得加以注<span class="_ _3"></span>意。第一，这些检测器不仅<span class="_ _3"></span>有选择地对连续运动</div><div class="t m0 x1 h5 ya1 ff2 fs2 fc0 sc0 ls16 ws1">作出响应<span class="ff1 ls0">,</span>而且对在</div><div class="t m0 x69 h1a ya2 ff5 fs13 fc0 sc0 ls0 ws1">p</div><div class="t m0 x6a h26 ya3 ff1 fs1e fc0 sc0 ls0 ws1">1</div><div class="t m0 x6b h5 ya2 ff2 fs2 fc0 sc0 ls16 ws1">位置和<span class="_ _e"> </span><span class="ff5 fs13 ls0">p</span></div><div class="t m0 x6c h26 ya3 ff1 fs1e fc0 sc0 ls0 ws1">2</div><div class="t m0 x33 h5 ya2 ff2 fs2 fc0 sc0 ls16 ws1">位置之间刺激物的跳跃也作出<span class="_ _2"></span>响应；其次<span class="ff1 ls0">,</span>这<span class="_ _2"></span>样的检测器有</div><div class="t m0 x1 h5 ya4 ff2 fs2 fc0 sc0 ls7 ws1">一些明显的局限性，例如<span class="ff1 ls0">,</span>运动的速度必须在某个由延迟<span class="ff1 ls0">(</span>或低通滤波<span class="ff1 ls0">)</span>接收器的分离距离决</div><div class="t m0 x1 h5 ya5 ff2 fs2 fc0 sc0 ls7 ws1">定的范围之内；最后，单个这<span class="_ _3"></span>种类型的检测器的输出不能<span class="_ _3"></span>可靠地决定运动测量。例如，<span class="_ _3"></span>在</div><div class="t m0 x1 h5 ya6 ff2 fs2 fc0 sc0 ls1c ws1">有许多运动物体的视场里，如果在</div><div class="t m0 x6d h1a ya7 ff5 fs13 fc0 sc0 ls0 ws1">p</div><div class="t m0 x6e h26 ya8 ff1 fs1e fc0 sc0 ls0 ws1">1</div><div class="t m0 x6f h5 ya7 ff2 fs2 fc0 sc0 ls1c ws1">点的检测器由一个运动物体所激发，而在<span class="_ _9"> </span><span class="ff5 fs13 ls0">p</span></div><div class="t m0 x70 h26 ya8 ff1 fs1e fc0 sc0 ls0 ws1">2</div><div class="t m0 x71 h5 ya7 ff2 fs2 fc0 sc0 ls1c ws1">处的检</div><div class="t m0 x1 h5 ya9 ff2 fs2 fc0 sc0 ls7 ws1">测器又由另一个物体所激发，<span class="_ _3"></span>这种类型的运动检测器就会<span class="_ _3"></span>错误动作。为了得到准确可靠<span class="_ _3"></span>的</div><div class="t m0 x1 h5 yaa ff2 fs2 fc0 sc0 ls0 ws1">运动测量，来自这样检测器阵列的输出应被组合在一起。<span class="ff1"> </span></div><div class="t m0 x1 h5 yab ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _13"> </span>另外的相关技术，例如利用原始灰度<span class="_ _3"></span>值上的交叉相关，已被作为<span class="_ _3"></span>人类视觉系统中的运</div><div class="t m0 x1 h5 yac ff2 fs2 fc0 sc0 ls7 ws1">动测量模型提出来。<span class="ff1 ls1e">Anstis<span class="_ _22"> </span></span>提一种相减的方法，按这种方法把两帧相继<span class="_ _3"></span>图象移位相减，所</div><div class="t m0 x1 h5 yad ff2 fs2 fc0 sc0 ls16 ws1">得图象中的减小点就标志偏离<span class="_ _2"></span>（<span class="ff1 ls1e">displacement</span>）。一般来说，还没有得到关于生<span class="_ _2"></span>理上实现这</div><div class="t m0 x1 h5 yae ff2 fs2 fc0 sc0 ls7 ws1">样技术的模型的描述。似乎还<span class="_ _3"></span>没有很有说服力的证据说明<span class="_ _3"></span>在人类视觉系统中存在这样的<span class="_ _3"></span>模</div><div class="t m0 x1 h5 yaf ff2 fs2 fc0 sc0 ls0 ws1">型。<span class="ff1"> </span></div><div class="t m0 x1 h5 yb0 ff2 fs2 fc0 sc0 ls28 ws1"> <span class="ff1 ls3">(2) </span><span class="ls0">梯度方案（<span class="ff1 ls1e ws9">gradient schem<span class="_ _3"></span>es<span class="ff2 ls0 ws1">）<span class="ff1"> </span></span></span></span></div><div class="t m0 x1 h5 yb1 ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _13"> </span>最近一种用于生理系统运动检测和量<span class="_ _3"></span>测运动的梯度方案，它被作<span class="_ _3"></span>为单个皮层细胞进行</div><div class="t m0 x1 h5 yb2 ff2 fs2 fc0 sc0 ls16 ws1">运动分析的模型。这些在猫和猴子的主要视觉皮层（<span class="ff1 ls43 wsa">perennial visual cortex</span>）中发现<span class="_ _3"></span>的细胞</div><div class="t m0 x1 h5 yb3 ff2 fs2 fc0 sc0 ls7 ws1">有选择地对边缘和光带（<span class="ff1 ls44 wsb">Bar of light<span class="_ _2"></span></span>）作出响应。这些细胞对方位，并且经常对运<span class="_ _2"></span>动的方</div><div class="t m0 x1 h5 yb4 ff2 fs2 fc0 sc0 ls7 ws1">向也是有选择性的。这就是说<span class="_ _3"></span>，要激发这样的单元，刺激<span class="_ _3"></span>物必须具有这种单元所选择的<span class="_ _3"></span>方</div><div class="t m0 x1 h5 yb5 ff2 fs2 fc0 sc0 ls7 ws1">位，并且必须沿所选择的方向<span class="_ _3"></span>运动。因此对这种简单细胞<span class="_ _3"></span>的结构和功能的分析揭示了视<span class="_ _3"></span>觉</div><div class="t m0 x1 h5 yb6 ff2 fs2 fc0 sc0 ls7 ws1">运动的早期检测和测量的机理<span class="_ _3"></span>。这些机理可被用于计算机<span class="_ _3"></span>视觉系统。为了理解简单细胞<span class="_ _3"></span>的</div><div class="t m0 x1 h5 yb7 ff2 fs2 fc0 sc0 ls0 ws1">作用，我们需要粗略地描述视网膜对图象的处理。<span class="ff1"> </span></div><div class="t m0 x1 h5 yb8 ff2 fs2 fc0 sc0 ls28 ws1"> <span class="ff1 ls3">(3) </span><span class="ls0">视网膜对图象的处理<span class="ff1"> </span></span></div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>

<div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/626e691615314c70c3957c53/bg4.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0"> 133</div><div class="t m0 x72 h5 yb9 ff2 fs2 fc0 sc0 ls7 ws1">视网膜结构主要完成两个功能。<span class="_ _3"></span>第一个是把进入的光线记<span class="_ _3"></span>录在对光敏感的光接收器阵</div><div class="t m0 x1 h5 yba ff2 fs2 fc0 sc0 ls7 ws1">列上。第二，所记录的图象完<span class="_ _3"></span>成初始的转换。所转换的图<span class="_ _3"></span>象从最后的视网膜细胞层（神<span class="_ _3"></span>经</div><div class="t m0 x1 h5 ybb ff2 fs2 fc0 sc0 ls0 ws1">节细胞层）沿着大约上百万的神经纤维送到<span class="_"> </span><span class="ff1 ls45">LGN</span>（外侧膝状<span class="_ _2"></span>体），并从<span class="_"> </span><span class="ff1 ls46">LGN<span class="_ _b"> </span></span><span class="ls16">送到视觉皮</span></div><div class="t m0 x1 h5 ybc ff2 fs2 fc0 sc0 ls0 ws1">层。如前所述，视网膜对图象<span class="_ _22"> </span><span class="ff1">I<span class="_ _7"> </span></span>进行</div><div class="t me x11 h28 ybd ff4 fs1f fc0 sc0 ls47 ws1">()</div><div class="t m0 x73 h29 ybe ff5 fs17 fc0 sc0 ls0 ws1">d</div><div class="t m0 x74 h29 ybf ff5 fs17 fc0 sc0 ls0 ws1">dx</div><div class="t m0 x75 h29 yc0 ff5 fs17 fc0 sc0 ls48 ws1">GI</div><div class="t m0 x1b h26 yc1 ff1 fs1e fc0 sc0 ls0 ws1">2</div><div class="t m0 x76 h26 yc2 ff1 fs1e fc0 sc0 ls0 ws1">2</div><div class="t m0 x77 h2a yc0 ff4 fs17 fc0 sc0 ls0 ws1">∗<span class="_ _23"> </span><span class="ff2 fs2">运算，<span class="_ _f"> </span></span><span class="ff5">G<span class="_ _4"> </span><span class="ff2 fs2">是高斯函数。运算后结果中的过</span></span></div><div class="t m0 x1 h5 yc3 ff2 fs2 fc0 sc0 ls0 ws1">零点对应于原始图象中灰度急剧变化处，利用附加的子单<span class="_ _2"></span>元可确定过零点的运动。设<span class="_"> </span><span class="ff1">Z<span class="_ _22"> </span></span>表</div><div class="t m0 x1 h5 yc4 ff2 fs2 fc0 sc0 ls1c ws1">示过零点当前的位置。从图<span class="_"> </span><span class="ff1 ls1">7.2<span class="_ _22"> </span></span>可看到，如<span class="_ _2"></span>果过零点向右运动，在位<span class="_ _2"></span>置<span class="_"> </span><span class="ff1 ls0">Z<span class="_ _22"> </span></span>的卷积值就增</div><div class="t m0 x1 h5 yc5 ff2 fs2 fc0 sc0 ls7 ws1">加；如果过零点向左运动，这<span class="_ _3"></span>个值就减小。因此，通过检<span class="_ _3"></span>查卷积对时间的导数的符号就<span class="_ _3"></span>可</div><div class="t m0 x1 h5 yc6 ff2 fs2 fc0 sc0 ls0 ws1">以明确地确定运动的方向。<span class="ff1"> </span></div><div class="t m0 x78 h4 yc7 ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x79 h5 yc8 ff2 fs2 fc0 sc0 ls0 ws1">图<span class="_ _4"> </span><span class="ff1 ls1d">7.2 </span></div><div class="t m0 x1 h5 yc9 ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _13"> </span>按这种方案，运动可由过零点的斜率<span class="_ _3"></span>和时间导数来确定，因此，<span class="_ _3"></span>这是以灰度为基础的</div><div class="t m0 x1 h5 yca ff2 fs2 fc0 sc0 ls6 ws1">方案，它不要求在时间域上作元<span class="_ _2"></span>素的匹配。在相反方向上<span class="_ _2"></span>的运动是由另外的单元来检测</div><div class="t m0 x1 h5 ycb ff2 fs2 fc0 sc0 ls0 ws1">的。这样的一个关于人类视觉的观点得到心理物理学证据的支持。<span class="ff1"> </span></div><div class="t m0 x72 h5 ycc ff2 fs2 fc0 sc0 ls1f ws1">利用这种方案，可以将过零点轮廓用于运动量测。然而，由于图<span class="_"> </span><span class="ff1 ls1d">7.3<span class="_ _b"> </span></span>中所示的孔径问</div><div class="t m0 x1 h5 ycd ff2 fs2 fc0 sc0 ls7 ws1">题，以纯粹的局部测量为基础<span class="_ _3"></span>既不可能完全地确定轮廓的<span class="_ _3"></span>运动，也不可能完全地确定任<span class="_ _3"></span>何</div><div class="t m0 x1 h5 yce ff2 fs2 fc0 sc0 ls7 ws1">其他线性特性。如果是由跟轮<span class="_ _3"></span>廓相比较小的单元来检测运<span class="_ _3"></span>动，可以抽取的唯一信息是垂<span class="_ _3"></span>直</div><div class="t m0 x1 h5 ycf ff2 fs2 fc0 sc0 ls7 ws1">于局部边缘方向的运动分量。<span class="_ _3"></span>沿边缘的运动是感觉不到的<span class="_ _3"></span>。要完全地确定运动，在第二<span class="_ _3"></span>阶</div><div class="t m0 x1 h5 yd0 ff2 fs2 fc0 sc0 ls0 ws1">段必须组合局部量测，或者在局部邻域中沿着轮廓检测。<span class="ff1"> </span></div><div class="t m0 x1 h5 yd1 ff2 fs2 fc0 sc0 ls28 ws1"> <span class="ff1 ls3">(4) </span><span class="ls0">计算机视觉中的以灰度为基础的技术<span class="ff1"> </span></span></div><div class="t m0 x1 h5 yd2 ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _13"> </span>已经提出了许多用于计算机视觉系统<span class="_ _3"></span>的以灰度为基础的运动检测<span class="_ _3"></span>和测量的方案。其中</div><div class="t m0 x1 h5 yd3 ff2 fs2 fc0 sc0 ls7 ws1">一个方案是用于测量图象对中<span class="_ _3"></span>运动的灰度交叉相关技术。<span class="_ _3"></span>例如，这种技术可用于根据卫<span class="_ _3"></span>星</div><div class="t m0 x1 h5 yd4 ff2 fs2 fc0 sc0 ls0 ws1">图象数据测量云层的运动，以及用于交通控制和用于<span class="_ _22"> </span><span class="ff1 ls49">SLR<span class="_ _e"> </span></span>图象的比较。已提出一种基于比</div><div class="t m0 x1 h5 yd5 ff2 fs2 fc0 sc0 ls7 ws1">较小的图象区域上灰度分布的<span class="_ _3"></span>方案。图象相减的方法已被<span class="_ _3"></span>用于运动和变化探测以及用于<span class="_ _3"></span>运</div><div class="t m0 x1 h5 yd6 ff2 fs2 fc0 sc0 ls0 ws1">动测量。<span class="ff1"> </span></div><div class="t m0 x1 h5 yd7 ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _13"> </span>大多数交叉相关法和相减法的基本问<span class="_ _3"></span>题是这些方法假设图象（或<span class="_ _3"></span>大部分图象）是作为</div><div class="t m0 x1 h5 yd8 ff2 fs2 fc0 sc0 ls7 ws1">整体在两帧图象之间运动。包<span class="_ _3"></span>含独立运动物体的图象以及<span class="_ _3"></span>由物体在空间无限制地运动引<span class="_ _3"></span>入</div><div class="t m0 x1 h5 yd9 ff2 fs2 fc0 sc0 ls0 ws1">的图象畸变造成了这些技术的困难。<span class="ff1"> </span></div><div class="t m0 x72 h4 yda ff1 fs2 fc0 sc0 ls0 ws1"> </div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>

<div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/626e691615314c70c3957c53/bg5.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0"> 134</div><div class="t m0 x7a h2b ydb ff1 fs18 fc0 sc0 ls0 ws1">C</div><div class="t m0 x7b h2b ydc ff1 fs18 fc0 sc0 ls0 ws1">B</div><div class="t m0 x67 h2b ydd ff1 fs18 fc0 sc0 ls0 ws1">A</div><div class="t m0 x33 h2b yde ff1 fs18 fc0 sc0 ls0 ws1">E</div><div class="t m0 x7c h20 ydf ff2 fs18 fc0 sc0 ls0 ws1">图<span class="_ _4"> </span><span class="ff1">7.3<span class="_"> </span></span>　孔径问题</div><div class="t m0 x23 h20 ye0 ff2 fs18 fc0 sc0 ls0 ws1">孔径比运动的轮<span class="_ _2"></span>廓小时，<span class="_ _2"></span>不能唯一<span class="_ _2"></span>地确定运动方<span class="_ _2"></span>法，从对</div><div class="c x7d ye1 w7 h2c"><div class="t m0 x0 h20 ye2 ff2 fs18 fc0 sc0 ls0 ws1">孔</div></div><div class="t m0 x23 h20 ye3 ff2 fs18 fc0 sc0 ls0 ws1">径<span class="_ _4"> </span><span class="ff1">A<span class="_"> </span></span>观察不可能确定边缘是朝<span class="_ _9"> </span><span class="ff1">B<span class="_"> </span></span>方向还是朝<span class="_ _4"> </span><span class="ff1">C<span class="_"> </span></span>方向运动。</div><div class="t m0 x14 h4 ye4 ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x1 h5 ye5 ff2 fs2 fc0 sc0 ls28 ws1"> <span class="ff1 ls3">(5) </span><span class="ls0">计算机视觉系统中的梯度方法<span class="ff1"> </span></span></div><div class="t m0 x1 h5 ye6 ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _13"> </span>这些方法都基于在给定点上的灰度梯<span class="_ _3"></span>度和在这些点当灰度图案运<span class="_ _3"></span>动时引入的灰度随时</div><div class="t m0 x1 h5 ye7 ff2 fs2 fc0 sc0 ls0 ws1">间变化之间关系。如果</div><div class="t mf x7e hc ye8 ff4 fs9 fc0 sc0 ls4a ws1">()</div><div class="t m0 x7f h5 ye7 ff5 fs17 fc0 sc0 ls4b ws1">Ex<span class="_ _4"> </span>y<span class="_ _24"></span><span class="ff1 ls0">,<span class="_ _d"> </span><span class="ff2 fs2">表示图象中的光强，那么<span class="ff1"> </span></span></span></div><div class="t m0 x80 h2d ye9 ff5 fs20 fc0 sc0 ls0 ws1">v<span class="_ _25"></span>E<span class="_ _26"></span>u<span class="_ _25"></span>E</div><div class="t m0 x81 h2d yea ff5 fs20 fc0 sc0 ls0 ws1">d</div><div class="c x81 yeb w8 h2e"><div class="t m0 x82 h2d yec ff5 fs20 fc0 sc0 ls0 ws1">t</div></div><div class="t m0 x83 h2d yed ff5 fs20 fc0 sc0 ls0 ws1">dE</div><div class="t m0 x84 h2f yee ff5 fs21 fc0 sc0 ls0 ws1">y<span class="_ _27"></span>x</div><div class="t m0 x15 h30 ye9 ff4 fs20 fc0 sc0 ls0 ws1">+<span class="_ _28"></span>=<span class="_ _29"></span>−<span class="_ _2a"> </span><span class="ff1 fs2"> </span></div><div class="t m0 x1 h5 yef ff2 fs2 fc0 sc0 ls4c ws1"> 其<span class="_ _2b"></span>中</div><div class="t m0 x85 h19 yf0 ff5 fsd fc0 sc0 ls4d ws1">dE<span class="_ _13"> </span>dt</div><div class="t m0 x29 h5 yf1 ff2 fs2 fc0 sc0 ls1f ws1">是在位置</div><div class="t m10 x86 hc yf2 ff4 fs9 fc0 sc0 ls4e ws1">()</div><div class="t m0 x4d h5 yf1 ff5 fs17 fc0 sc0 ls4f ws1">xy<span class="_ _1d"></span><span class="ff1 ls0">,<span class="_ _d"> </span><span class="ff2 fs2 ls1f">处灰度随时间的变化；<span class="_ _0"> </span></span><span class="ff5 ls50">EE</span></span></div><div class="t m0 x87 h2d yf3 ff5 fs20 fc0 sc0 ls51 ws1">xy</div><div class="t m0 x88 h31 yf1 ff2 fs17 fc0 sc0 ls0 ws1">和<span class="_ _2c"> </span><span class="fs2 ls1f">表示在这个图象点的灰度</span></div><div class="t m0 x1 h5 yf4 ff2 fs2 fc0 sc0 ls0 ws1">梯度；</div><div class="t m0 x89 h29 yf5 ff5 fs17 fc0 sc0 ls0 ws1">u</div><div class="c x8a yf6 w9 h32"><div class="t m0 x0 h29 y64 ff5 fs17 fc0 sc0 ls0 ws1">v</div></div><div class="t m0 x8b h5 yf5 ff1 fs12 fc0 sc0 ls0 ws1">,<span class="_ _2d"> </span><span class="ff2 fs2">是沿</span></div><div class="t m0 x8c h33 yf7 ff5 fs22 fc0 sc0 ls52 ws1">xy<span class="_ _29"></span><span class="ff2 ls0">和</span></div><div class="t m0 x8d h5 yf5 ff2 fs2 fc0 sc0 ls0 ws1">方向的局部速度。<span class="ff1"> </span></div><div class="t m0 x1 h5 yf8 ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _13"> </span>梯度方法和过零点方法在几个方面是<span class="_ _3"></span>相似的。这两种方法都利用<span class="_ _3"></span>时间变化和图象梯度</div><div class="t m0 x1 h5 yf9 ff2 fs2 fc0 sc0 ls0 ws1">去测量在梯度方向上的局部运动。<span class="ff1"> </span></div><div class="t m0 x1 h5 yfa ff2 fs2 fc0 sc0 ls7 ws1"> <span class="_"> </span> <span class="_ _13"> </span>以灰度为基础的图象速度场计算方法<span class="_ _3"></span>还有一些困难问题有待解决<span class="_ _3"></span>。因为在一般情况下</div><div class="t m0 x1 h5 yfb ff2 fs2 fc0 sc0 ls7 ws1">（无限制的运动，几个物体）<span class="_ _3"></span>图象的不同部分有不同的运<span class="_ _3"></span>动。所以，原先的初始量测是<span class="_ _3"></span>局</div><div class="t m0 x1 h5 yfc ff2 fs2 fc0 sc0 ls7 ws1">部的。这些量测不足以完全确<span class="_ _3"></span>定运动。因此，在稍后的阶<span class="_ _3"></span>段必须将局部测量组合起来。<span class="_ _3"></span>组</div><div class="t m0 x1 h5 yfd ff2 fs2 fc0 sc0 ls0 ws1">合阶段是理解生理系统和构成计算机视觉系统中主要的未被解决的问题。<span class="ff1"> </span></div><div class="t m0 x1 hf yfe ff3 fsc fc0 sc0 ls1a ws1">3. <span class="ff6 sc1 ls53">标记匹配方案</span><span class="ls0"> </span></div><div class="t m0 x1 h5 yff ff2 fs2 fc0 sc0 ls54 ws1"> <span class="_ _1"> </span> <span class="_ _1"> </span>按测量运动的标记匹配方法，首先要确定可识别的<span class="_ _2"></span>基</div><div class="t m0 x1 h5 y100 ff2 fs2 fc0 sc0 ls19 ws1">元—标记，然后匹配不同时间的标记。以上所讨论的表观<span class="_ _3"></span>运</div><div class="t m0 x1 h5 y101 ff2 fs2 fc0 sc0 ls0 ws1">动现象（<span class="ff1 ls55 wsc">apperent motion <span class="_ _3"></span>phenomena<span class="ff2 ls0 ws1">）说明了人类视觉系统有</span></span></div><div class="t m0 x1 h5 y102 ff2 fs2 fc0 sc0 ls19 ws1">能力通过匹配在空间和时间上相距相当间隔的标记来建立<span class="_ _3"></span>运</div><div class="t m0 x1 h5 y103 ff2 fs2 fc0 sc0 ls19 ws1">动感觉。在检测相继出现的基元之间的连续运动时，视觉<span class="_ _3"></span>系</div><div class="t m0 x1 h5 y104 ff2 fs2 fc0 sc0 ls19 ws1">统必须建立依次出现的基元之间的对应关系。这就是说，<span class="_ _3"></span>在</div><div class="t m0 x1 h5 y105 ff2 fs2 fc0 sc0 ls19 ws1">第二帧图象中必须找到跟第一帧中的基元相对应的基元的<span class="_ _3"></span>位</div><div class="t m0 x1 h5 y106 ff2 fs2 fc0 sc0 ls7 ws1">置。一个简单的对应问题如图<span class="_"> </span><span class="ff1 ls30">7-4<span class="_ _22"> </span></span>中所示。图中实心的小<span class="_ _2"></span>圆</div><div class="t m0 x1 h5 y107 ff2 fs2 fc0 sc0 ls19 ws1">表示在第一帧中的，空心小圆表示在第二帧圆的。在这两<span class="_ _3"></span>帧</div><div class="t m0 x1 h5 y108 ff2 fs2 fc0 sc0 ls19 ws1">图中有两种可能的一对一的匹配，这导致两种可能的可感<span class="_ _3"></span>觉</div><div class="t m0 x1 h5 y109 ff2 fs2 fc0 sc0 ls0 ws1">的运动：水平的和对角线的。<span class="ff1"> </span></div><div class="t m0 x1 h5 y10a ff2 fs2 fc0 sc0 ls56 ws1"> 在<span class="_ _2b"></span>图<span class="ff1 ls30">7-4<span class="_ _22"> </span></span><span class="ls7">中只有两<span class="_ _2"></span>种方式的多义性，在实际中，每帧图</span></div><div class="t m0 x1 h5 y10b ff2 fs2 fc0 sc0 ls19 ws1">中可包含许多排列成复杂图形的基元，因此必须在它们之<span class="_ _3"></span>间</div><div class="t m0 x1 h5 y10c ff2 fs2 fc0 sc0 ls19 ws1">建立对应关系。对控制人类视觉系统中对应过程的规律已<span class="_ _3"></span>进</div><div class="t m0 x1 h5 y10d ff2 fs2 fc0 sc0 ls0 ws1">行了若干研究，但离完全理解这个问题还很远。<span class="ff1"> </span></div><div class="t m0 x1 h5 y10e ff2 fs2 fc0 sc0 ls19 ws1"> <span class="_ _1"> </span> <span class="_ _1"> </span>当参加运动的基元是一些孤立的点，它们的对应关系<span class="_ _3"></span>主</div><div class="t m0 x1 h5 y10f ff2 fs2 fc0 sc0 ls7 ws1">要由点之间的距离来控制。在<span class="_ _3"></span>其他参数相同的条件下，每<span class="_ _3"></span>个点优先跟下一帧中相距最近<span class="_ _3"></span>的</div><div class="t m0 x1 h5 y110 ff2 fs2 fc0 sc0 ls0 ws1">点匹配。<span class="ff1"> </span></div><div class="t m0 x8e h4 y111 ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x8e h4 y112 ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x8e h4 y113 ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x8e h4 y114 ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x8e h4 y115 ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x8e h4 y116 ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x8e h4 y117 ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x8e h4 y118 ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x8e h4 y119 ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x8e h4 y11a ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x8e h4 y11b ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x8e h4 y11c ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x8e h4 y11d ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x8e h5 y11e ff2 fs2 fc0 sc0 ls0 ws1">图<span class="_ _2e"> </span><span class="ff1 ls30">7-4<span class="_ _2f"></span></span><span class="ls9"> <span class="_ _1"> </span>对应性问题，</span><span class="ff1">P</span></div><div class="t m0 x8f h11 y11f ff1 fse fc0 sc0 ls0 ws1">1</div><div class="t m0 x8e h5 y120 ff2 fs2 fc0 sc0 ls0 ws1">和<span class="_ _18"> </span><span class="ff1">P</span></div><div class="t m0 x90 h11 y121 ff1 fse fc0 sc0 ls0 ws1">2</div><div class="t m0 x91 h5 y120 ff2 fs2 fc0 sc0 ls0 ws1">在第一帧，<span class="ff1">Q</span></div><div class="t m0 x92 h11 y121 ff1 fse fc0 sc0 ls0 ws1">1</div><div class="t m0 x93 h5 y120 ff2 fs2 fc0 sc0 ls0 ws1">和<span class="_ _18"> </span><span class="ff1">Q</span></div><div class="t m0 x8f h11 y121 ff1 fse fc0 sc0 ls0 ws1">2</div><div class="t m0 x8e h5 y122 ff2 fs2 fc0 sc0 ls0 ws1">在下一帧。<span class="ff1"> </span></div><div class="t m0 x94 h4 y123 ff1 fs2 fc0 sc0 ls0 ws1">o</div><div class="c x94 y124 wa h34"><div class="t m0 x82 h4 y125 ff1 fs2 fc0 sc0 ls0 ws1">r</div></div><div class="t m0 x95 h4 y126 ff1 fs2 fc0 sc0 ls0 ws1">P</div><div class="t m0 x96 h11 y127 ff1 fse fc0 sc0 ls0 ws1">2</div><div class="t m0 x97 h4 y126 ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x98 h4 y128 ff1 fs2 fc0 sc0 ls1d ws1">d </div><div class="t m0 x63 h4 y129 ff1 fs2 fc0 sc0 ls0 ws1">Q</div><div class="t m0 x92 h11 y12a ff1 fse fc0 sc0 ls0 ws1">1</div><div class="t m0 x98 h4 y12b ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x99 h4 y12c ff1 fs2 fc0 sc0 ls0 ws1">c</div><div class="t m0 x9a h4 y12d ff1 fs2 fc0 sc0 ls0 ws1">Q</div><div class="t m0 x94 h11 y12e ff1 fse fc0 sc0 ls0 ws1">2</div><div class="t m0 x19 h4 y12b ff1 fs2 fc0 sc0 ls0 ws1">P</div><div class="t m0 x56 h11 y12a ff1 fse fc0 sc0 ls0 ws1">1</div><div class="t m0 x9b h4 y12b ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x9c h4 y12f ff1 fs2 fc0 sc0 ls0 ws1">Q</div><div class="t m0 x63 h11 y130 ff1 fse fc0 sc0 ls57 ws1">1 </div><div class="t m0 x9d h4 y131 ff1 fs2 fc0 sc0 ls0 ws1">P</div><div class="t m0 x9e h11 y132 ff1 fse fc0 sc0 ls0 ws1">2</div><div class="t m0 x9f h4 y131 ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="c xa0 y133 w9 h34"><div class="t m0 x0 h4 y125 ff1 fs2 fc0 sc0 ls0 ws1">b</div></div><div class="t m0 xa1 h4 y134 ff1 fs2 fc0 sc0 ls0 ws1"> </div><div class="t m0 x90 h4 y135 ff1 fs2 fc0 sc0 ls0 ws1">P</div><div class="t m0 x91 h11 y136 ff1 fse fc0 sc0 ls0 ws1">1</div><div class="t m0 xa2 h4 y137 ff1 fs2 fc0 sc0 ls0 ws1">Q</div><div class="t m0 xa3 h11 y138 ff1 fse fc0 sc0 ls0 ws1">2</div><div class="t m0 xa4 h4 y139 ff1 fs2 fc0 sc0 ls42 ws1">a </div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>