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<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/622b5fc03d2fbb0007cfe9e8/bg1.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">糊聚类<span class="fc1 sc0">的图像分割实验报告</span></div><div class="t m0 x2 h4 y3 ff1 fs1 fc0 sc0 ls0 ws0">班</div><div class="t m0 x3 h4 y4 ff1 fs1 fc0 sc0 ls0 ws0">级：<span class="ff2">020851</span></div><div class="t m0 x1 h4 y5 ff1 fs1 fc0 sc0 ls0 ws0">姓名：张宁 <span class="fc1 sc0">陈文艺 </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0">学号：</span></div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></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/622b5fc03d2fbb0007cfe9e8/bg2.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x4 h5 y6 ff1 fs2 fc0 sc0 ls0 ws0">实验一 模糊聚类的图像分割</div><div class="t m0 x3 h6 y7 ff1 fs3 fc0 sc1 ls0 ws0">一、实验目的</div><div class="t m0 x5 h7 y8 ff1 fs4 fc0 sc0 ls0 ws0">通过模糊<span class="_ _0"> </span><span class="ff3">c-</span>均值（<span class="ff3">FCM</span>）聚类实现图像的分割。</div><div class="t m0 x3 h6 y9 ff1 fs3 fc0 sc1 ls0 ws0">二、算法描述</div><div class="t m0 x2 h8 ya ff3 fs4 fc0 sc0 ls0 ws0">F</div><div class="t m0 x3 h7 yb ff3 fs4 fc0 sc0 ls0 ws0">CM<span class="_ _0"> </span><span class="ff1">聚类算法目标函数为：</span></div><div class="t m0 x6 h7 yc ff1 fs4 fc0 sc0 ls0 ws0">（<span class="ff3">1-1</span>）</div><div class="t m0 x3 h7 yd ff1 fs4 fc0 sc0 ls0 ws0">如<span class="_ _1"></span>果<span class="_ _2"> </span>表<span class="_ _1"></span>示<span class="_ _1"></span>每<span class="_ _1"></span>一<span class="_ _1"></span>个<span class="_ _1"></span>样<span class="_ _1"></span>本<span class="_ _3"> </span>的<span class="_ _1"></span>维<span class="_ _1"></span>数<span class="_ _1"></span>，<span class="_ _4"> </span>是<span class="_ _1"></span>一<span class="_ _1"></span>个<span class="_ _5"> </span>矩<span class="_ _1"></span>阵<span class="_ _1"></span>；<span class="_ _6"> </span>表<span class="_ _1"></span>示<span class="_ _1"></span>样<span class="_ _1"></span>本<span class="_ _1"></span>数</div><div class="t m0 x3 h7 ye ff1 fs4 fc0 sc0 ls0 ws0">目，通<span class="_ _1"></span>常表示<span class="_ _1"></span>图像像<span class="_ _1"></span>素数；<span class="_ _7"> </span>表示聚<span class="_ _1"></span>类数目<span class="_ _1"></span>；<span class="_ _8"> </span>是矢量<span class="_ _6"> </span>隶属于第<span class="_ _9"> </span>类的隶</div><div class="t m0 x3 h7 yf ff1 fs4 fc0 sc0 ls0 ws0">属<span class="_ _a"> </span>度<span class="_ _a"> </span>函<span class="_ _a"> </span>数<span class="_ _a"> </span>，<span class="_ _a"> </span>满<span class="_ _a"> </span>足<span class="_ _b"> </span>且<span class="_ _c"> </span>；<span class="_ _a"> </span>聚<span class="_ _a"> </span>类<span class="_ _a"> </span>中<span class="_ _a"> </span>心<span class="_ _d"> </span>是</div><div class="t m0 x7 h7 y10 ff1 fs4 fc0 sc0 ls0 ws0">矩阵，<span class="_ _7"> </span>和<span class="_ _e"> </span>更新等式分别为：</div><div class="t m0 x6 h7 y11 ff1 fs4 fc0 sc0 ls0 ws0">（<span class="ff3">1-2</span>）</div><div class="t m0 x3 h7 y12 ff1 fs4 fc0 sc0 ls0 ws0">对于每一个<span class="_ _1"></span>模糊隶属度，<span class="_ _1"></span>由<span class="_ _b"> </span>控制模<span class="_ _1"></span>糊度的权重指<span class="_ _1"></span>数；<span class="_ _f"> </span>为相似性</div><div class="t m0 x8 h9 y13 ff3 fs5 fc0 sc0 ls0 ws0">2</div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></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/622b5fc03d2fbb0007cfe9e8/bg3.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x3 h7 y14 ff1 fs4 fc0 sc0 ls0 ws0">测度。</div><div class="t m0 x2 h7 y15 ff1 fs4 fc0 sc0 ls0 ws0">其</div><div class="t m0 x3 h7 y16 ff1 fs4 fc0 sc0 ls0 ws0">中：</div><div class="t m0 x3 h7 y17 ff1 fs4 fc0 sc0 ls0 ws0">数据样本维数（灰度图像时为<span class="_ _0"> </span><span class="ff3">1</span>）；</div><div class="t m0 x3 h7 y18 ff1 fs4 fc0 sc0 ls0 ws0">像素点数目；</div><div class="t m0 x3 h7 y19 ff1 fs4 fc0 sc0 ls0 ws0">像素<span class="_ _10"> </span>特征（灰度图像时，表示灰度值）；</div><div class="t m0 x3 h7 y1a ff1 fs4 fc0 sc0 ls0 ws0">图像分割类别数；</div><div class="t m0 x3 h7 y1b ff1 fs4 fc0 sc0 ls0 ws0">像素点<span class="_ _10"> </span>属于第<span class="_ _11"> </span>类的隶属度；</div><div class="t m0 x3 h7 y1c ff1 fs4 fc0 sc0 ls0 ws0">第<span class="_ _10"> </span>类聚类中心。</div><div class="t m0 x3 h6 y1d ff1 fs3 fc0 sc1 ls0 ws0">三、算法步骤及流程图</div><div class="t m0 x5 h7 y1e ff3 fs4 fc0 sc0 ls0 ws0">Step1<span class="ff1">：设置目标函数精度<span class="_ _12"> </span>，模糊指数<span class="_ _e"> </span>（<span class="_ _e"> </span>通常取<span class="_ _0"> </span></span>2<span class="ff1">），最大迭代次数<span class="_ _13"> </span>；</span></div><div class="t m0 x5 h7 y1f ff3 fs4 fc0 sc0 ls0 ws0">Step2<span class="ff1">：初始化模糊聚类中心<span class="_ _e"> </span>；</span></div><div class="t m0 x5 h7 y20 ff3 fs4 fc0 sc0 ls0 ws0">Step3<span class="ff1">：由式（</span>1-2<span class="ff1">）更新模糊划分矩阵<span class="_ _14"> </span>和聚类中心</span></div><div class="t m0 x5 h7 y21 ff3 fs4 fc0 sc0 ls0 ws0">Step4<span class="ff1">：若<span class="_ _15"> </span>或<span class="_ _16"> </span>则结束聚类；否则，<span class="_ _17"> </span>并转<span class="_ _0"> </span></span>Step3<span class="ff1">；</span></div><div class="t m0 x5 h7 y22 ff3 fs4 fc0 sc0 ls0 ws0">Step5<span class="ff1">：由所得<span class="_ _14"> </span>得到各像素点分类结果。</span></div><div class="t m0 x8 h9 y13 ff3 fs5 fc0 sc0 ls0 ws0">3</div></div><div class="t m0 x9 h7 y23 ff1 fs4 fc0 sc0 ls0 ws0">否</div><div class="c xa y24 w3 ha"><div class="t m0 xb h7 y25 ff1 fs4 fc2 sc2 ls0 ws0">否<span class="fc1 sc0">达到最大 </span><span class="fc1 sc0"> </span><span class="fc1 sc0"> </span><span class="fc1 sc0">迭代次数</span></div></div><div class="c xc y26 w4 hb"><div class="t m0 xd h7 y27 ff1 fs4 fc0 sc0 ls0 ws0">是</div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
