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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/622b3ec3ff7f9c46a628d575/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">收稿日期<span class="_ _0"> </span><span class="ff2 fs1">:200<span class="_ _1"></span>6<span class="_ _2"></span><span class="ff3 fs0">2<span class="_ _2"></span><span class="ff2 fs1">0<span class="_ _1"></span>4<span class="_ _2"></span><span class="ff3 fs0">2<span class="_ _2"></span><span class="ff2 fs1">2<span class="_ _1"></span>0</span></span></span></span></span></div><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">作者简介<span class="_ _0"> </span><span class="ff2 fs1">:<span class="_ _3"></span></span><span class="ff4">刘振</span></div><div class="t m0 x2 h4 y3 ff2 fs1 fc0 sc0 ls0 ws0">(</div><div class="t m0 x3 h4 y2 ff2 fs1 fc0 sc0 ls0 ws0">19<span class="_ _1"></span>77<span class="_"> </span>-</div><div class="t m0 x4 h4 y3 ff2 fs1 fc0 sc0 ls0 ws0">)</div><div class="t m0 x5 h3 y2 ff2 fs1 fc0 sc0 ls0 ws0">,<span class="ff4 fs0">男<span class="_ _4"> </span></span>,<span class="ff4 fs0">硕士研究生<span class="_ _4"> </span></span>,<span class="ff4 fs0">讲师<span class="_ _4"> </span></span>,<span class="ff4 fs0">研究方向<span class="_ _1"></span>为模式识别与智能系统<span class="_ _5"></span>。</span></div><div class="t m0 x1 h5 y4 ff1 fs2 fc0 sc0 ls0 ws0">文章编号<span class="_ _4"> </span><span class="ff2 fs3">:10<span class="_ _1"></span>02<span class="_ _6"></span><span class="ff3 fs2">2<span class="_ _6"></span><span class="ff2 fs3">402<span class="_ _1"></span>6</span></span></span></div><div class="t m0 x4 h6 y5 ff2 fs3 fc0 sc0 ls0 ws0">(</div><div class="t m0 x6 h6 y4 ff2 fs3 fc0 sc0 ls0 ws0">20<span class="_ _1"></span>06</div><div class="t m0 x7 h6 y5 ff2 fs3 fc0 sc0 ls0 ws0">)</div><div class="t m0 x8 h5 y4 ff2 fs3 fc0 sc0 ls0 ws0">04<span class="_ _6"></span><span class="ff3 fs2">2<span class="_ _2"></span><span class="ff2 fs3">0<span class="_ _1"></span>06<span class="_ _1"></span>3<span class="_ _2"></span><span class="ff3 fs2">2<span class="_ _6"></span><span class="ff2 fs3">05</span></span></span></span></div><div class="t m0 x9 h7 y6 ff4 fs4 fc0 sc0 ls0 ws0">基于<span class="_ _7"> </span><span class="ff2 fs5">P<span class="_ _6"></span>C<span class="_ _8"></span>A<span class="_ _9"> </span><span class="ff4 fs4">和神经网络的人<span class="_ _1"></span>脸识别</span></span></div><div class="t m0 xa h8 y7 ff4 fs6 fc0 sc0 ls0 ws0">刘<span class="_ _a"> </span> <span class="_ _b"></span>振<span class="_ _a"> </span><span class="ff2 fs7">,</span>吴<span class="_ _a"> </span> <span class="_ _b"></span>鹏<span class="_ _a"> </span><span class="ff2 fs7">,<span class="_ _3"></span></span>陈月辉</div><div class="t m0 xb h6 y8 ff2 fs3 fc0 sc0 ls0 ws0">(</div><div class="t m0 xc h9 y9 ff4 fs2 fc0 sc0 ls0 ws0">济南大学信息科学与工程<span class="_ _3"></span>学院<span class="_ _4"> </span><span class="ff2 fs3">,</span>山东<span class="_ _a"> </span>济南<span class="_ _c"> </span><span class="ff2 fs3">25<span class="_ _1"></span>00<span class="_ _1"></span>22</span></div><div class="t m0 xd h6 y8 ff2 fs3 fc0 sc0 ls0 ws0">)</div><div class="t m0 xe h9 ya ff1 fs2 fc0 sc0 ls0 ws0">摘要<span class="_ _4"> </span><span class="ff2 fs3">:</span><span class="ff4">介绍一种基于<span class="_ _d"> </span><span class="ff2 fs3">P<span class="_ _2"></span>C<span class="_ _6"></span>A<span class="_"> </span><span class="ff4 fs2">和神经网络结合的人<span class="_ _3"></span>脸识<span class="_ _3"></span>别<span class="_ _3"></span>方<span class="_ _3"></span>法<span class="_ _0"></span>。<span class="_ _6"></span>该<span class="_ _3"></span>方法<span class="_ _3"></span>首<span class="_ _3"></span>先<span class="_ _3"></span>利<span class="_ _3"></span>用主<span class="_ _3"></span>成<span class="_ _3"></span>分<span class="_ _3"></span>分<span class="_ _3"></span>析方<span class="_ _3"></span>法<span class="_ _3"></span>对<span class="_ _3"></span>整<span class="_ _3"></span>幅<span class="_ _3"></span>图像<span class="_ _3"></span>进</span></span></span></div><div class="t m0 xe h9 yb ff4 fs2 fc0 sc0 ls0 ws0">行特征提取<span class="_ _c"> </span><span class="ff2 fs3">,</span>获得最佳描述特征<span class="_ _e"> </span><span class="ff2 fs3">,</span>从而减小神经网络的<span class="_ _3"></span>输入<span class="_ _0"></span>。<span class="_ _6"></span>然后<span class="_ _3"></span>将<span class="_ _3"></span>降维<span class="_ _3"></span>之后<span class="_ _3"></span>的图<span class="_ _3"></span>像<span class="_ _3"></span>数据<span class="_ _3"></span>输入<span class="_ _3"></span>到一<span class="_ _3"></span>个<span class="_ _3"></span>前向<span class="_ _3"></span>传</div><div class="t m0 xe h9 yc ff4 fs2 fc0 sc0 ls0 ws0">播神经网络中训练<span class="_ _0"></span>。<span class="_ _6"></span>神经网络的权值采用粒子群算法<span class="_ _3"></span>进行<span class="_ _3"></span>优化<span class="_ _c"> </span><span class="ff2 fs3">,</span>用<span class="_ _3"></span>标准<span class="_ _3"></span>人脸<span class="_ _3"></span>数据<span class="_ _3"></span>库<span class="_ _3"></span>中的<span class="_ _3"></span>样本<span class="_ _3"></span>进行<span class="_ _3"></span>测试<span class="_ _c"> </span><span class="ff2 fs3">,</span>最<span class="_ _3"></span>后</div><div class="t m0 xe h9 yd ff4 fs2 fc0 sc0 ls0 ws0">将该方法与其他方法作了<span class="_ _3"></span>比较<span class="_ _0"></span>。<span class="_ _f"></span>实验结果表明<span class="_ _e"> </span><span class="ff2 fs3">,</span>该方法能<span class="_ _3"></span>够取得更好的效果<span class="_ _0"></span>。</div><div class="t m0 xe h9 ye ff1 fs2 fc0 sc0 ls0 ws0">关键词<span class="_ _4"> </span><span class="ff2 fs3">:</span><span class="ff4">主成<span class="_ _3"></span>分分析<span class="_ _10"> </span><span class="ff2 fs3">;<span class="_ _3"></span></span>神经网络<span class="_ _10"> </span><span class="ff2 fs3">;<span class="_ _3"></span></span>粒子群算法<span class="_ _10"> </span><span class="ff2 fs3">;<span class="_ _3"></span></span>人脸识别</span></div><div class="t m0 xe h9 yf ff1 fs2 fc0 sc0 ls0 ws0">中图分类号<span class="_ _10"> </span><span class="ff2 fs3">:<span class="_ _11"></span>T<span class="_ _2"></span>P<span class="_ _2"></span>39<span class="_ _1"></span>1<span class="_ _3"></span>.<span class="_ _10"> </span>41<span class="_ _10"> </span><span class="ff4 fs2">     <span class="_ _8"></span><span class="ff1">文献标识码<span class="_ _10"> </span><span class="ff2 fs3">:<span class="_ _3"></span>A</span></span></span></span></div><div class="t m0 x1 ha y10 ff5 fs8 fc0 sc0 ls0 ws0">1<span class="_"> </span><span class="ff1 fs9"> <span class="_ _12"></span>引言</span></div><div class="t m0 xf hb y11 ff4 fsa fc0 sc0 ls0 ws0">人脸识别技术</div><div class="t m0 x5 hc y12 ff2 fsb fc0 sc0 ls0 ws0">[<span class="_ _3"></span>1<span class="ff4 fsc">~</span>3<span class="_ _5"></span>]</div><div class="t m0 x10 hb y11 ff4 fsa fc0 sc0 ls0 ws0">就是通过计算机提取人脸的特<span class="_ _1"></span>征<span class="_ _c"> </span><span class="ff2 fsd">,<span class="_ _3"></span></span>并根<span class="_ _3"></span>据<span class="_ _3"></span>这些<span class="_ _3"></span>特<span class="_ _3"></span>征<span class="_ _3"></span>进行<span class="_ _3"></span>身<span class="_ _3"></span>份验<span class="_ _3"></span>证<span class="_ _3"></span>的一<span class="_ _3"></span>种<span class="_ _3"></span>技<span class="_ _3"></span>术<span class="_ _11"></span>。<span class="_ _6"></span>人<span class="_ _3"></span>脸</div><div class="t m0 x1 hb y13 ff4 fsa fc0 sc0 ls0 ws0">与人体的其他生物特征</div><div class="t m0 x11 hd y14 ff2 fsd fc0 sc0 ls0 ws0">(</div><div class="t m0 x12 hb y13 ff4 fsa fc0 sc0 ls0 ws0">指纹<span class="_ _0"></span>、<span class="_ _13"></span>虹膜等</div><div class="t m0 x13 hd y14 ff2 fsd fc0 sc0 ls0 ws0">)</div><div class="t m0 x14 hb y13 ff4 fsa fc0 sc0 ls0 ws0">一样与生俱来<span class="_ _c"> </span><span class="ff2 fsd">,</span>它们所具有的唯一<span class="_ _1"></span>性和不易被复制的良好特性为身份</div><div class="t m0 x1 hb y15 ff4 fsa fc0 sc0 ls0 ws0">鉴别提供了必要的前提<span class="_ _11"></span>。<span class="_ _f"></span>同其他生物特征识别技术相比<span class="_ _c"> </span><span class="ff2 fsd">,<span class="_ _3"></span></span>人脸<span class="_ _3"></span>识别<span class="_ _3"></span>技术具<span class="_ _3"></span>有<span class="_ _3"></span>操作<span class="_ _3"></span>简<span class="_ _3"></span>单<span class="_ _0"></span>、<span class="_ _14"></span>结<span class="_ _3"></span>果直<span class="_ _3"></span>观<span class="_ _0"></span>、<span class="_ _14"></span>隐<span class="_ _3"></span>蔽性<span class="_ _3"></span>好</div><div class="t m0 x1 hb y16 ff4 fsa fc0 sc0 ls0 ws0">等优点<span class="_ _0"></span>。<span class="_ _f"></span>因此<span class="_ _c"> </span><span class="ff2 fsd">,</span>人脸识别在信息安全<span class="_ _11"></span>、<span class="_ _13"></span>刑事侦破<span class="_ _0"></span>、<span class="_ _13"></span>出入口控制等领域具有广泛的应用前景<span class="_ _11"></span>。</div><div class="t m0 xf hb y17 ff4 fsa fc0 sc0 ls0 ws0">人脸图<span class="_ _1"></span>像的特征提取是人脸识别过程中至关<span class="_ _3"></span>重<span class="_ _3"></span>要的<span class="_ _3"></span>一<span class="_ _3"></span>个环<span class="_ _3"></span>节<span class="_ _c"> </span><span class="ff2 fsd">,<span class="_ _15"> </span></span>该<span class="_ _3"></span>环节<span class="_ _3"></span>又<span class="_ _3"></span>是进<span class="_ _3"></span>行<span class="_ _3"></span>识别<span class="_ _3"></span>的<span class="_ _3"></span>前<span class="_ _3"></span>提环<span class="_ _3"></span>节<span class="_ _c"> </span><span class="ff2 fsd">,<span class="_ _3"></span></span>如<span class="_ _3"></span>何</div><div class="t m0 x1 hb y18 ff4 fsa fc0 sc0 ls0 ws0">做好人脸图像的特征提取显得<span class="_ _1"></span>尤为<span class="_ _3"></span>重<span class="_ _3"></span>要<span class="_ _0"></span>。<span class="_ _f"></span>人<span class="_ _3"></span>脸<span class="_ _3"></span>图<span class="_ _3"></span>像<span class="_ _3"></span>是<span class="_ _3"></span>一<span class="_ _3"></span>个<span class="_ _3"></span>高<span class="_ _3"></span>维<span class="_ _3"></span>向<span class="_ _3"></span>量<span class="_ _c"> </span><span class="ff2 fsd">,<span class="_ _3"></span></span>如<span class="_ _3"></span>果<span class="_ _3"></span>不<span class="_ _3"></span>进<span class="_ _3"></span>行<span class="_ _3"></span>适<span class="_ _3"></span>当<span class="_ _3"></span>处<span class="_ _3"></span>理则<span class="_ _3"></span>计<span class="_ _3"></span>算<span class="_ _3"></span>量<span class="_ _3"></span>很<span class="_ _3"></span>大<span class="_ _c"> </span><span class="ff2 fsd">,</span></div><div class="t m0 x1 hb y19 ff4 fsa fc0 sc0 ls0 ws0">因此必须对其进行降维处理<span class="_ _e"> </span><span class="ff2 fsd">,</span>降维过程中要保留其主要的特征<span class="_ _c"> </span><span class="ff2 fsd">,</span>也就是说希望用图像的少<span class="_ _1"></span>量特征来近似表示</div><div class="t m0 x1 hb y1a ff4 fsa fc0 sc0 ls0 ws0">整个图像<span class="_ _e"> </span><span class="ff2 fsd">,</span>以达到降维并保留图像主要特征的效果<span class="_ _c"> </span><span class="ff2 fsd">,</span>国内<span class="_ _3"></span>外的<span class="_ _3"></span>学者已<span class="_ _3"></span>经研<span class="_ _3"></span>究出<span class="_ _3"></span>了很<span class="_ _3"></span>多<span class="_ _3"></span>关于<span class="_ _3"></span>特<span class="_ _3"></span>征<span class="_ _3"></span>提取<span class="_ _3"></span>的<span class="_ _3"></span>方法<span class="_ _c"> </span><span class="ff2 fsd">,</span></div><div class="t m0 x1 hb y1b ff4 fsa fc0 sc0 ls0 ws0">大致分为两类<span class="_ _e"> </span><span class="ff2 fsd">,</span>一类是基于代数特征的特征提<span class="_ _3"></span>取方<span class="_ _3"></span>法<span class="_ _c"> </span><span class="ff2 fsd">,<span class="_ _3"></span></span>如<span class="_ _3"></span>主成<span class="_ _3"></span>分<span class="_ _3"></span>分<span class="_ _3"></span>析</div><div class="t m0 x15 hd y1c ff2 fsd fc0 sc0 ls0 ws0">(</div><div class="t m0 x16 hd y1b ff2 fsd fc0 sc0 ls0 ws0">P<span class="_ _2"></span>C<span class="_ _6"></span>A</div><div class="t m0 x17 hd y1c ff2 fsd fc0 sc0 ls0 ws0">)</div><div class="t m0 x18 hc y1d ff2 fsb fc0 sc0 ls0 ws0">[<span class="_ _3"></span>4<span class="ff4 fsc">~</span>6<span class="_ _5"></span>]</div><div class="t m0 x19 hb y1b ff4 fsa fc0 sc0 ls0 ws0">、<span class="_ _14"></span>离<span class="_ _3"></span>散<span class="_ _3"></span>余弦<span class="_ _3"></span>变<span class="_ _3"></span>换</div><div class="t m0 x1a hd y1c ff2 fsd fc0 sc0 ls0 ws0">(</div><div class="t m0 x1b hd y1b ff2 fsd fc0 sc0 ls0 ws0">D<span class="_ _1"></span>CT</div><div class="t m0 x1c hd y1c ff2 fsd fc0 sc0 ls0 ws0">)</div><div class="t m0 x1d he y1d ff2 fsb fc0 sc0 ls0 ws0">[<span class="_ _3"></span>7<span class="_ _11"> </span>]</div><div class="t m0 x1e hb y1b ff4 fsa fc0 sc0 ls0 ws0">、<span class="_ _14"></span>独</div><div class="t m0 x1 hb y1e ff4 fsa fc0 sc0 ls0 ws0">立成分分析</div><div class="t m0 x1f hd y1f ff2 fsd fc0 sc0 ls0 ws0">(</div><div class="t m0 x20 hd y1e ff2 fsd fc0 sc0 ls0 ws0">I<span class="_ _2"></span>C<span class="_ _f"></span>A</div><div class="t m0 x21 hd y1f ff2 fsd fc0 sc0 ls0 ws0">)</div><div class="t m0 x22 he y20 ff2 fsb fc0 sc0 ls0 ws0">[<span class="_ _3"></span>8<span class="_ _11"> </span>]</div><div class="t m0 x23 hb y1e ff4 fsa fc0 sc0 ls0 ws0">、<span class="_ _13"></span>线性判别式分析</div><div class="t m0 x24 hd y1f ff2 fsd fc0 sc0 ls0 ws0">(</div><div class="t m0 x25 hd y1e ff2 fsd fc0 sc0 ls0 ws0">L<span class="_ _1"></span>D<span class="_ _2"></span>A</div><div class="t m0 x26 hd y1f ff2 fsd fc0 sc0 ls0 ws0">)</div><div class="t m0 x27 he y20 ff2 fsb fc0 sc0 ls0 ws0">[<span class="_ _3"></span>9<span class="_ _11"> </span>]</div><div class="t m0 x28 hb y1e ff4 fsa fc0 sc0 ls0 ws0">等<span class="_ _4"> </span><span class="ff2 fsd">;<span class="_ _3"></span></span>二是基<span class="_ _3"></span>于几<span class="_ _3"></span>何特<span class="_ _3"></span>征的特<span class="_ _3"></span>征提<span class="_ _3"></span>取方<span class="_ _3"></span>法<span class="_ _c"> </span><span class="ff2 fsd">,</span>如<span class="_ _3"></span>模<span class="_ _3"></span>版<span class="_ _3"></span>匹配<span class="_ _3"></span>方<span class="_ _3"></span>法</div><div class="t m0 x29 he y20 ff2 fsb fc0 sc0 ls0 ws0">[<span class="_ _3"></span>10<span class="_ _11"></span>]</div><div class="t m0 x2a hd y1e ff2 fsd fc0 sc0 ls0 ws0">,</div><div class="t m0 x1 hb y21 ff4 fsa fc0 sc0 ls0 ws0">此外还有人工神经网络</div><div class="t m0 x2b he y22 ff2 fsb fc0 sc0 ls0 ws0">[<span class="_ _3"></span>11<span class="_ _11"></span>]</div><div class="t m0 x2c hb y21 ff4 fsa fc0 sc0 ls0 ws0">的方法等<span class="_ _c"> </span><span class="ff2 fsd">,</span>其中<span class="_ _d"> </span><span class="ff2 fsd">P<span class="_ _2"></span>C<span class="_ _6"></span>A<span class="_"> </span><span class="ff4 fsa">方法是应用最广泛的<span class="_ _1"></span>一种方法<span class="_ _0"></span>。</span></span></div><div class="t m0 x1 ha y23 ff5 fs8 fc0 sc0 ls0 ws0">2<span class="_"> </span><span class="ff1 fs9"> <span class="_ _12"></span>主成分分析</span></div><div class="t m0 xf hb y24 ff4 fsa fc0 sc0 ls0 ws0">主成分分析方法</div><div class="t m0 x2d hd y25 ff2 fsd fc0 sc0 ls0 ws0">(</div><div class="t m0 x2e hd y26 ff2 fsd fc0 sc0 ls0 ws0">P<span class="_ _2"></span>r<span class="_ _1"></span>i<span class="_ _3"></span>n<span class="_ _1"></span>ci<span class="_ _2"></span>p<span class="_ _3"></span>a<span class="_ _1"></span>l<span class="_ _15"> </span>C<span class="_ _f"></span>om<span class="_ _f"></span>p<span class="_ _1"></span>o<span class="_ _3"></span>n<span class="_ _1"></span>en<span class="_ _1"></span>t<span class="_ _a"> </span>An<span class="_ _2"></span>aly<span class="_ _1"></span>s<span class="_ _2"></span>i<span class="_ _3"></span>s<span class="_"> </span>,<span class="_ _3"></span>P<span class="_ _1"></span>C<span class="_ _6"></span>A</div><div class="t m0 x2f hd y25 ff2 fsd fc0 sc0 ls0 ws0">)</div><div class="t m0 x30 hb y26 ff4 fsa fc0 sc0 ls0 ws0">也称为主元法<span class="_ _c"> </span><span class="ff2 fsd">,</span>主分量分析法<span class="_ _e"> </span><span class="ff2 fsd">,</span>是一种常用<span class="_ _0"></span>、<span class="_ _13"></span>简单有效</div><div class="t m0 x1 hb y27 ff4 fsa fc0 sc0 ls0 ws0">的方法<span class="_ _11"></span>。<span class="_ _6"></span>它是<span class="_ _e"> </span><span class="ff2 fsd">20<span class="_"> </span></span>世纪<span class="_ _c"> </span><span class="ff2 fsd">9<span class="_ _1"></span>0<span class="_"> </span><span class="ff4 fsa">年代初期由<span class="_ _d"> </span></span>T<span class="_ _2"></span>u<span class="_ _1"></span>rk<span class="_"> </span><span class="ff4 fsa">和<span class="_ _d"> </span></span>P<span class="_ _2"></span>en<span class="_ _1"></span>tla<span class="_ _3"></span>n<span class="_ _1"></span>d</span></div><div class="t m0 x31 he y28 ff2 fsb fc0 sc0 ls0 ws0">[<span class="_ _3"></span>4<span class="_ _11"> </span>]</div><div class="t m0 x32 hb y27 ff4 fsa fc0 sc0 ls0 ws0">提出<span class="_ _3"></span>的<span class="_ _0"></span>。<span class="_ _f"></span>它<span class="_ _3"></span>根据<span class="_ _3"></span>图像<span class="_ _3"></span>的统计<span class="_ _3"></span>特性<span class="_ _3"></span>进行<span class="_ _3"></span>正交<span class="_ _3"></span>变换</div><div class="t m0 x33 hd y29 ff2 fsd fc0 sc0 ls0 ws0">(</div><div class="t m0 x1e hf y27 ff2 fsd fc0 sc0 ls0 ws0">K<span class="_ _16"></span><span class="ff3 fsa">2<span class="_ _17"></span><span class="ff2 fsd">L</span></span></div><div class="t m0 x1 hb y2a ff4 fsa fc0 sc0 ls0 ws0">变换</div><div class="t m0 xf hd y2b ff2 fsd fc0 sc0 ls0 ws0">)</div><div class="t m0 x34 hf y2a ff2 fsd fc0 sc0 ls0 ws0">,<span class="ff4 fsa">以消除原有向量各个分量间的<span class="_ _1"></span>相关性<span class="_ _0"></span>。<span class="_ _f"></span>变换<span class="_ _3"></span>得到<span class="_ _3"></span>对应<span class="_ _3"></span>特征<span class="_ _3"></span>值依次<span class="_ _3"></span>递<span class="_ _3"></span>减<span class="_ _3"></span>的特<span class="_ _3"></span>征<span class="_ _3"></span>向量<span class="_ _0"></span>。<span class="_ _6"></span>通<span class="_ _3"></span>过<span class="_ _15"> </span><span class="ff2 fsd">K<span class="_ _16"></span><span class="ff3 fsa">2<span class="_ _17"></span><span class="ff2 fsd">L<span class="_ _d"> </span><span class="ff4 fsa">变<span class="_ _3"></span>换<span class="_ _c"> </span></span>,</span></span></span></span></div><div class="t m0 x1 hb y2c ff4 fsa fc0 sc0 ls0 ws0">可以把图像在高维空间表示转<span class="_ _1"></span>换到低维空间表示<span class="_ _c"> </span><span class="ff2 fsd">,</span>而由低维空间恢复的图像和原图<span class="_ _1"></span>像具有最小的均方误差<span class="_ _0"></span>。</div><div class="t m0 x1 hf y2d ff4 fsa fc0 sc0 ls0 ws0">从而可以以图像在低维空间的<span class="_ _1"></span>变换系数作为人脸图像的描述特征<span class="_ _11"></span>。<span class="ff2 fsd">K<span class="_ _16"></span><span class="ff3 fsa">2<span class="_ _8"></span><span class="ff2 fsd">L<span class="_ _d"> </span><span class="ff4 fsa">变换<span class="_ _3"></span>用于人<span class="_ _3"></span>脸识<span class="_ _3"></span>别的<span class="_ _3"></span>前提<span class="_ _3"></span>是人<span class="_ _3"></span>脸图</span></span></span></span></div><div class="t m0 x1 hb y2e ff4 fsa fc0 sc0 ls0 ws0">像处于低维空间<span class="_ _c"> </span><span class="ff2 fsd">,</span>并且不同人脸是线<span class="_ _1"></span>性可分的<span class="_ _0"></span>。</div><div class="t m0 x1 h9 y2f ff4 fs2 fc0 sc0 ls0 ws0">第<span class="_ _4"> </span><span class="ff2 fs3">19<span class="_"> </span></span>卷<span class="_ _e"> </span> <span class="_ _16"></span>第<span class="_ _4"> </span><span class="ff2 fs3">4<span class="_"> </span></span>期</div><div class="t m0 x1 h9 y30 ff2 fs3 fc0 sc0 ls0 ws0">20<span class="_ _1"></span>06<span class="_ _10"> </span><span class="ff4 fs2">年<span class="_ _e"> </span></span>8<span class="_"> </span><span class="ff4 fs2">月</span></div><div class="t m0 x35 h9 y31 ff4 fs2 fc0 sc0 ls0 ws0">山<span class="_ _18"> </span>东<span class="_ _18"> </span>科<span class="_ _18"> </span>学</div><div class="t m0 x35 h6 y32 ff2 fs3 fc0 sc0 ls0 ws0">S<span class="_ _1"></span>H<span class="_ _6"></span>A<span class="_ _2"></span>N<span class="_ _2"></span>D<span class="_ _2"></span>O<span class="_ _2"></span>N<span class="_ _3"></span>G<span class="_ _10"> </span>S<span class="_ _2"></span>CI<span class="_ _1"></span>E<span class="_ _6"></span>N<span class="_ _1"></span>CE</div><div class="t m0 x36 h9 y2f ff2 fs3 fc0 sc0 ls0 ws0">V<span class="_ _6"></span>ol<span class="_ _3"></span>.<span class="_ _10"> </span>19<span class="_"> </span><span class="ff4 fs2"> <span class="_ _19"></span><span class="ff2 fs3">N<span class="_ _6"></span>o<span class="_ _5"></span>.<span class="_ _10"> </span>4</span></span></div><div class="t m0 x37 h6 y30 ff2 fs3 fc0 sc0 ls0 ws0">A<span class="_ _1"></span>ug.<span class="_ _0"> </span>200<span class="_ _1"></span>6</div></div><div class="pi" data-data='{"ctm":[1.646845,0.000000,0.000000,1.646845,0.000000,0.000000]}'></div></div>
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