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<link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/css/base.min.css" rel="stylesheet"/><link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/css/fancy.min.css" rel="stylesheet"/><link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89705463/raw.css" rel="stylesheet"/><div id="sidebar" style="display: none"><div id="outline"></div></div><div class="pf w0 h0" data-page-no="1" id="pf1"><div class="pc pc1 w0 h0"><img alt="" class="bi x0 y0 w1 h1" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89705463/bg1.jpg"/><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">1<span class="_ _0"> </span><span class="ff2">前言（一级标题）</span></div><div class="t m0 x1 h2 y2 ff2 fs0 fc0 sc0 ls0 ws0">轮廓描述是图像目标形状边缘特性的重要表示方法，<span class="_ _1"></span>结合边缘提取的特点，<span class="_ _1"></span>其表</div><div class="t m0 x1 h2 y3 ff2 fs0 fc0 sc0 ls0 ws0">示的<span class="_ _2"></span>精确<span class="_ _2"></span>性由<span class="_ _2"></span>以下<span class="_ _2"></span>三个<span class="_ _2"></span>方面<span class="_ _2"></span>的因<span class="_ _2"></span>素<span class="ff1">[1]<span class="_ _2"></span></span>决定<span class="_ _2"></span>：⑴<span class="_ _2"></span><span class="ff1"> </span>边<span class="_ _2"></span>缘点<span class="_ _2"></span>位置<span class="_ _2"></span>估计<span class="_ _2"></span>的精<span class="_ _2"></span>确度<span class="_ _2"></span>；⑵<span class="_ _2"></span><span class="ff1"> </span></div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 ls0 ws0">曲线拟合算法的<span class="_ _2"></span>性能；⑶<span class="ff1"> </span>用于轮廓建模的<span class="_ _2"></span>曲线形式。基于几何特性<span class="_ _2"></span>的形状描述</div><div class="t m0 x1 h2 y5 ff2 fs0 fc0 sc0 ls0 ws0">方法能够提供较为直接的形象感知，<span class="_ _3"></span>其表现为空间域的特性使得后续的处理变得</div><div class="t m0 x1 h2 y6 ff2 fs0 fc0 sc0 ls0 ws0">复杂、代价大<span class="_ _2"></span><span class="ff1">[2]</span>。基于<span class="_ _0"> </span><span class="ff1">Fourier<span class="_ _0"> </span></span>变换的形状描<span class="_ _2"></span>述方法将形状变换到频<span class="_ _2"></span>率域来处</div><div class="t m0 x1 h2 y7 ff2 fs0 fc0 sc0 ls0 ws0">理，<span class="_ _4"></span>使得形状分析变得更加快捷高效。<span class="_ _4"></span><span class="ff1">Wavelet<span class="_ _0"> </span><span class="ff2">变换理论是在窗口<span class="_ _0"> </span></span>Fourier<span class="_ _0"> </span><span class="ff2">变换</span></span></div><div class="t m0 x1 h2 y8 ff2 fs0 fc0 sc0 ls0 ws0">的基础上发展起来的，<span class="_ _1"></span>它更是提供天然的多分辨率表示，<span class="_ _1"></span>基于<span class="_ _0"> </span><span class="ff1">Wavelet<span class="_ _0"> </span></span>变换的形</div><div class="t m0 x1 h2 y9 ff2 fs0 fc0 sc0 ls0 ws0">状表示方法则提供了对形状的多尺度描述<span class="ff1">[3] [4]</span>。</div><div class="t m0 x1 h2 ya ff2 fs0 fc0 sc0 ls0 ws0">围绕第⑶方面因素，<span class="_ _1"></span>本文将通过实验对频率域特性描述子的描述性、<span class="_ _1"></span>视觉不变性</div><div class="t m0 x1 h2 yb ff2 fs0 fc0 sc0 ls0 ws0">和鲁<span class="_ _2"></span>棒性<span class="_ _2"></span>的对<span class="_ _2"></span>比分<span class="_ _2"></span>析，<span class="_ _2"></span>讨论<span class="_ _2"></span>两种<span class="_ _2"></span>基于<span class="_ _2"></span>频率<span class="_ _2"></span>域特<span class="_ _2"></span>性的<span class="_ _2"></span>平面<span class="_ _2"></span>闭合<span class="_ _2"></span>轮廓<span class="_ _2"></span>曲线<span class="_ _2"></span>描述<span class="_ _2"></span>方法</div><div class="t m0 x1 h2 yc ff2 fs0 fc0 sc0 ls0 ws0">（傅立叶描述子，<span class="_ _5"></span><span class="ff1">Fourier Descriptor, FD<span class="_ _6"> </span><span class="ff2">和小波描述子，<span class="_ _5"></span><span class="ff1">Wavelet Descriptor, </span></span></span></div><div class="t m0 x1 h2 yd ff1 fs0 fc0 sc0 ls0 ws0">WD<span class="ff2">）<span class="_ _1"></span>在形状分析及识别过程中的性能，<span class="_ _1"></span>并提出一种基于小波包分解的轮廓曲线描</span></div><div class="t m0 x1 h2 ye ff2 fs0 fc0 sc0 ls0 ws0">述方法<span class="_ _1"></span>（<span class="ff1">Wavelet Packet Descriptor, WPD</span>）<span class="_ _5"></span>，<span class="_ _1"></span>通过与<span class="_ _0"> </span><span class="ff1">WD<span class="_ _0"> </span></span>的对比表明其更强的细</div><div class="t m0 x1 h2 yf ff2 fs0 fc0 sc0 ls0 ws0">节刻画能力。</div><div class="t m0 x1 h2 y10 ff1 fs0 fc0 sc0 ls0 ws0">2 FD<span class="_ _0"> </span><span class="ff2">和<span class="_ _0"> </span></span>WD<span class="_ _0"> </span><span class="ff2">的描述性对比（一级标题）</span></div><div class="t m0 x1 h2 y11 ff2 fs0 fc0 sc0 ls0 ws0">对曲线的<span class="_ _0"> </span><span class="ff1">Fourier<span class="_ _0"> </span></span>变换而言，<span class="_ _1"></span>系数的个数是无限的，<span class="_ _1"></span>但是数字图像目标形状的轮</div><div class="t m0 x1 h2 y12 ff2 fs0 fc0 sc0 ls0 ws0">廓是有限点集，<span class="_ _1"></span>我们不可能用一个无限的对象来对应一个有限的对象，<span class="_ _1"></span>因此导致</div><div class="t m0 x1 h2 y13 ff2 fs0 fc0 sc0 ls0 ws0">了<span class="_ _0"> </span><span class="ff1">Fourier<span class="_ _0"> </span></span>系数的截取问题，系数的截取代表了信息的损失。</div><div class="c x2 y14 w2 h3"><div class="t m0 x3 h2 y15 ff1 fs0 fc0 sc0 ls0 ws0">(a) <span class="_ _7"> </span><span class="ff2">目<span class="_ _7"> </span>标<span class="_ _7"> </span>的<span class="_ _7"> </span>原<span class="_ _7"> </span>始</span></div><div class="t m0 x3 h2 y16 ff2 fs0 fc0 sc0 ls0 ws0">轮廓</div></div><div class="c x4 y14 w3 h3"><div class="t m0 x3 h2 y17 ff1 fs0 fc0 sc0 ls0 ws0">(b) </div></div><div class="c x5 y18 w4 h4"><div class="t m1 x6 h5 y19 ff3 fs1 fc0 sc0 ls0 ws0">64<span class="_ _8"></span><span class="ff4">�<span class="_ _9"></span><span class="ff5">n</span></span></div></div><div class="c x2 y1a w2 h3"><div class="t m0 x3 h2 y17 ff1 fs0 fc0 sc0 ls0 ws0">(c) </div></div><div class="c x7 y1b w4 h4"><div class="t m1 x6 h5 y19 ff3 fs1 fc0 sc0 ls0 ws0">32<span class="_ _8"></span><span class="ff4">�<span class="_ _9"></span><span class="ff5">n</span></span></div></div><div class="c x4 y1a w3 h3"><div class="t m0 x3 h2 y17 ff1 fs0 fc0 sc0 ls0 ws0">(d) </div></div><div class="c x5 y1b w5 h4"><div class="t m2 x8 h5 y19 ff3 fs1 fc0 sc0 ls0 ws0">16<span class="_ _a"></span><span class="ff4">�<span class="_ _9"></span><span class="ff5">n</span></span></div></div><div class="c x2 y1c w2 h3"><div class="t m0 x3 h2 y17 ff1 fs0 fc0 sc0 ls0 ws0">(e) </div></div><div class="c x7 y1d w6 h4"><div class="t m0 x6 h6 y19 ff3 fs2 fc0 sc0 ls0 ws0">8<span class="_ _b"></span><span class="ff4">�<span class="_ _c"></span><span class="ff5">n</span></span></div></div><div class="c x4 y1c w3 h3"><div class="t m0 x3 h2 y17 ff1 fs0 fc0 sc0 ls0 ws0">(f) </div></div><div class="c x5 y1d w7 h4"><div class="t m0 x9 h6 y19 ff3 fs3 fc0 sc0 ls0 ws0">4<span class="_ _9"></span><span class="ff4">�<span class="_ _c"></span><span class="ff5">n</span></span></div></div><div class="c x2 y1e w8 h7"><div class="t m0 x3 h2 y1f ff2 fs0 fc0 sc0 ls0 ws0">图<span class="_ _0"> </span><span class="ff1">2-1 FD<span class="_ _0"> </span></span>不同系数截取对轮廓曲线的重建</div></div><div class="t m0 x1 h2 y20 ff2 fs0 fc0 sc0 ls0 ws0">实验结果如图<span class="_ _0"> </span><span class="ff1">2-1<span class="_ _d"> </span></span>所示，对德国豹<span class="_ _2"></span>式<span class="_ _0"> </span><span class="ff1">II<span class="_ _0"> </span></span>主战坦克的原始轮廓<span class="_ _2"></span>的基于等弧长的二</div><div class="t m0 x1 h2 y21 ff2 fs0 fc0 sc0 ls0 ws0">次采样点</div><div class="c xa y21 w9 h4"><div class="t m3 x9 h5 y19 ff3 fs1 fc0 sc0 ls0 ws0">512<span class="_ _e"></span><span class="ff4">�<span class="_ _f"></span><span class="ff5">S</span></span></div></div><div class="t m0 xb h2 y21 ff2 fs0 fc0 sc0 ls0 ws0">个，<span class="_ _10"></span>对于<span class="_ _0"> </span><span class="ff1">Fourier<span class="_ _0"> </span></span>系数的截取，<span class="_ _10"></span>当</div><div class="c xc y22 wa h8"><div class="t m4 xd h9 y23 ff5 fs4 fc0 sc0 ls0 ws0">S<span class="_ _11"></span>n</div><div class="t m4 xe h9 y24 ff5 fs4 fc0 sc0 ls0 ws0">S</div><div class="t m4 xf ha y23 ff4 fs4 fc0 sc0 ls0 ws0">�<span class="_ _e"></span>�</div><div class="t m4 xe h9 y25 ff3 fs4 fc0 sc0 ls0 ws0">4</div></div><div class="t m0 x10 h2 y21 ff2 fs0 fc0 sc0 ls0 ws0">时，<span class="_ _10"></span><span class="ff1">FD<span class="_ _0"> </span><span class="ff2">对曲线的重</span></span></div><div class="t m0 x1 h2 y26 ff2 fs0 fc0 sc0 ls0 ws0">建能够比较有效地反映原始曲线的形状。<span class="_ _10"></span>通常情况下<span class="_ _12"></span>，<span class="_ _10"></span>针对不同的应用，<span class="_ _13"></span>如果目</div><div class="t m0 x1 h2 y27 ff2 fs0 fc0 sc0 ls0 ws0">标轮廓曲线比较平滑，则</div><div class="c x11 y27 wb hb"><div class="t m0 x12 hc y28 ff5 fs5 fc0 sc0 ls0 ws0">n</div></div><div class="t m0 x13 h2 y27 ff2 fs0 fc0 sc0 ls0 ws0">的取值可以小些；如果曲线复杂细致，则</div><div class="c x14 y27 wb hb"><div class="t m0 x12 hc y28 ff5 fs5 fc0 sc0 ls0 ws0">n</div></div><div class="t m0 x15 h2 y27 ff2 fs0 fc0 sc0 ls0 ws0">的取值应</div><div class="t m0 x1 h2 y29 ff2 fs0 fc0 sc0 ls0 ws0">该大些，甚至可以大于</div><div class="c x16 y29 wc h4"><div class="t m0 x12 hd y19 ff5 fs1 fc0 sc0 ls0 ws0">S</div></div><div class="t m0 x17 h2 y29 ff2 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x1 h2 y2a ff1 fs0 fc0 sc0 ls0 ws0">WD<span class="_ _0"> </span><span class="ff2">的描述性除了与图像目标形状的采样有关外，还与参数最粗尺度</span></div><div class="c x18 y2a wd hb"><div class="t m5 x12 he y2b ff5 fs6 fc0 sc0 ls0 ws0">M</div></div><div class="t m0 x15 h2 y2a ff2 fs0 fc0 sc0 ls0 ws0">与截断系</div></div><div class="pi" data-data='{"ctm":[1.611830,0.000000,0.000000,1.611830,0.000000,0.000000]}'></div></div><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="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89705463/bg2.jpg"><div class="t m0 x1 h2 y2c ff2 fs0 fc0 sc0 ls0 ws0">数</div><div class="c x19 y2c wd hf"><div class="t m6 x1a h10 y2d ff3 fs7 fc0 sc0 ls0 ws0">0</div><div class="t m6 x12 h11 y2e ff5 fs8 fc0 sc0 ls0 ws0">m</div></div><div class="t m0 x1b h2 y2c ff2 fs0 fc0 sc0 ls0 ws0">有关。<span class="_ _1"></span>根据离散小波变换，<span class="_ _1"></span>采样点为</div><div class="c x1c y2c wb hb"><div class="t m0 x12 hc y28 ff5 fs5 fc0 sc0 ls0 ws0">n</div></div><div class="t m0 x1d h2 y2c ff2 fs0 fc0 sc0 ls0 ws0">的源信号被分解成</div><div class="c x1e y2c wb hb"><div class="t m0 x12 hc y28 ff5 fs5 fc0 sc0 ls0 ws0">n</div></div><div class="t m0 x1f h2 y2c ff2 fs0 fc0 sc0 ls0 ws0">个高频部分的系</div><div class="t m0 x1 h2 y2f ff2 fs0 fc0 sc0 ls0 ws0">数和</div><div class="c x20 y2f wb hb"><div class="t m0 x12 hc y28 ff5 fs5 fc0 sc0 ls0 ws0">n</div></div><div class="t m0 x21 h2 y2f ff2 fs0 fc0 sc0 ls0 ws0">个低频<span class="_ _2"></span>部分的系<span class="_ _2"></span>数，此时<span class="_ _2"></span>造成信息<span class="_ _2"></span>冗余<span class="ff1">[5]<span class="_ _2"></span></span>。采用间隔<span class="_ _2"></span>抽取，即<span class="_ _2"></span>使截断系</div><div class="t m0 x1 h2 y30 ff2 fs0 fc0 sc0 ls0 ws0">数</div><div class="c x19 y30 w4 hf"><div class="t m7 x22 h11 y2e ff3 fs8 fc0 sc0 ls0 ws0">1</div><div class="t m7 x1a h10 y2d ff3 fs7 fc0 sc0 ls0 ws0">0</div><div class="t m7 x8 h12 y2e ff4 fs8 fc0 sc0 ls0 ws0">�<span class="_ _11"></span><span class="ff5">m</span></div></div><div class="t m0 x23 h2 y30 ff2 fs0 fc0 sc0 ls0 ws0">，<span class="ff1">WD<span class="_ _0"> </span></span>的系数个数也不会超过原始轮廓的采样点数。</div><div class="t m0 x1 h2 y31 ff2 fs0 fc0 sc0 ls0 ws0">最粗尺度</div><div class="c xa y31 wd hb"><div class="t m5 x12 he y2b ff5 fs6 fc0 sc0 ls0 ws0">M</div></div><div class="t m0 x24 h2 y31 ff2 fs0 fc0 sc0 ls0 ws0">决定小波分解的层数，直接关系着计算量<span class="_ _4"></span>；<span class="_ _4"></span>截断系数</div><div class="c x25 y31 wd hf"><div class="t m6 x1a h10 y2d ff3 fs7 fc0 sc0 ls0 ws0">0</div><div class="t m6 x12 h11 y2e ff5 fs8 fc0 sc0 ls0 ws0">m</div></div><div class="t m0 x26 h2 y31 ff2 fs0 fc0 sc0 ls0 ws0">则决定着舍</div><div class="t m0 x1 h2 y32 ff2 fs0 fc0 sc0 ls0 ws0">弃细<span class="_ _2"></span>节的程<span class="_ _2"></span>度，如<span class="_ _2"></span>果</div><div class="c x27 y32 wd hf"><div class="t m6 x1a h10 y2d ff3 fs7 fc0 sc0 ls0 ws0">0</div><div class="t m6 x12 h11 y2e ff5 fs8 fc0 sc0 ls0 ws0">m</div></div><div class="t m0 x28 h2 y32 ff2 fs0 fc0 sc0 ls0 ws0">过大<span class="_ _2"></span>，则会<span class="_ _2"></span>造成细<span class="_ _2"></span>节的过度<span class="_ _2"></span>丢失，<span class="_ _2"></span>如果</div><div class="c x29 y32 wd hf"><div class="t m6 x1a h10 y2d ff3 fs7 fc0 sc0 ls0 ws0">0</div><div class="t m6 x12 h11 y2e ff5 fs8 fc0 sc0 ls0 ws0">m</div></div><div class="t m0 x2a h2 y32 ff2 fs0 fc0 sc0 ls0 ws0">太小<span class="_ _2"></span>，则<span class="_ _0"> </span><span class="ff1">WD</span></div><div class="t m0 x1 h2 y33 ff2 fs0 fc0 sc0 ls0 ws0">系数的个数又太多。因此就有着两方面的权衡问题。</div><div class="c x2b y34 we h3"><div class="t m0 x3 h2 y35 ff1 fs0 fc0 sc0 ls0 ws0">(a) </div></div><div class="c x2c y36 wf h13"><div class="t m8 x2d h14 y37 ff3 fs9 fc0 sc0 ls0 ws0">2<span class="_ _14"></span>,<span class="_ _15"></span>8</div><div class="t m8 x2e h15 y38 ff3 fsa fc0 sc0 ls0 ws0">0</div><div class="t m8 x2f h16 y37 ff4 fs9 fc0 sc0 ls0 ws0">�<span class="_ _16"></span>�<span class="_ _17"> </span><span class="ff5">m<span class="_ _18"></span>M</span></div></div><div class="c x30 y34 w10 h3"><div class="t m0 x3 h2 y35 ff1 fs0 fc0 sc0 ls0 ws0">(b) </div></div><div class="c x31 y36 wf h13"><div class="t m9 x2d h14 y37 ff3 fs9 fc0 sc0 ls0 ws0">4<span class="_ _19"></span>,<span class="_ _15"></span>8</div><div class="t m9 x2e h15 y38 ff3 fsa fc0 sc0 ls0 ws0">0</div><div class="t m9 x2f h16 y37 ff4 fs9 fc0 sc0 ls0 ws0">�<span class="_ _1a"></span>�<span class="_"> </span><span class="ff5">m<span class="_ _18"></span>M</span></div></div><div class="c x2b y39 we h3"><div class="t m0 x3 h2 y17 ff1 fs0 fc0 sc0 ls0 ws0">(c) </div></div><div class="c x2c y3a w11 h4"><div class="t m0 x32 h17 y3b ff3 fsb fc0 sc0 ls0 ws0">6<span class="_ _1b"></span>,<span class="_ _1c"></span>8</div><div class="t m0 x33 h18 y3c ff3 fsc fc0 sc0 ls0 ws0">0</div><div class="t m0 xd h19 y3b ff4 fsb fc0 sc0 ls0 ws0">�<span class="_ _1d"></span>�<span class="_ _1e"> </span><span class="ff5">m<span class="_ _1f"></span>M</span></div></div><div class="c x30 y39 w10 h3"><div class="t m0 x3 h2 y17 ff1 fs0 fc0 sc0 ls0 ws0">(d) </div></div><div class="c x31 y3a w12 h4"><div class="t m0 x34 h17 y3b ff3 fsb fc0 sc0 ls0 ws0">8<span class="_ _20"></span>,<span class="_ _15"></span>8</div><div class="t m0 x35 h18 y3c ff3 fsc fc0 sc0 ls0 ws0">0</div><div class="t m0 x36 h19 y3b ff4 fsb fc0 sc0 ls0 ws0">�<span class="_ _21"></span>�<span class="_ _22"> </span><span class="ff5">m<span class="_ _23"></span>M</span></div></div><div class="c x2b y3d w13 h1a"><div class="t m0 x3 h2 y3e ff2 fs0 fc0 sc0 ls0 ws0">图<span class="_ _0"> </span><span class="ff1">2-2 WD<span class="_ _0"> </span></span>对轮廓曲线的重建</div></div><div class="t m0 x1 h2 y3f ff2 fs0 fc0 sc0 ls0 ws0">实<span class="_ _24"></span>验<span class="_ _24"></span>结<span class="_ _24"></span>果<span class="_ _24"></span>如<span class="_ _24"></span>图<span class="_ _25"> </span><span class="ff1">2-2<span class="_ _25"> </span></span>所<span class="_ _24"></span>示<span class="_ _24"></span>，<span class="_ _24"></span>对<span class="_ _24"></span>德<span class="_ _24"></span>国<span class="_ _24"></span>豹<span class="_ _24"></span>式<span class="_ _25"> </span><span class="ff1">II<span class="_ _25"> </span></span>主<span class="_ _24"></span>战<span class="_ _24"></span>坦<span class="_ _24"></span>克<span class="_ _24"></span>的<span class="_ _24"></span>原<span class="_ _24"></span>始<span class="_ _24"></span>轮<span class="_ _24"></span>廓<span class="_ _24"></span>的<span class="_ _24"></span>二<span class="_ _24"></span>次<span class="_ _24"></span>采<span class="_ _24"></span>样<span class="_ _24"></span>点</div><div class="c x1 y40 w9 h4"><div class="t m3 x9 h5 y19 ff3 fs1 fc0 sc0 ls0 ws0">512<span class="_ _e"></span><span class="ff4">�<span class="_ _f"></span><span class="ff5">S</span></span></div></div><div class="t m0 x37 h2 y40 ff2 fs0 fc0 sc0 ls0 ws0">个，<span class="_ _2"></span>对于<span class="_ _d"> </span><span class="ff1">WD<span class="_ _d"> </span></span>的截<span class="_ _2"></span>断系<span class="_ _2"></span>数</div><div class="c x38 y40 w14 hf"><div class="t ma x39 h11 y2e ff3 fs8 fc0 sc0 ls0 ws0">6</div><div class="t ma x1a h10 y2d ff3 fs7 fc0 sc0 ls0 ws0">0</div><div class="t ma x8 h12 y2e ff4 fs8 fc0 sc0 ls0 ws0">�<span class="_ _26"></span><span class="ff5">m</span></div></div><div class="t m0 x3a h2 y40 ff2 fs0 fc0 sc0 ls0 ws0">时，<span class="_ _2"></span><span class="ff1">WD<span class="_ _0"> </span></span>对<span class="_ _2"></span>曲线<span class="_ _2"></span>的重建<span class="_ _2"></span>能够<span class="_ _2"></span>比较<span class="_ _2"></span>有效<span class="_ _2"></span>地反</div><div class="t m0 x1 h2 y41 ff2 fs0 fc0 sc0 ls0 ws0">映原始曲线的细节部分，而当</div><div class="c x3b y41 w14 hf"><div class="t ma x39 h11 y2e ff3 fs8 fc0 sc0 ls0 ws0">6</div><div class="t ma x1a h10 y2d ff3 fs7 fc0 sc0 ls0 ws0">0</div><div class="t ma x8 h12 y2e ff4 fs8 fc0 sc0 ls0 ws0">�<span class="_ _11"></span><span class="ff5">m</span></div></div><div class="t m0 x3c h2 y41 ff2 fs0 fc0 sc0 ls0 ws0">时，重建后的轮廓变得平滑。<span class="_ _2"></span><span class="ff1">Chuang[6]</span>认</div><div class="t m0 x1 h2 y42 ff2 fs0 fc0 sc0 ls0 ws0">为分解的层数只需要使最粗尺度的系数个数<span class="_ _27"> </span><span class="ff1">4<span class="_ _27"> </span></span>到<span class="_ _27"> </span><span class="ff1">16<span class="_ _27"> </span></span>个即可<span class="_ _28"></span>；<span class="_ _28"></span>杨<span class="_ _4"></span><span class="ff1">[9]<span class="ff2">认为当</span></span></div><div class="c x3d y42 w9 h4"><div class="t m0 x9 h5 y19 ff3 fs1 fc0 sc0 ls0 ws0">256<span class="_ _29"></span><span class="ff4">�<span class="_ _f"></span><span class="ff5">S</span></span></div></div><div class="t m0 x1 h2 y43 ff2 fs0 fc0 sc0 ls0 ws0">时，截断系数在<span class="_ _d"> </span><span class="ff1">3<span class="_ _0"> </span></span>到<span class="_ _0"> </span><span class="ff1">5<span class="_ _0"> </span></span>之间。<span class="ff1"> <span class="_ _2"></span></span>分解层数和截断系数的确定<span class="_ _2"></span>都必须根据应用特点</div><div class="t m0 x1 h2 y44 ff2 fs0 fc0 sc0 ls0 ws0">和需求来决定，轮廓采样点越多，分解层数越多并且截断系数也可越大<span class="_ _1"></span>；<span class="_ _1"></span>当轮廓</div><div class="t m0 x1 h2 y45 ff2 fs0 fc0 sc0 ls0 ws0">点本身较少，分解层数自然也少，同时也限制着截断系数。</div><div class="t m0 x1 h2 y46 ff2 fs0 fc0 sc0 ls0 ws0">从上<span class="_ _2"></span>述<span class="_ _0"> </span><span class="ff1">FD<span class="_ _0"> </span></span>和<span class="_ _0"> </span><span class="ff1">WD<span class="_ _d"> </span></span>的描<span class="_ _2"></span>述性看<span class="_ _2"></span>，<span class="ff1">FD<span class="_ _0"> </span></span>具<span class="_ _2"></span>有计算相<span class="_ _2"></span>对简单<span class="_ _2"></span>，结构<span class="_ _2"></span>单一的特<span class="_ _2"></span>点，但<span class="_ _2"></span>其描</div><div class="t m0 x1 h2 y47 ff2 fs0 fc0 sc0 ls0 ws0">述目标形状轮廓的能力相对较弱，并且受如下局限<span class="_ _4"></span>：<span class="_ _4"></span>①<span class="ff1">Fourier<span class="_ _0"> </span></span>描绘子要求轮廓</div><div class="t m0 x1 h2 y48 ff2 fs0 fc0 sc0 ls0 ws0">曲线必须是闭合的<span class="_ _10"></span>；<span class="_ _4"></span>②要求均匀间隔地选取轮廓上的点<span class="_ _10"></span>；<span class="_ _10"></span>③快速<span class="_ _0"> </span><span class="ff1">Fourier<span class="_ _0"> </span></span>变换要</div><div class="t m0 x1 h2 y49 ff2 fs0 fc0 sc0 ls0 ws0">求点序列的长度是<span class="_ _0"> </span><span class="ff1">2<span class="_ _0"> </span></span>的整数次幂。</div><div class="t m0 x1 h2 y4a ff2 fs0 fc0 sc0 ls0 ws0">对于<span class="_ _0"> </span><span class="ff1">WD<span class="_ _0"> </span></span>来讲，其<span class="_ _2"></span>自身的多尺度描述能力更<span class="_ _2"></span>为有利于对目标轮廓描述的<span class="_ _2"></span>准确性，</div><div class="t m0 x1 h2 y4b ff2 fs0 fc0 sc0 ls0 ws0">同时<span class="_ _0"> </span><span class="ff1">WD<span class="_ _0"> </span></span>可以用更少的系数来表示<span class="_ _0"> </span><span class="ff1">FD<span class="_ _0"> </span></span>所能表示的轮廓精细程度，<span class="_ _1"></span>换句话说，<span class="_ _1"></span>就是</div><div class="t m0 x1 h2 y4c ff2 fs0 fc0 sc0 ls0 ws0">相同数量的系数<span class="_ _2"></span>，<span class="ff1">WD<span class="_ _0"> </span></span>具有更强的描述能力<span class="_ _2"></span>。<span class="ff1">WD<span class="_ _0"> </span></span>也要求轮廓曲线必须是<span class="_ _2"></span>闭合的，</div><div class="t m0 x1 h2 y4d ff2 fs0 fc0 sc0 ls0 ws0">但不受其他条件的约束，<span class="_ _2a"></span>具有更简洁的结构。<span class="_ _2a"></span>当然，<span class="_ _2a"></span>从计算量来看，<span class="_ _2a"></span>基于<span class="_ _0"> </span><span class="ff1">Wavelet</span></div><div class="t m0 x1 h2 y4e ff2 fs0 fc0 sc0 ls0 ws0">变换的方法要高于基于<span class="_ _0"> </span><span class="ff1">Fourier<span class="_ _0"> </span></span>变换的方法。</div><div class="t m0 x1 h2 y4f ff1 fs0 fc0 sc0 ls0 ws0">3 <span class="ff2">闭合轮廓描述方法不变性分析（一级标题）</span></div><div class="t m0 x1 h2 y50 ff1 fs0 fc0 sc0 ls0 ws0">3.1 FD<span class="_ _0"> </span><span class="ff2">的不变性分析（二级标题）</span></div><div class="t m0 x1 h2 y51 ff2 fs0 fc0 sc0 ls0 ws0">针对形状描述子的不变性要求，<span class="_ _2b"></span><span class="ff1">Fourier<span class="_ _0"> </span><span class="ff2">描述在轮廓发生平移、<span class="_ _2b"></span>旋转、<span class="_ _2b"></span>尺度和起</span></span></div><div class="t m0 x1 h2 y52 ff2 fs0 fc0 sc0 ls0 ws0">始点发生变化的结果<span class="ff1">[7]</span>，如表<span class="_ _0"> </span><span class="ff1">3-1<span class="_ _0"> </span></span>所示。</div></div><div class="pi" data-data='{"ctm":[1.611830,0.000000,0.000000,1.611830,0.000000,0.000000]}'></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="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89705463/bg3.jpg"><div class="t m0 x3e h2 y1 ff2 fs0 fc0 sc0 ls0 ws0">表<span class="_ _0"> </span><span class="ff1">3-1 FD<span class="_ _0"> </span></span>受轮廓变化的影响</div><div class="c x3f y53 w15 h1b"><div class="t m0 xe h2 y15 ff2 fs0 fc0 sc0 ls0 ws0">变<span class="_ _2c"> </span>化</div><div class="t m0 xe h2 y16 ff2 fs0 fc0 sc0 ls0 ws0">量</div></div><div class="c x40 y53 w16 h1b"><div class="t m0 xe h2 y54 ff1 fs0 fc0 sc0 ls0 ws0">FD</div></div><div class="c x41 y55 w17 hf"><div class="t mb x12 h1c y56 ff4 fsd fc0 sc0 ls0 ws0">�<span class="_ _2d"> </span>�</div><div class="t mc x42 h10 y2d ff5 fs7 fc0 sc0 ls0 ws0">n</div><div class="t mc x3 h11 y2e ff5 fs8 fc0 sc0 ls0 ws0">a</div><div class="t mc x42 h12 y57 ff4 fs8 fc0 sc0 ls0 ws0">�</div></div><div class="c x43 y58 w18 h1d"><div class="t m0 xe h2 y59 ff2 fs0 fc0 sc0 ls0 ws0">平移</div></div><div class="c x44 y5a wc hf"><div class="t m0 x45 h10 y2d ff3 fs7 fc0 sc0 ls0 ws0">0</div><div class="t m0 x12 h1e y2e ff5 fse fc0 sc0 ls0 ws0">l</div></div><div class="c x46 y5b w19 h1f"><div class="t m0 x6 h20 y5c ff4 fsf fc0 sc0 ls0 ws0">�</div><div class="t m0 x6 h20 y5d ff4 fsf fc0 sc0 ls0 ws0">�</div><div class="t m0 x6 h20 y5e ff4 fsf fc0 sc0 ls0 ws0">�</div><div class="t m0 x47 h20 y5f ff4 fsf fc0 sc0 ls0 ws0">�<span class="_ _2e"></span>�</div><div class="t m0 x47 h20 y60 ff4 fsf fc0 sc0 ls0 ws0">�</div><div class="t m0 x48 h20 y61 ff4 fsf fc0 sc0 ls0 ws0">�</div><div class="t m0 x45 h20 y62 ff4 fsf fc0 sc0 ls0 ws0">�</div><div class="t m0 x49 h21 y5f ff3 fsf fc0 sc0 ls0 ws0">0<span class="_ _2f"></span>,</div><div class="t m0 x49 h21 y60 ff3 fsf fc0 sc0 ls0 ws0">0<span class="_ _30"></span>,</div><div class="t m0 x4a h22 y63 ff3 fs10 fc0 sc0 ls0 ws0">0</div><div class="t m0 x4b h21 y5f ff5 fsf fc0 sc0 ls0 ws0">n<span class="_ _31"></span>l<span class="_ _32"></span>a</div><div class="t m0 x4b h21 y60 ff5 fsf fc0 sc0 ls0 ws0">n<span class="_ _1d"></span>a</div><div class="t m0 x12 h21 y61 ff5 fsf fc0 sc0 ls0 ws0">a</div><div class="t m0 x4c h22 y63 ff5 fs10 fc0 sc0 ls0 ws0">n</div><div class="t m0 x4d h22 y64 ff5 fs10 fc0 sc0 ls0 ws0">n</div><div class="t m0 x45 h22 y65 ff5 fs10 fc0 sc0 ls0 ws0">n</div></div><div class="c x43 y66 w18 h1b"><div class="t m0 xe h2 y67 ff2 fs0 fc0 sc0 ls0 ws0">旋转</div></div><div class="c x44 y68 w1a hf"><div class="t m0 x4e h10 y2d ff3 fs7 fc0 sc0 ls0 ws0">0</div><div class="t md x4f h23 y2e ff6 fs11 fc0 sc0 ls0 ws0">�</div></div><div class="c x46 y69 wf h24"><div class="t m0 x50 h25 y6a ff5 fs12 fc0 sc0 ls0 ws0">n</div><div class="t m0 x4c h25 y6b ff5 fs12 fc0 sc0 ls0 ws0">i</div><div class="t m0 x4e h25 y6a ff5 fs12 fc0 sc0 ls0 ws0">n</div><div class="t m0 x51 h26 y6c ff5 fs13 fc0 sc0 ls0 ws0">a<span class="_ _1b"></span>e<span class="_ _1b"></span>a<span class="_ _33"> </span><span class="ff4">�<span class="_ _34"></span>�</span></div><div class="t m0 x4e h26 y6d ff4 fs13 fc0 sc0 ls0 ws0">�</div><div class="t m0 x33 h27 y6e ff3 fs14 fc0 sc0 ls0 ws0">0</div><div class="t md xf h28 y6b ff6 fs15 fc0 sc0 ls0 ws0">�</div></div><div class="c x43 y6f w18 h1b"><div class="t m0 xe h2 y67 ff2 fs0 fc0 sc0 ls0 ws0">尺度</div></div><div class="c x44 y70 wd hf"><div class="t m6 x52 h10 y2d ff3 fs7 fc0 sc0 ls0 ws0">0</div><div class="t m6 x12 h11 y2e ff5 fs8 fc0 sc0 ls0 ws0">C</div></div><div class="c x46 y70 w1b hf"><div class="t m0 x2f h29 y2d ff5 fs16 fc0 sc0 ls0 ws0">n<span class="_ _30"></span>n</div><div class="t m0 x53 h12 y2e ff5 fs8 fc0 sc0 ls0 ws0">a<span class="_ _35"></span>C<span class="_ _36"></span>a<span class="_ _37"> </span><span class="ff4">�<span class="_ _38"></span>�</span></div><div class="t m0 x4e h12 y57 ff4 fs8 fc0 sc0 ls0 ws0">�</div><div class="t m0 x54 h29 y2d ff3 fs16 fc0 sc0 ls0 ws0">0</div></div><div class="c x43 y71 w18 h1b"><div class="t m0 xe h2 y15 ff2 fs0 fc0 sc0 ls0 ws0">起<span class="_ _2"></span>始</div><div class="t m0 xe h2 y16 ff2 fs0 fc0 sc0 ls0 ws0">点</div></div><div class="c x44 y72 wc hf"><div class="t m0 x4e h10 y2d ff3 fs17 fc0 sc0 ls0 ws0">0</div><div class="t m0 x12 h2a y2e ff5 fs18 fc0 sc0 ls0 ws0">k</div></div><div class="c x46 y73 w1c h2b"><div class="t m0 x55 h2c y19 ff5 fs19 fc0 sc0 ls0 ws0">n</div><div class="t m0 x56 h2c y74 ff5 fs19 fc0 sc0 ls0 ws0">k</div><div class="t m0 x57 h2c y75 ff5 fs19 fc0 sc0 ls0 ws0">L</div><div class="t m0 x58 h2c y76 ff5 fs19 fc0 sc0 ls0 ws0">n</div><div class="t m0 x59 h2c y74 ff5 fs19 fc0 sc0 ls0 ws0">i<span class="_ _39"></span>k<span class="_ _3a"></span>l</div><div class="t m0 xd h2c y75 ff5 fs19 fc0 sc0 ls0 ws0">L</div><div class="t m0 x5a h2c y76 ff5 fs19 fc0 sc0 ls0 ws0">n</div><div class="t m0 x33 h2c y74 ff5 fs19 fc0 sc0 ls0 ws0">i</div><div class="t m0 x5b h2c y19 ff5 fs19 fc0 sc0 ls0 ws0">n<span class="_ _31"></span>n</div><div class="t m0 x5c h6 y77 ff5 fs3 fc0 sc0 ls0 ws0">a<span class="_ _1a"></span>e<span class="_ _3b"></span>e<span class="_ _3c"></span>a<span class="_ _29"></span>a<span class="_ _3d"> </span><span class="ff4">�<span class="_ _30"></span>�<span class="_ _3e"></span>�</span></div><div class="t m0 x5d h6 y78 ff4 fs3 fc0 sc0 ls0 ws0">�</div><div class="t m0 x50 h2d y74 ff4 fs19 fc0 sc0 ls0 ws0">�</div><div class="t m0 x5e h2e y79 ff3 fs1a fc0 sc0 ls0 ws0">0<span class="_ _2e"></span>0</div><div class="t m0 x5f h2c y76 ff3 fs19 fc0 sc0 ls0 ws0">2</div><div class="t m0 x60 h2c y74 ff3 fs19 fc0 sc0 ls0 ws0">)<span class="_ _c"></span>(</div><div class="t m0 x4d h2c y76 ff3 fs19 fc0 sc0 ls0 ws0">2</div><div class="t md x57 h2f y76 ff6 fs1b fc0 sc0 ls0 ws0">�<span class="_ _3f"></span>�</div></div><div class="t m0 x1 h2 y7a ff2 fs0 fc0 sc0 ls0 ws0">由表<span class="_ _0"> </span><span class="ff1">3-1<span class="_ _0"> </span></span>可知，<span class="_ _12"></span>平移只改变</div><div class="c x61 y7a w1a hf"><div class="t m0 x4e h10 y2d ff3 fs7 fc0 sc0 ls0 ws0">0</div><div class="t m0 x12 h1e y2e ff5 fse fc0 sc0 ls0 ws0">a</div><div class="t m0 x4e h12 y57 ff4 fse fc0 sc0 ls0 ws0">�</div></div><div class="t m0 x62 h2 y7a ff2 fs0 fc0 sc0 ls0 ws0">，<span class="_ _12"></span>旋转后新系数等于原系数乘以</div><div class="c x63 y7a w1d h30"><div class="t me x48 h31 y7b ff3 fs1c fc0 sc0 ls0 ws0">0</div><div class="t mf x64 h32 y7c ff6 fs1d fc0 sc0 ls0 ws0">�</div><div class="t me x5d h33 y7c ff5 fs1e fc0 sc0 ls0 ws0">i</div><div class="t me x12 h34 y7d ff5 fs1f fc0 sc0 ls0 ws0">e</div></div><div class="t m0 x65 h2 y7a ff2 fs0 fc0 sc0 ls0 ws0">，<span class="_ _12"></span>尺度变化后</div><div class="t m0 x1 h2 y7e ff2 fs0 fc0 sc0 ls0 ws0">新系数<span class="_ _2"></span>等于原系<span class="_ _2"></span>数乘以<span class="_ _2"></span>尺度变化<span class="_ _2"></span>因子</div><div class="c x66 y7e w1e hf"><div class="t m10 x64 h10 y2d ff3 fs7 fc0 sc0 ls0 ws0">0</div><div class="t m10 x12 h11 y2e ff5 fs8 fc0 sc0 ls0 ws0">C</div></div><div class="t m0 x67 h2 y7e ff2 fs0 fc0 sc0 ls0 ws0">，起始<span class="_ _2"></span>点沿曲线<span class="_ _2"></span>移动一<span class="_ _2"></span>个距离</div><div class="c x68 y7e wc hf"><div class="t m0 x5d h10 y2d ff3 fs17 fc0 sc0 ls0 ws0">0</div><div class="t m0 x12 h2a y2e ff5 fs18 fc0 sc0 ls0 ws0">k</div></div><div class="t m0 x69 h2 y7e ff2 fs0 fc0 sc0 ls0 ws0">后系数</div><div class="c x1 y7f w1a hf"><div class="t m0 x4e h10 y2d ff5 fs7 fc0 sc0 ls0 ws0">n</div><div class="t m0 x12 h1e y2e ff5 fse fc0 sc0 ls0 ws0">a</div></div><div class="t m0 x6a h2 y7f ff2 fs0 fc0 sc0 ls0 ws0">的幅值不变，仅相位变化了</div><div class="c x62 y7f w1d hf"><div class="t m0 x48 h10 y2d ff3 fs7 fc0 sc0 ls0 ws0">0</div><div class="t m0 x12 h1e y2e ff5 fs8 fc0 sc0 ls0 ws0">nk</div></div><div class="t m0 x6b h2 y7f ff2 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x1 h2 y80 ff2 fs0 fc0 sc0 ls0 ws0">由上述<span class="_ _2"></span>分析可<span class="_ _2"></span>知，在对<span class="_ _2"></span>曲线的<span class="_ _2"></span>形状进行<span class="_ _2"></span>描述或识<span class="_ _2"></span>别时，<span class="_ _2"></span>若只考虑</div><div class="c x25 y80 wa hf"><div class="t m11 x2f h12 y2e ff3 fs8 fc0 sc0 ls0 ws0">}<span class="_ _40"></span>0<span class="_ _36"></span>,<span class="_ _8"></span>{<span class="_ _41"> </span><span class="ff4">�<span class="_ _f"></span><span class="ff5">n<span class="_ _42"></span>a</span></span></div><div class="t m11 x42 h10 y2d ff5 fs7 fc0 sc0 ls0 ws0">n</div></div><div class="t m0 x6c h2 y80 ff2 fs0 fc0 sc0 ls0 ws0">，可</div><div class="t m0 x1 h2 y81 ff2 fs0 fc0 sc0 ls0 ws0">以消除平移带来的影响<span class="_ _28"></span>；<span class="_ _28"></span>若再对它们取幅值，<span class="_ _13"></span>可以消除起始点位置和旋转的影响<span class="_ _28"></span>；</div><div class="t m0 x1 h2 y82 ff2 fs0 fc0 sc0 ls0 ws0">若<span class="_ _24"></span>它<span class="_ _2"></span>们<span class="_ _24"></span>的<span class="_ _24"></span>幅<span class="_ _2"></span>值<span class="_ _24"></span>都<span class="_ _24"></span>除<span class="_ _2"></span>以</div><div class="c x6d y82 w1d h35"><div class="t m12 x64 h36 y83 ff3 fs20 fc0 sc0 ls0 ws0">1</div><div class="t m12 x6e h37 y84 ff5 fs21 fc0 sc0 ls0 ws0">a</div></div><div class="t m0 x17 h2 y82 ff2 fs0 fc0 sc0 ls0 ws0">来<span class="_ _24"></span>对<span class="_ _2"></span>归<span class="_ _24"></span>一<span class="_ _24"></span>化<span class="_ _2"></span>处<span class="_ _24"></span>理<span class="_ _24"></span>，<span class="_ _2"></span>那<span class="_ _24"></span>么<span class="_ _24"></span>无<span class="_ _2"></span>论<span class="_ _24"></span>轮<span class="_ _24"></span>廓<span class="_ _24"></span>发<span class="_ _2"></span>生<span class="_ _24"></span>何<span class="_ _24"></span>种<span class="_ _2"></span>变<span class="_ _24"></span>换<span class="_ _24"></span>，<span class="_ _2"></span>其</div><div class="t m0 x1 h2 y85 ff1 fs0 fc0 sc0 ls0 ws0">Fourier<span class="_ _0"> </span><span class="ff2">系数<span class="_ _4"></span>（除</span></div><div class="c x6f y85 w1a hf"><div class="t m0 x4e h10 y2d ff3 fs7 fc0 sc0 ls0 ws0">0</div><div class="t m0 x12 h1e y2e ff5 fse fc0 sc0 ls0 ws0">a</div></div><div class="t m0 x70 h2 y85 ff2 fs0 fc0 sc0 ls0 ws0">外）<span class="_ _4"></span>幅值是相同的。<span class="_ _4"></span>换句话说，<span class="_ _4"></span>经过处理的</div><div class="c x1f y85 w1f h38"><div class="t m13 x71 h5 y86 ff4 fs1 fc0 sc0 ls0 ws0">�</div><div class="t m13 x71 h5 y87 ff4 fs1 fc0 sc0 ls0 ws0">�</div><div class="t m13 x71 h5 y88 ff4 fs1 fc0 sc0 ls0 ws0">�</div><div class="t m13 x71 h5 y89 ff4 fs1 fc0 sc0 ls0 ws0">�</div><div class="t m13 x71 h5 y8a ff4 fs1 fc0 sc0 ls0 ws0">�</div><div class="t m13 x12 h5 y86 ff4 fs1 fc0 sc0 ls0 ws0">�</div><div class="t m13 x12 h5 y87 ff4 fs1 fc0 sc0 ls0 ws0">�</div><div class="t m13 x12 h5 y88 ff4 fs1 fc0 sc0 ls0 ws0">�</div><div class="t m13 x12 h5 y89 ff4 fs1 fc0 sc0 ls0 ws0">�</div><div class="t m13 x12 h5 y8a ff4 fs1 fc0 sc0 ls0 ws0">�</div><div class="t m13 x36 h5 y8b ff4 fs1 fc0 sc0 ls0 ws0">�<span class="_ _7"> </span><span class="ff3">0<span class="_ _39"></span>,</span></div><div class="t m13 x39 h2c y8c ff3 fs19 fc0 sc0 ls0 ws0">1</div><div class="t m13 x72 hd y8b ff5 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m13 x73 hd y8d ff5 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m13 x74 hd y8e ff5 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m13 x4e hd y8b ff5 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m13 x39 h2c y8f ff5 fs19 fc0 sc0 ls0 ws0">n</div><div class="t m13 x75 h2c y90 ff5 fs19 fc0 sc0 ls0 ws0">n</div></div><div class="t m0 x76 h2 y85 ff2 fs0 fc0 sc0 ls0 ws0">具</div><div class="t m0 x1 h2 y91 ff2 fs0 fc0 sc0 ls0 ws0">有平移、旋转、刻度改变及起始点位置不变性。</div><div class="t m0 x1 h2 y92 ff1 fs0 fc0 sc0 ls0 ws0">3.2 WD<span class="_ _0"> </span><span class="ff2">的不变性分析（二级标题）</span></div><div class="t m0 x1 h2 y93 ff2 fs0 fc0 sc0 ls0 ws0">基于窗口<span class="_ _0"> </span><span class="ff1">Fourier<span class="_ _0"> </span></span>变换理论发展起来的<span class="_ _0"> </span><span class="ff1">Wavelet<span class="_ _0"> </span></span>变换理论，<span class="_ _3"></span>具有天生的多尺度分</div><div class="t m0 x1 h2 y94 ff2 fs0 fc0 sc0 ls0 ws0">析<span class="_ _2"></span>能力<span class="_ _2"></span>。<span class="_ _2"></span><span class="ff1">Wavelet<span class="_ _d"> </span></span>描<span class="_ _2"></span>述<span class="_ _2"></span>在<span class="_ _2"></span>轮廓<span class="_ _2"></span>发<span class="_ _2"></span>生<span class="_ _2"></span>平移<span class="_ _2"></span>、<span class="_ _2"></span>旋<span class="_ _2"></span>转、<span class="_ _2"></span>尺<span class="_ _2"></span>度<span class="_ _2"></span>和<span class="_ _2"></span>起始<span class="_ _2"></span>点<span class="_ _2"></span>发<span class="_ _2"></span>生变<span class="_ _2"></span>化<span class="_ _2"></span>的<span class="_ _2"></span>结果</div><div class="t m0 x1 h2 y95 ff1 fs0 fc0 sc0 ls0 ws0">[22]<span class="ff2">，如表<span class="_ _0"> </span></span>3-2<span class="_ _0"> </span><span class="ff2">所示。</span></div><div class="t m0 x77 h2 y96 ff2 fs0 fc0 sc0 ls0 ws0">表<span class="ff1"> 3-2 WD<span class="_ _0"> </span></span>受轮廓变化的影响</div><div class="c x78 y97 w20 h1b"><div class="t m0 x4f h2 y15 ff2 fs0 fc0 sc0 ls0 ws0">变<span class="_ _43"> </span>化</div><div class="t m0 x4f h2 y16 ff2 fs0 fc0 sc0 ls0 ws0">量</div></div><div class="c x79 y97 w21 h1b"><div class="t m0 x4f h2 y54 ff1 fs0 fc0 sc0 ls0 ws0">WD{</div></div><div class="c x46 y98 w22 hf"><div class="t m14 x42 h39 y99 ff5 fs22 fc0 sc0 ls0 ws0">M</div><div class="t m14 x64 h39 y9a ff5 fs22 fc0 sc0 ls0 ws0">n</div><div class="t m14 x12 h3a y9b ff5 fs23 fc0 sc0 ls0 ws0">a</div><div class="t m14 x64 h3b y9c ff4 fs23 fc0 sc0 ls0 ws0">�</div></div><div class="c x79 y97 w21 h1b"><div class="t m0 x72 h2 y54 ff2 fs0 fc0 sc0 ls0 ws0">，</div></div><div class="c x30 y98 w23 hf"><div class="t m15 x1a h39 y99 ff5 fs22 fc0 sc0 ls0 ws0">M</div><div class="t m15 x5d h39 y9a ff5 fs22 fc0 sc0 ls0 ws0">n</div><div class="t m15 x12 h3a y9b ff5 fs23 fc0 sc0 ls0 ws0">c</div><div class="t m15 x5d h3b y9c ff4 fs23 fc0 sc0 ls0 ws0">�</div></div><div class="c x79 y97 w21 h1b"><div class="t m0 x7a h2 y54 ff2 fs0 fc0 sc0 ls0 ws0">，</div></div><div class="c x7b y98 wd hf"><div class="t m0 x64 h39 y99 ff5 fs22 fc0 sc0 ls0 ws0">m</div><div class="t m0 x3 h39 y9a ff5 fs22 fc0 sc0 ls0 ws0">n</div><div class="t m0 x12 h3a y9b ff5 fs24 fc0 sc0 ls0 ws0">r</div><div class="t m0 x45 h3b y9c ff4 fs24 fc0 sc0 ls0 ws0">�</div></div><div class="c x79 y97 w21 h1b"><div class="t m0 x19 h2 y54 ff2 fs0 fc0 sc0 ls0 ws0">，</div></div><div class="c x7c y98 w1d hf"><div class="t m0 x42 h39 y99 ff5 fs22 fc0 sc0 ls0 ws0">m</div><div class="t m0 x7d h39 y9a ff5 fs22 fc0 sc0 ls0 ws0">n</div><div class="t m0 x12 h3a y9b ff5 fs23 fc0 sc0 ls0 ws0">d</div><div class="t m0 x7d h3b y9c ff4 fs23 fc0 sc0 ls0 ws0">�</div></div><div class="c x79 y97 w21 h1b"><div class="t m0 x7e h2 y54 ff1 fs0 fc0 sc0 ls0 ws0">}</div></div><div class="c x7f y9d w24 h1b"><div class="t m0 x4f h2 y15 ff2 fs0 fc0 sc0 ls0 ws0">平</div><div class="t m0 x4f h2 y16 ff2 fs0 fc0 sc0 ls0 ws0">移</div></div><div class="c x16 y9e w25 h4"><div class="t m16 x22 h17 y3b ff3 fsb fc0 sc0 ls0 ws0">)<span class="_ _b"></span>,<span class="_ _b"></span>(</div><div class="t m16 x74 h18 y3c ff3 fs25 fc0 sc0 ls0 ws0">0<span class="_ _44"></span>0</div><div class="t m17 x80 h3c y3b ff6 fs26 fc0 sc0 ls0 ws0">�<span class="_ _45"></span>�</div></div><div class="c x3b y9f w26 h2b"><div class="t m18 x81 h3d ya0 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x81 h3d ya1 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x81 h3d ya2 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x81 h3d ya3 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x39 h3d ya0 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x39 h3d ya1 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x39 h3d ya2 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x39 h3d ya3 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x82 h3d ya4 ff4 fs27 fc0 sc0 ls0 ws0">�<span class="_ _36"></span>�</div><div class="t m18 x82 h3d ya5 ff4 fs27 fc0 sc0 ls0 ws0">�<span class="_ _36"></span>�</div><div class="t m18 x74 h3d ya6 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x83 h3d ya0 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x83 h3d ya1 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x83 h3d ya2 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x83 h3d ya3 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x4f h3d ya0 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x4f h3d ya1 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x4f h3d ya2 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x4f h3d ya3 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x64 h3d ya7 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x64 h3d ya8 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m18 x84 h3e ya9 ff3 fs28 fc0 sc0 ls0 ws0">0</div><div class="t m18 x71 h3e yaa ff3 fs28 fc0 sc0 ls0 ws0">2<span class="_ _3"></span>/</div><div class="t m18 x85 h3e yab ff3 fs28 fc0 sc0 ls0 ws0">0</div><div class="t m18 x71 h3e yac ff3 fs28 fc0 sc0 ls0 ws0">2<span class="_ _3"></span>/</div><div class="t m18 x2d h3f ya4 ff3 fs27 fc0 sc0 ls0 ws0">2</div><div class="t m18 x86 h3f ya5 ff3 fs27 fc0 sc0 ls0 ws0">2</div><div class="t m19 x87 h40 ya4 ff6 fs29 fc0 sc0 ls0 ws0">�</div><div class="t m19 x88 h40 ya5 ff6 fs29 fc0 sc0 ls0 ws0">�</div><div class="t m18 x89 h3e yaa ff5 fs28 fc0 sc0 ls0 ws0">M<span class="_ _46"></span>M</div><div class="t m18 x2e h3e ya9 ff5 fs28 fc0 sc0 ls0 ws0">n</div><div class="t m18 x89 h3e yac ff5 fs28 fc0 sc0 ls0 ws0">M<span class="_ _46"></span>M</div><div class="t m18 x2e h3e yab ff5 fs28 fc0 sc0 ls0 ws0">n</div><div class="t m18 x1a h3e yaa ff5 fs28 fc0 sc0 ls0 ws0">M</div><div class="t m18 x64 h3e ya9 ff5 fs28 fc0 sc0 ls0 ws0">n</div><div class="t m18 x1a h3e yac ff5 fs28 fc0 sc0 ls0 ws0">M</div><div class="t m18 x64 h3e yab ff5 fs28 fc0 sc0 ls0 ws0">n</div><div class="t m18 x8a h3f ya4 ff5 fs27 fc0 sc0 ls0 ws0">c</div><div class="t m18 x8b h3f ya5 ff5 fs27 fc0 sc0 ls0 ws0">a</div><div class="t m18 x3 h3f ya4 ff5 fs27 fc0 sc0 ls0 ws0">c</div><div class="t m18 x3 h3f ya5 ff5 fs27 fc0 sc0 ls0 ws0">a</div></div><div class="c x79 y9d w21 h1b"><div class="t m0 x8c h2 yad ff2 fs0 fc0 sc0 ls0 ws0">，</div></div><div class="c x8d y9f w27 h2b"><div class="t m0 x51 h41 ya0 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 x51 h41 ya1 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 x51 h41 ya2 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 x51 h41 ya3 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 xf h41 ya0 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 xf h41 ya1 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 xf h41 ya2 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 xf h41 ya3 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 x8e h41 ya6 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 x8 h41 ya0 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 x8 h41 ya1 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 x8 h41 ya2 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 x8 h41 ya3 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 x4f h41 ya0 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 x4f h41 ya1 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 x4f h41 ya2 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 x4f h41 ya3 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 x1a h41 ya7 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 x52 h41 ya8 ff4 fs2a fc0 sc0 ls0 ws0">�</div><div class="t m0 xd h3e yaa ff5 fs28 fc0 sc0 ls0 ws0">m</div><div class="t m0 x35 h3e ya9 ff5 fs28 fc0 sc0 ls0 ws0">n</div><div class="t m0 xd h3e yac ff5 fs28 fc0 sc0 ls0 ws0">m</div><div class="t m0 x72 h3e yab ff5 fs28 fc0 sc0 ls0 ws0">n</div><div class="t m0 x75 h3e yaa ff5 fs28 fc0 sc0 ls0 ws0">m</div><div class="t m0 x52 h3e ya9 ff5 fs28 fc0 sc0 ls0 ws0">n</div><div class="t m0 x48 h3e yac ff5 fs28 fc0 sc0 ls0 ws0">m</div><div class="t m0 x64 h3e yab ff5 fs28 fc0 sc0 ls0 ws0">n</div><div class="t m0 x33 h42 ya4 ff5 fs2a fc0 sc0 ls0 ws0">d</div><div class="t m0 x2e h42 ya5 ff5 fs2a fc0 sc0 ls0 ws0">r</div><div class="t m0 x3 h42 ya4 ff5 fs2a fc0 sc0 ls0 ws0">d</div><div class="t m0 x45 h42 ya5 ff5 fs2a fc0 sc0 ls0 ws0">r</div></div><div class="c x7f yae w24 h3"><div class="t m0 x4f h2 yaf ff2 fs0 fc0 sc0 ls0 ws0">旋</div><div class="t m0 x4f h2 y59 ff2 fs0 fc0 sc0 ls0 ws0">转</div></div><div class="c x16 yb0 wb h43"><div class="t m1a x4f h44 yb1 ff6 fs2b fc0 sc0 ls0 ws0">�</div></div><div class="c x3b yb2 w28 h45"><div class="t m0 x1 h46 yb3 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x1 h46 yb4 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x1 h46 yb5 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x1 h46 yb6 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x49 h46 yb3 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x49 h46 yb4 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x49 h46 yb5 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x49 h46 yb6 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x8f h46 yb7 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x88 h46 yb8 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x88 h46 yb9 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x88 h46 yba ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x88 h46 ybb ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x8e h46 yb8 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x8e h46 yb9 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x8e h46 yba ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x8e h46 ybb ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x32 h46 ybc ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x8 h46 yb7 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x90 h46 yb3 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x90 h46 yb4 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x90 h46 yb5 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x90 h46 yb6 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x4f h46 yb3 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x4f h46 yb4 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x4f h46 yb5 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x4f h46 yb6 ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x5d h46 ybd ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x5d h46 ybe ff4 fs2c fc0 sc0 ls0 ws0">�</div><div class="t m0 x5f h47 ybf ff5 fs2d fc0 sc0 ls0 ws0">M</div><div class="t m0 x91 h47 yc0 ff5 fs2d fc0 sc0 ls0 ws0">n</div><div class="t m0 x5f h47 yc1 ff5 fs2d fc0 sc0 ls0 ws0">M</div><div class="t m0 x91 h47 yc2 ff5 fs2d fc0 sc0 ls0 ws0">n</div><div class="t m0 x64 h47 ybf ff5 fs2d fc0 sc0 ls0 ws0">M</div><div class="t m0 x5d h47 yc0 ff5 fs2d fc0 sc0 ls0 ws0">n</div><div class="t m0 x64 h47 yc1 ff5 fs2d fc0 sc0 ls0 ws0">M</div><div class="t m0 x5d h47 yc2 ff5 fs2d fc0 sc0 ls0 ws0">n</div><div class="t m0 x81 h48 yc3 ff5 fs2c fc0 sc0 ls0 ws0">c</div><div class="t m0 x81 h48 yc4 ff5 fs2c fc0 sc0 ls0 ws0">a</div><div class="t m0 x6e h48 yc3 ff5 fs2c fc0 sc0 ls0 ws0">c</div><div class="t m0 x6e h48 yc4 ff5 fs2c fc0 sc0 ls0 ws0">a</div><div class="t m0 x92 h48 yc5 ff3 fs2c fc0 sc0 ls0 ws0">)<span class="_ _47"></span>cos(<span class="_ _31"></span>)<span class="_ _9"></span>sin(</div><div class="t m0 x82 h48 ybc ff3 fs2c fc0 sc0 ls0 ws0">)<span class="_ _c"></span>sin(<span class="_ _26"></span>)<span class="_ _47"></span>cos(</div><div class="t md x60 h49 yc5 ff6 fs2e fc0 sc0 ls0 ws0">�<span class="_ _14"></span>�</div><div class="t md x93 h49 ybc ff6 fs2e fc0 sc0 ls0 ws0">�<span class="_ _2f"></span>�</div></div><div class="c x79 yae w21 h3"><div class="t m0 x56 h2 yc6 ff2 fs0 fc0 sc0 ls0 ws0">，</div></div><div class="c x3b yc7 w29 h1a"><div class="t m0 x94 h4a yc8 ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x94 h4a yc9 ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x94 h4a yca ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x94 h4a ycb ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x47 h4a yc8 ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x47 h4a yc9 ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x47 h4a yca ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x47 h4a ycb ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x92 h4a ycc ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x71 h4a ycd ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x71 h4a yce ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x71 h4a ycf ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x71 h4a yd0 ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x9 h4a ycd ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x9 h4a yce ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x9 h4a ycf ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x9 h4a yd0 ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x5a h4a yd1 ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x80 h4a ycc ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x48 h4a yc8 ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x48 h4a yc9 ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x48 h4a yca ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x48 h4a ycb ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x4f h4a yc8 ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x4f h4a yc9 ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x4f h4a yca ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x4f h4a ycb ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x5d h4a yd2 ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x5d h4a yd3 ff4 fs2f fc0 sc0 ls0 ws0">�</div><div class="t m0 x84 h4b yd4 ff5 fs30 fc0 sc0 ls0 ws0">m</div><div class="t m0 x8f h4b yd5 ff5 fs30 fc0 sc0 ls0 ws0">n</div><div class="t m0 x8f h4b yd6 ff5 fs30 fc0 sc0 ls0 ws0">m</div><div class="t m0 x8f h4b yd7 ff5 fs30 fc0 sc0 ls0 ws0">n</div><div class="t m0 x64 h4b yd4 ff5 fs30 fc0 sc0 ls0 ws0">m</div><div class="t m0 x5d h4b yd5 ff5 fs30 fc0 sc0 ls0 ws0">n</div><div class="t m0 x7d h4b yd6 ff5 fs30 fc0 sc0 ls0 ws0">m</div><div class="t m0 x45 h4b yd7 ff5 fs30 fc0 sc0 ls0 ws0">n</div><div class="t m0 x88 h4c yd8 ff5 fs2f fc0 sc0 ls0 ws0">d</div><div class="t m0 x7a h4c yd9 ff5 fs2f fc0 sc0 ls0 ws0">r</div><div class="t m0 xe h4c yd8 ff5 fs2f fc0 sc0 ls0 ws0">d</div><div class="t m0 x6e h4c yd9 ff5 fs2f fc0 sc0 ls0 ws0">r</div><div class="t m0 x95 h4c yda ff3 fs2f fc0 sc0 ls0 ws0">)<span class="_ _48"></span>cos(<span class="_ _49"></span>)<span class="_ _44"></span>sin(</div><div class="t m0 x96 h4c yd1 ff3 fs2f fc0 sc0 ls0 ws0">)<span class="_ _44"></span>sin(<span class="_ _46"></span>)<span class="_ _48"></span>cos(</div><div class="t md x89 h4d yda ff6 fs31 fc0 sc0 ls0 ws0">�<span class="_ _38"></span>�</div><div class="t md x97 h4d yd1 ff6 fs31 fc0 sc0 ls0 ws0">�<span class="_ _4a"></span>�</div></div><div class="c x7f ydb w24 h1d"><div class="t m0 x4f h2 ydc ff2 fs0 fc0 sc0 ls0 ws0">尺</div><div class="t m0 x4f h2 y67 ff2 fs0 fc0 sc0 ls0 ws0">度</div></div><div class="c x16 ydd wc h13"><div class="t md x12 h4e yde ff6 fs32 fc0 sc0 ls0 ws0">�</div></div><div class="c x3b ydf w12 h2b"><div class="t m1b x98 h3d ya0 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m1b x98 h3d ya1 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m1b x98 h3d ya2 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m1b x98 h3d ya3 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m1b xd h3d ya0 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m1b xd h3d ya1 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m1b xd h3d ya2 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m1b xd h3d ya3 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m1b x4d h3d ya6 ff4 fs27 fc0 sc0 ls0 ws0">�<span class="_ _4b"></span>�</div><div class="t m1b x8 h3d ya0 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m1b x8 h3d ya1 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m1b x8 h3d ya2 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m1b x8 h3d ya3 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m1b x4f h3d ya0 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m1b x4f h3d ya1 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m1b x4f h3d ya2 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m1b x4f h3d ya3 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m1b x64 h3d ya7 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m1b x52 h3d ya8 ff4 fs27 fc0 sc0 ls0 ws0">�</div><div class="t m1b x86 h3e yaa ff5 fs28 fc0 sc0 ls0 ws0">M</div><div class="t m1b x86 h3e ya9 ff5 fs28 fc0 sc0 ls0 ws0">n</div><div class="t m1b x86 h3e yac ff5 fs28 fc0 sc0 ls0 ws0">M</div><div class="t m1b x86 h3e yab ff5 fs28 fc0 sc0 ls0 ws0">n</div><div class="t m1b x42 h3e yaa ff5 fs28 fc0 sc0 ls0 ws0">M</div><div class="t m1b x64 h3e ya9 ff5 fs28 fc0 sc0 ls0 ws0">n</div><div class="t m1b x42 h3e yac ff5 fs28 fc0 sc0 ls0 ws0">M</div><div class="t m1b x52 h3e yab ff5 fs28 fc0 sc0 ls0 ws0">n</div><div class="t m1b x51 h3f ya4 ff5 fs27 fc0 sc0 ls0 ws0">c</div><div class="t m1b x4a h3f ya5 ff5 fs27 fc0 sc0 ls0 ws0">a</div><div class="t m1b x3 h3f ya4 ff5 fs27 fc0 sc0 ls0 ws0">c</div><div class="t m1b x3 h3f ya5 ff5 fs27 fc0 sc0 ls0 ws0">a</div><div class="t m1c x99 h4f ya6 ff6 fs33 fc0 sc0 ls0 ws0">�</div></div><div class="c x79 ydb w21 h1d"><div class="t m0 x71 h2 ye0 ff2 fs0 fc0 sc0 ls0 ws0">，</div></div><div class="c x9a ydf w12 h50"><div class="t m1d x98 h51 ye1 ff4 fs34 fc0 sc0 ls0 ws0">�</div><div class="t m1d x98 h51 ye2 ff4 fs34 fc0 sc0 ls0 ws0">�</div><div class="t m1d x98 h51 ye3 ff4 fs34 fc0 sc0 ls0 ws0">�</div><div class="t m1d x98 h51 ye4 ff4 fs34 fc0 sc0 ls0 ws0">�</div><div class="t m1d xd h51 ye1 ff4 fs34 fc0 sc0 ls0 ws0">�</div><div class="t m1d xd h51 ye2 ff4 fs34 fc0 sc0 ls0 ws0">�</div><div class="t m1d xd h51 ye3 ff4 fs34 fc0 sc0 ls0 ws0">�</div><div class="t m1d xd h51 ye4 ff4 fs34 fc0 sc0 ls0 ws0">�</div><div class="t m1d x53 h51 ye5 ff4 fs34 fc0 sc0 ls0 ws0">�<span class="_ _32"></span>�</div><div class="t m1d x8 h51 ye1 ff4 fs34 fc0 sc0 ls0 ws0">�</div><div class="t m1d x8 h51 ye2 ff4 fs34 fc0 sc0 ls0 ws0">�</div><div class="t m1d x8 h51 ye3 ff4 fs34 fc0 sc0 ls0 ws0">�</div><div class="t m1d x8 h51 ye4 ff4 fs34 fc0 sc0 ls0 ws0">�</div><div class="t m1d x4f h51 ye1 ff4 fs34 fc0 sc0 ls0 ws0">�</div><div class="t m1d x4f h51 ye2 ff4 fs34 fc0 sc0 ls0 ws0">�</div><div class="t m1d x4f h51 ye3 ff4 fs34 fc0 sc0 ls0 ws0">�</div><div class="t m1d x4f h51 ye4 ff4 fs34 fc0 sc0 ls0 ws0">�</div><div class="t m1d x1a h51 ye6 ff4 fs34 fc0 sc0 ls0 ws0">�</div><div class="t m1d x52 h51 ye7 ff4 fs34 fc0 sc0 ls0 ws0">�</div><div class="t m1d x9b h52 ye8 ff5 fs35 fc0 sc0 ls0 ws0">m</div><div class="t m1d x2d h52 ye9 ff5 fs35 fc0 sc0 ls0 ws0">n</div><div class="t m1d x2d h52 yea ff5 fs35 fc0 sc0 ls0 ws0">m</div><div class="t m1d x32 h52 yeb ff5 fs35 fc0 sc0 ls0 ws0">n</div><div class="t m1d x48 h52 ye8 ff5 fs35 fc0 sc0 ls0 ws0">m</div><div class="t m1d x52 h52 ye9 ff5 fs35 fc0 sc0 ls0 ws0">n</div><div class="t m1d x48 h52 yea ff5 fs35 fc0 sc0 ls0 ws0">m</div><div class="t m1d x64 h52 yeb ff5 fs35 fc0 sc0 ls0 ws0">n</div><div class="t m1d x51 h53 ya7 ff5 fs34 fc0 sc0 ls0 ws0">d</div><div class="t m1d x51 h53 yec ff5 fs34 fc0 sc0 ls0 ws0">r</div><div class="t m1d x3 h53 ya7 ff5 fs34 fc0 sc0 ls0 ws0">d</div><div class="t m1d x45 h53 yec ff5 fs34 fc0 sc0 ls0 ws0">r</div><div class="t m1e x99 h54 ye5 ff6 fs36 fc0 sc0 ls0 ws0">�</div></div><div class="t m0 x1 h2 yed ff2 fs0 fc0 sc0 ls0 ws0">由表<span class="_ _0"> </span><span class="ff1">3-2<span class="_ _0"> </span></span>可知，<span class="_ _13"></span>平移和尺度缩放时，<span class="_ _10"></span>差异均为常量，<span class="_ _13"></span>可通过约简和归一化的方法</div></div><div class="pi" data-data='{"ctm":[1.611830,0.000000,0.000000,1.611830,0.000000,0.000000]}'></div></div>

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