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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/89551058/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/89551058/bg1.jpg"/><div class="c x0 y1 w0 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">基金项目：国家自然科学基金资助项目（<span class="ff2 sc1">62106206</span>）</div><div class="t m0 x1 h3 y3 ff1 fs0 fc0 sc0 ls0 ws0">通信作者<span class="_ _0"> </span><span class="ff2 sc1">E-mail</span>：<span class="ff2 sc1">wangmw@swjtu.edu.cn</span></div></div><div class="t m0 x2 h4 y4 ff3 fs1 fc0 sc0 ls0 ws0">基于双分支深度图卷积网络的指静脉识别研究</div><div class="t m0 x3 h5 y5 ff4 fs2 fc0 sc1 ls0 ws0">程俊军，王明文</div><div class="t m0 x4 h5 y6 ff4 fs2 fc0 sc1 ls0 ws0">（西南交通大学，数学学院，四川成都<span class="ff5"> <span class="_"> </span>610000</span>）</div><div class="t m0 x1 h6 y7 ff1 fs0 fc0 sc0 ls0 ws0">摘要：<span class="ff4 sc1">基于图卷积神<span class="_ _1"></span>经网络的手指静脉识<span class="_ _1"></span>别方法不仅可以解决<span class="_ _1"></span>传统指静脉识别方法<span class="_ _1"></span>识别率较低的问题，<span class="_ _1"></span>还</span></div><div class="t m0 x1 h6 y8 ff4 fs0 fc0 sc1 ls0 ws0">可以解决其计算量大<span class="_ _1"></span>的问题。针对目前指<span class="_ _1"></span>静脉图模型在图结构<span class="_ _1"></span>不稳定性和匹配效率<span class="_ _1"></span>因模型增大而下降的<span class="_ _1"></span>问</div><div class="t m0 x1 h6 y9 ff4 fs0 fc0 sc1 ls0 ws0">题，采<span class="_ _1"></span>用了<span class="_ _0"> </span><span class="ff5">SLIC<span class="_ _2"> </span></span>超像素<span class="_ _1"></span>分割算<span class="_ _1"></span>法来<span class="_ _1"></span>构建加<span class="_ _1"></span>权图<span class="_ _1"></span>并改变<span class="_ _1"></span>了图<span class="_ _1"></span>卷积神<span class="_ _1"></span>经网<span class="_ _1"></span>络提取<span class="_ _1"></span>加权<span class="_ _1"></span>图的图<span class="_ _1"></span>级特征<span class="_ _1"></span>。为<span class="_ _1"></span>了有</div><div class="t m0 x1 h6 ya ff4 fs0 fc0 sc1 ls0 ws0">效抓取图数据中的高<span class="_ _1"></span>阶特征并避免过平滑<span class="_ _1"></span>，研究了一种双分支<span class="_ _1"></span>多交互的深度图卷积<span class="_ _1"></span>网络，旨在提升节点<span class="_ _1"></span>对</div><div class="t m0 x1 h6 yb ff4 fs0 fc0 sc1 ls0 ws0">高阶特征的掌握能力<span class="_ _1"></span>。该方法首先根据节<span class="_ _1"></span>点特征对图结构进行<span class="_ _1"></span>调整，然后通过结合<span class="_ _1"></span>原始和重构后的图结<span class="_ _1"></span>构，</div><div class="t m0 x1 h6 yc ff4 fs0 fc0 sc1 ls0 ws0">构建了双分支网络架<span class="_ _1"></span>构以充分挖掘高阶特<span class="_ _1"></span>征。此外，通过设计<span class="_ _1"></span>一种通道信息互动机<span class="_ _1"></span>制，以促进不同分支<span class="_ _1"></span>间</div><div class="t m0 x1 h6 yd ff4 fs0 fc0 sc1 ls0 ws0">的信息交流，从而提<span class="_ _1"></span>高特征的多样性。实<span class="_ _1"></span>验结果显示，该网络<span class="_ _1"></span>结构在多个标准数据<span class="_ _1"></span>集上进行指静脉识别<span class="_ _1"></span>任</div><div class="t m0 x1 h6 ye ff4 fs0 fc0 sc1 ls0 ws0">务时，能提高识别精度，减少单张图片识别时间，提高效率，并有效减轻过平滑现象。</div><div class="t m0 x1 h6 yf ff1 fs0 fc0 sc0 ls0 ws0">关键词：<span class="ff4 sc1">指静脉识别；图像分割算法；图卷积神经网络；交叉熵函数；通道信息交互</span></div><div class="t m0 x5 h7 y10 ff2 fs1 fc0 sc1 ls0 ws0">Finger-vein Recognition Research Based on Deep Graph </div><div class="t m0 x6 h7 y11 ff2 fs1 fc0 sc1 ls0 ws0">Convolutional Network With Dual-Branch</div><div class="t m0 x7 h6 y12 ff5 fs0 fc0 sc1 ls0 ws0">CHENG Junjun<span class="ff4">，</span>WANG Mingwen</div><div class="t m0 x8 h6 y13 ff4 fs0 fc0 sc1 ls0 ws0">（<span class="ff5">School of Mathematics,Southwest Jiaotong University,Chengdu 610000,Si Chuan,China</span>）</div><div class="t m0 x1 h3 y14 ff2 fs0 fc0 sc1 ls0 ws0">[Abstract]<span class="ff5"> The <span class="_ _3"></span>finger-vein recognition <span class="_ _3"></span>method based <span class="_ _3"></span>on graph <span class="_ _3"></span>convolutional neural <span class="_ _3"></span>network can <span class="_ _3"></span>not only <span class="_ _3"></span>solve the </span></div><div class="t m0 x1 h8 y15 ff5 fs0 fc0 sc1 ls0 ws0">problem of <span class="_ _3"></span>low recognition <span class="_ _3"></span>rate of <span class="_ _3"></span>traditional finger <span class="_ _3"></span>vein recognition <span class="_ _3"></span>method, but <span class="_ _3"></span>also solve <span class="_ _3"></span>the problem <span class="_ _3"></span>of i<span class="_ _3"></span>ts large </div><div class="t m0 x1 h8 y16 ff5 fs0 fc0 sc1 ls0 ws0">computational volume. To address the current finger vein graph model's problems of graph structure instability and </div><div class="t m0 x1 h8 y17 ff5 fs0 fc0 sc1 ls0 ws0">matching <span class="_ _3"></span>efficiency <span class="_ _3"></span>decreasing <span class="_ _3"></span>due <span class="_ _3"></span>to <span class="_ _3"></span>model <span class="_ _3"></span>increase, <span class="_ _3"></span>SLIC <span class="_ _3"></span>super-pixel <span class="_ _3"></span>segmentation <span class="_ _4"></span>algorithm <span class="_ _4"></span>is used <span class="_ _4"></span>to construct </div><div class="t m0 x1 h8 y18 ff5 fs0 fc0 sc1 ls0 ws0">the <span class="_ _5"></span>weighted <span class="_ _5"></span>graph <span class="_ _5"></span>and <span class="_ _5"></span>change <span class="_ _5"></span>the <span class="_ _5"></span>graph <span class="_ _5"></span>convolutional <span class="_ _5"></span>neural <span class="_ _5"></span>network <span class="_ _5"></span>to <span class="_ _5"></span>extract <span class="_ _5"></span>the <span class="_ _5"></span>graph-level <span class="_ _5"></span>features <span class="_ _5"></span>of <span class="_ _5"></span>the </div><div class="t m0 x1 h8 y19 ff5 fs0 fc0 sc1 ls0 ws0">weighted <span class="_ _4"></span>graph. In <span class="_ _4"></span>order <span class="_ _3"></span>to <span class="_ _4"></span>effectively capture <span class="_ _4"></span>the <span class="_ _4"></span>higher-order features <span class="_ _4"></span>in the <span class="_ _4"></span>graph <span class="_ _4"></span>data and <span class="_ _4"></span>avoid <span class="_ _4"></span>over-smoothing, </div><div class="t m0 x1 h8 y1a ff5 fs0 fc0 sc1 ls0 ws0">a <span class="_ _6"> </span>two-branch <span class="_ _6"> </span>multi-interaction <span class="_ _6"> </span>deep <span class="_ _6"> </span>graph <span class="_ _6"> </span>convolutional <span class="_ _6"> </span>network <span class="_ _6"> </span>is <span class="_ _6"> </span>investigated, <span class="_ _6"> </span>aiming <span class="_ _6"> </span>to <span class="_ _6"> </span>improve <span class="_ _6"> </span>the <span class="_ _6"> </span>node's </div><div class="t m0 x1 h8 y1b ff5 fs0 fc0 sc1 ls0 ws0">ability to <span class="_ _4"></span>grasp the higher-order features. <span class="_ _4"></span>The method first adapts <span class="_ _4"></span>the graph structure <span class="_ _4"></span>according to the node <span class="_ _4"></span>features, </div><div class="t m0 x1 h8 y1c ff5 fs0 fc0 sc1 ls0 ws0">and <span class="_ _7"> </span>then <span class="_ _7"> </span>by <span class="_ _7"> </span>combining <span class="_ _7"> </span>the <span class="_ _7"> </span>original <span class="_ _7"> </span>and <span class="_ _7"> </span>reconstructed <span class="_ _7"> </span>graph <span class="_ _7"> </span>structures, <span class="_ _7"> </span>a <span class="_ _7"> </span>two-branch <span class="_ _7"> </span>network <span class="_ _7"> </span>architecture <span class="_ _7"> </span>is </div><div class="t m0 x1 h8 y1d ff5 fs0 fc0 sc1 ls0 ws0">constructed to fully mine the higher-order features. In <span class="_ _1"></span>addition, the diversity of features is <span class="_ _1"></span>improved by designing a </div><div class="t m0 x1 h8 y1e ff5 fs0 fc0 sc1 ls0 ws0">channel <span class="_ _8"> </span>information <span class="_ _8"> </span>interaction <span class="_ _8"> </span>mechanism <span class="_ _8"> </span>to <span class="_ _8"> </span>facilitate <span class="_ _8"> </span>information <span class="_ _8"> </span>exchange <span class="_ _8"> </span>between <span class="_ _8"> </span>different <span class="_ _8"> </span>branches. </div><div class="t m0 x1 h8 y1f ff5 fs0 fc0 sc1 ls0 ws0">Experimental <span class="_ _5"></span>results <span class="_ _5"></span>show <span class="_ _5"> </span>that <span class="_ _6"> </span>this <span class="_ _5"></span>network <span class="_ _5"></span>architecture <span class="_ _5"></span>can <span class="_ _5"></span>improve <span class="_ _5"> </span>recognition <span class="_ _6"> </span>accuracy, <span class="_ _5"></span>reduce <span class="_ _5"></span>single-image </div><div class="t m0 x1 h8 y20 ff5 fs0 fc0 sc1 ls0 ws0">recognition <span class="_ _2"> </span>time, <span class="_ _8"> </span>improve <span class="_ _2"> </span>efficiency, <span class="_ _9"> </span>and <span class="_ _2"> </span>effectively <span class="_ _9"> </span>mitigate <span class="_ _9"> </span>oversmoothing <span class="_ _9"> </span>when <span class="_ _9"> </span>performing <span class="_ _9"> </span>finger <span class="_ _9"> </span>vein </div><div class="t m0 x1 h8 y21 ff5 fs0 fc0 sc1 ls0 ws0">recognition tasks on multiple standard datasets.</div><div class="t m0 x1 h8 y22 ff6 fs0 fc0 sc1 ls0 ws0">[keywords]<span class="ff5">Finger-vein <span class="_ _1"></span>Recognition;Image <span class="_ _a"></span>Segmentation <span class="_ _1"></span>Algorithm;Graph <span class="_ _a"></span>Convolutional <span class="_ _1"></span>Neural <span class="_ _a"></span>Network;Cross-</span></div><div class="t m0 x1 h8 y23 ff5 fs0 fc0 sc1 ls0 ws0">entropy function;Channel Information Interaction</div><div class="t m1 x1 h9 y24 ff6 fs3 fc0 sc1 ls0 ws0">0<span class="_ _8"> </span><span class="ff1 sc0">概<span class="_ _a"></span>述</span></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/89551058/bg2.jpg"><div class="t m0 x9 ha y25 ff7 fs2 fc0 sc1 ls0 ws0">手指静脉识别近年来成为生物特征识别领域的一项热门研究，<span class="_ _b"></span>因其不易被伪造、<span class="_ _b"></span>不易被</div><div class="t m0 x1 ha y26 ff7 fs2 fc0 sc1 ls0 ws0">磨损、<span class="_ _c"></span>活体性强等突出优点，<span class="_ _c"></span>已经逐渐发展至实际应用当中，<span class="_ _c"></span>比如门禁系统等</div><div class="t m0 xa hb y27 ff8 fs4 fc0 sc1 ls0 ws0">[1]</div><div class="t m0 xb ha y26 ff7 fs2 fc0 sc1 ls0 ws0">。<span class="_ _c"></span>手指静脉</div><div class="t m0 x1 ha y28 ff7 fs2 fc0 sc1 ls0 ws0">血管的网络结构是指静脉的特征体现，<span class="_ _b"></span>因此对指静脉的研究，<span class="_ _b"></span>关键在于对血管网状结构特征</div><div class="t m0 x1 ha y29 ff7 fs2 fc0 sc1 ls0 ws0">的提取</div><div class="t m0 xc hb y2a ff8 fs4 fc0 sc1 ls0 ws0">[2]</div><div class="t m0 xd ha y29 ff7 fs2 fc0 sc1 ls0 ws0">。<span class="_ _b"></span>指静脉传统的特征提取方法主要是借鉴于其他生物特征提取方法，<span class="_ _b"></span>比如人脸识别</div><div class="t m0 x1 ha y2b ff7 fs2 fc0 sc1 ls0 ws0">和指纹识别，均以图像为研究对象进行指静脉的识别工作</div><div class="t m0 xe hb y2c ff8 fs4 fc0 sc1 ls0 ws0">[3-4]</div><div class="t m0 xf ha y2b ff7 fs2 fc0 sc1 ls0 ws0">。</div><div class="t m0 x9 ha y2d ff7 fs2 fc0 sc1 ls0 ws0">传统的特征提取方法如编码特征等，容易忽略图像特征间的结构关系。而图论中的</div><div class="t m0 x1 ha y2e ff7 fs2 fc0 sc1 ls0 ws0">“图”作为一种图像描述方式，能够描述图像局部特征以及区域间关联性，表达图像全局</div><div class="t m0 x1 ha y2f ff7 fs2 fc0 sc1 ls0 ws0">信息。由于其优异的特性，图论在图像检索、图像分割等领域都取得了很大进展</div><div class="t m0 x10 hb y30 ff8 fs4 fc0 sc1 ls0 ws0">[5]</div><div class="t m0 x11 ha y2f ff7 fs2 fc0 sc1 ls0 ws0">。叶子</div><div class="t m0 x1 ha y31 ff7 fs2 fc0 sc1 ls0 ws0">云等人提出把一幅手指静脉图像表示为一个加权图，在识别效率上较传统方法有所提升，</div><div class="t m0 x1 ha y32 ff7 fs2 fc0 sc1 ls0 ws0">但识别率有待提高</div><div class="t m0 x12 hb y33 ff8 fs4 fc0 sc1 ls0 ws0">[6]</div><div class="t m0 x4 ha y32 ff7 fs2 fc0 sc1 ls0 ws0">。为了提高识别率，<span class="ff8">Das Rig<span class="_ _2"> </span></span>等人提出基于深度学习的手指静脉识别</div><div class="t m0 x1 ha y34 ff7 fs2 fc0 sc1 ls0 ws0">方法，但是在计算效率方面存在很大的提升空间</div><div class="t m0 x13 hb y35 ff8 fs4 fc0 sc1 ls0 ws0">[7]</div><div class="t m0 x14 ha y34 ff7 fs2 fc0 sc1 ls0 ws0">。</div><div class="t m0 x9 ha y36 ff7 fs2 fc0 sc1 ls0 ws0">针对<span class="_ _1"></span>以<span class="_ _1"></span>上<span class="_ _1"></span>问<span class="_ _1"></span>题<span class="_ _1"></span>，<span class="_ _1"></span>本<span class="_ _1"></span>文<span class="_ _1"></span>提<span class="_ _1"></span>出<span class="_ _1"></span>一<span class="_ _1"></span>种基<span class="_ _1"></span>于<span class="_ _1"></span>图<span class="_ _1"></span>卷<span class="_ _1"></span>积<span class="_ _1"></span>网<span class="_ _1"></span>络<span class="_ _1"></span>（<span class="_ _1"></span><span class="ff8">Graph <span class="_ _1"></span>Convolutional <span class="_ _1"></span>Network<span class="_ _1"></span></span>，<span class="_ _1"></span><span class="ff8">GCN</span>）</div><div class="t m0 x1 ha y37 ff7 fs2 fc0 sc1 ls0 ws0">的手指静脉识别方法。<span class="_ _c"></span><span class="ff8">GCN<span class="_ _2"> </span><span class="ff7">由<span class="_ _2"> </span></span>Joan Bruna<span class="_ _2"> </span><span class="ff7">等人于<span class="_ _9"> </span></span>2014<span class="_ _2"> </span><span class="ff7">年提出，<span class="_ _c"></span>图数据各个顶点的相邻顶点</span></span></div><div class="t m0 x1 ha y38 ff7 fs2 fc0 sc1 ls0 ws0">数目不尽相同，<span class="_ _d"></span>是一种不规则的数据结构，<span class="_ _d"></span>称为非欧氏数据。<span class="_ _d"></span>而传统的离散卷积在这类数据</div><div class="t m0 x1 ha y39 ff7 fs2 fc0 sc1 ls0 ws0">上无法保持平移不变性，<span class="_ _b"></span>即不能用一个同样尺寸的卷积核进行卷积运算</div><div class="t m0 x15 hb y3a ff8 fs4 fc0 sc1 ls0 ws0">[8]</div><div class="t m0 x16 ha y39 ff7 fs2 fc0 sc1 ls0 ws0">。<span class="_ _b"></span>图卷积自提出以</div><div class="t m0 x1 ha y3b ff7 fs2 fc0 sc1 ls0 ws0">来，在结点分类、疾病预测、网络安全等许多方面都取得很大进展。</div><div class="t m0 x9 ha y3c ff7 fs2 fc0 sc1 ls0 ws0">虽然图神经网络取得一定效果，<span class="_ _e"></span>但浅层架构的特点限制其从高阶邻居节点中获取信息的</div><div class="t m0 x1 ha y3d ff7 fs2 fc0 sc1 ls0 ws0">能力。<span class="_ _c"></span>而深度图神经网络可利用节点较远的聚合范围，<span class="_ _c"></span>提取相对丰富的高阶特征。<span class="_ _c"></span>然而，<span class="_ _c"></span>简</div><div class="t m0 x1 ha y3e ff7 fs2 fc0 sc1 ls0 ws0">单叠加多个图卷积层的深度网络往往存在一些固有的缺陷，<span class="_ _b"></span>如产生过平滑现象</div><div class="t m0 x17 hb y3f ff8 fs4 fc0 sc1 ls0 ws0">[9]</div><div class="t m0 x18 ha y3e ff7 fs2 fc0 sc1 ls0 ws0">。<span class="_ _b"></span>过平滑现</div><div class="t m0 x1 ha y40 ff7 fs2 fc0 sc1 ls0 ws0">象是指图<span class="_ _1"></span>节点信息经<span class="_ _1"></span>过多次图<span class="_ _1"></span>卷积操作<span class="_ _1"></span>后会趋于<span class="_ _1"></span>一致，丧<span class="_ _1"></span>失节点特<span class="_ _1"></span>征多样性<span class="_ _1"></span>。<span class="ff8">He</span></div><div class="t m0 x19 hb y41 ff8 fs4 fc0 sc1 ls0 ws0">[10]</div><div class="t m0 x1a ha y40 ff7 fs2 fc0 sc1 ls0 ws0">等利用</div><div class="t m0 x1 ha y42 ff7 fs2 fc0 sc1 ls0 ws0">深度残差网络，<span class="_ _d"></span>解决计算机视觉中的网络退化问题，<span class="_ _d"></span>有效提升训练深层网络的可行性。<span class="_ _d"></span>基于</div><div class="t m0 x1 ha y43 ff7 fs2 fc0 sc1 ls0 ws0">该工作，<span class="ff8">Kipf</span></div><div class="t m0 x1b hb y44 ff8 fs4 fc0 sc1 ls0 ws0">[11]</div><div class="t m0 x1c ha y43 ff7 fs2 fc0 sc1 ls0 ws0">等在<span class="_ _2"> </span><span class="ff8">GCN<span class="_ _2"> </span></span>中引入残差连接，一定程度上缓解过平滑现象。进一步<span class="ff8">, <span class="_ _c"></span>Rong</span></div><div class="t m0 x1d hb y44 ff8 fs4 fc0 sc1 ls0 ws0">[12]</div><div class="t m0 x1 ha y45 ff7 fs2 fc0 sc1 ls0 ws0">等使用随机丢弃部分节点之间的边，减轻过平滑现象的影响。</div><div class="t m0 x9 ha y46 ff7 fs2 fc0 sc1 ls0 ws0">尽管上述方法增加图卷积网络的深度，但忽略图卷积操作固有的缺陷<span class="_ _b"></span>：<span class="_ _b"></span>基于图卷积网络</div><div class="t m0 x1 ha y47 ff7 fs2 fc0 sc1 ls0 ws0">学习的节点<span class="_ _1"></span>表示往往<span class="_ _1"></span>会破坏原<span class="_ _1"></span>始特征空<span class="_ _1"></span>间的节点<span class="_ _1"></span>相似性</div><div class="t m0 x1e hb y48 ff8 fs4 fc0 sc1 ls0 ws0">[13]</div><div class="t m0 x1f ha y47 ff7 fs2 fc0 sc1 ls0 ws0">。事实上，<span class="_ _1"></span>节点相似<span class="_ _1"></span>性在许多<span class="_ _1"></span>场</div><div class="t m0 x1 ha y49 ff7 fs2 fc0 sc1 ls0 ws0">景中发挥至关重要的作用，<span class="_ _b"></span>这一结果会大幅影响捕获的节点表示的有效性，<span class="_ _b"></span>并阻碍其下游任</div><div class="t m0 x1 ha y4a ff7 fs2 fc0 sc1 ls0 ws0">务的性能。<span class="_ _d"></span>此外，<span class="_ _d"></span>真实世界中的图结构数据往往存在长尾分布的现象，<span class="_ _d"></span>即图中的大多数节点</div><div class="t m0 x1 ha y4b ff7 fs2 fc0 sc1 ls0 ws0">只存在少量的邻居节点，<span class="_ _b"></span>这些尾节点往往不能在聚合操作时获得足够的信息，<span class="_ _b"></span>这一现象影响</div><div class="t m0 x1 ha y4c ff7 fs2 fc0 sc1 ls0 ws0">网络获取节点表示的准确性。</div><div class="t m0 x9 ha y4d ff7 fs2 fc0 sc1 ls0 ws0">因此，<span class="_ _f"></span>本文提出双分支多交互的深度图卷积网络，<span class="_ _f"></span>有效改善节点分类任务的性能。<span class="_ _f"></span>首先<span class="ff8">,</span></div><div class="t m0 x1 ha y4e ff7 fs2 fc0 sc1 ls0 ws0">利<span class="_ _1"></span>用<span class="_ _9"> </span><span class="ff8">SLIC<span class="_ _1"></span></span>（<span class="_ _1"></span><span class="ff8">Simple <span class="_ _1"></span>Linear <span class="_ _1"></span>Iterative <span class="_ _1"></span>Clustering<span class="_ _1"></span></span>）<span class="_ _10"></span>超<span class="_ _1"></span>像<span class="_ _1"></span>素<span class="_ _1"></span>分<span class="_ _1"></span>割<span class="_ _1"></span>算<span class="_ _1"></span>法<span class="_ _1"></span>对<span class="_ _1"></span>手<span class="_ _1"></span>指<span class="_ _1"></span>静<span class="_ _1"></span>脉<span class="_ _a"></span>图<span class="_ _1"></span>像<span class="_ _1"></span>构<span class="_ _1"></span>建</div><div class="t m0 x1 ha y4f ff7 fs2 fc0 sc1 ls0 ws0">加权图。<span class="_ _d"></span>该图数据作为图卷积网络的输入，<span class="_ _d"></span>利用<span class="_ _2"> </span><span class="ff8">K<span class="_ _2"> </span></span>近邻算法对图数据结构进行重构，<span class="_ _d"></span>学习具</div><div class="t m0 x1 ha y50 ff7 fs2 fc0 sc1 ls0 ws0">有节点相似性的重构图，<span class="_ _b"></span>由于重构的图结构中节点具有较平衡的邻居数量，<span class="_ _b"></span>可避免长尾分布</div><div class="t m0 x1 ha y51 ff7 fs2 fc0 sc1 ls0 ws0">带来的影响。<span class="_ _d"></span>然后，<span class="_ _d"></span>利用原始图和重构图构造双分支深度图卷积网络，<span class="_ _d"></span>既保留原始图的结构</div><div class="t m0 x1 ha y52 ff7 fs2 fc0 sc1 ls0 ws0">信息，<span class="_ _c"></span>又考虑节点间的相似性信息，<span class="_ _c"></span>充分提取高阶特征。<span class="_ _c"></span>设计通道信息交互机制，<span class="_ _c"></span>建立对不</div><div class="t m0 x1 ha y53 ff7 fs2 fc0 sc1 ls0 ws0">同分支信息的多次交互，<span class="_ _d"></span>增加特征的多样性，<span class="_ _d"></span>进一步增强网络获取高阶特征的能力，<span class="_ _d"></span>避免过</div><div class="t m0 x1 ha y54 ff7 fs2 fc0 sc1 ls0 ws0">平滑现象。<span class="_ _d"></span>最后，<span class="_ _d"></span>将不同分支的特征进行融合以获得分类结果。<span class="_ _d"></span>实验表明本文网络在多个数</div><div class="t m0 x1 ha y55 ff7 fs2 fc0 sc1 ls0 ws0">据集上取得较优性能。</div><div class="t m1 x1 h9 y56 ff6 fs3 fc0 sc1 ls0 ws0">1<span class="_ _8"> </span><span class="ff1 sc0">指<span class="_ _a"></span>静<span class="_ _a"></span>脉<span class="_ _1"></span>加<span class="_ _a"></span>权<span class="_ _1"></span>图<span class="_ _a"></span>的<span class="_ _a"></span>构<span class="_ _1"></span>建</span></div><div class="t m0 x9 ha y57 ff7 fs2 fc0 sc1 ls0 ws0">一<span class="_ _5"></span>个</div><div class="c x20 y58 w2 hc"><div class="t m0 x21 hd y59 ff9 fs5 fc0 sc1 ls0 ws0">N</div></div><div class="t m0 x22 ha y57 ff7 fs2 fc0 sc1 ls0 ws0">个<span class="_ _5"></span>节<span class="_ _5"></span>点<span class="_ _5"></span>的<span class="_ _5"></span>加<span class="_ _5"></span>权<span class="_ _6"></span>图<span class="_ _a"></span>可<span class="_ _5"></span>以<span class="_ _5"></span>表<span class="_ _6"></span>示<span class="_ _a"></span>为</div><div class="c x23 y5a w3 he"><div class="t m0 x24 ha y5b ff8 fs2 fc0 sc1 ls0 ws0">G</div></div><div class="c x25 y5a w4 hf"><div class="t m0 x24 h10 y5c ffa fs2 fc0 sc1 ls0 ws0">=</div></div><div class="c x26 y5a w5 h11"><div class="t m0 x24 h10 y5d ffa fs2 fc0 sc1 ls0 ws0">(</div></div><div class="c x27 y5a w6 h12"><div class="t m0 x24 ha y5e ff8 fs2 fc0 sc1 ls0 ws0">V,E,A</div></div><div class="c x28 y5a w5 h11"><div class="t m0 x24 h10 y5d ffa fs2 fc0 sc1 ls0 ws0">)</div></div><div class="t m0 x29 ha y57 ff7 fs2 fc0 sc1 ls0 ws0">，</div><div class="c x2a y5a w3 he"><div class="t m0 x24 ha y5b ff8 fs2 fc0 sc1 ls0 ws0">V</div></div><div class="c x2b y5a w4 hf"><div class="t m0 x24 h10 y5c ffa fs2 fc0 sc1 ls0 ws0">=</div></div><div class="c x2c y5a w7 h13"><div class="t m0 x24 h10 y5f ffa fs2 fc0 sc1 ls0 ws0">{</div></div><div class="c x2d y5a w3 h14"><div class="t m0 x24 ha y60 ff8 fs2 fc0 sc1 ls0 ws0">v</div></div><div class="c x2e y5a w8 h15"><div class="t m2 x2f h16 y61 ff8 fs6 fc0 sc1 ls0 ws0">1</div></div><div class="c x30 y5a w3 h14"><div class="t m0 x24 ha y60 ff8 fs2 fc0 sc1 ls0 ws0">,</div></div><div class="c x31 y5a w3 h14"><div class="t m0 x24 ha y60 ff8 fs2 fc0 sc1 ls0 ws0">v</div></div><div class="c x32 y5a w8 h15"><div class="t m2 x2f h16 y61 ff8 fs6 fc0 sc1 ls0 ws0">2</div></div><div class="c x33 y5a w9 h14"><div class="t m0 x24 ha y60 ff8 fs2 fc0 sc1 ls0 ws0">,…,</div></div><div class="c x34 y5a w3 h14"><div class="t m0 x24 ha y60 ff8 fs2 fc0 sc1 ls0 ws0">v</div></div><div class="c x35 y5a w8 h15"><div class="t m2 x2f h16 y61 ff8 fs6 fc0 sc1 ls0 ws0">N</div></div><div class="c x36 y5a w7 h13"><div class="t m0 x24 h10 y5f ffa fs2 fc0 sc1 ls0 ws0">}</div></div><div class="t m0 x37 ha y57 ff7 fs2 fc0 sc1 ls0 ws0">是<span class="_ _5"></span>节<span class="_ _5"></span>点<span class="_ _5"></span>集<span class="_ _5"></span>，</div><div class="c x38 y5a w3 he"><div class="t m0 x24 ha y5b ff8 fs2 fc0 sc1 ls0 ws0">E</div></div><div class="c x39 y5a w4 hf"><div class="t m0 x24 h10 y5c ffa fs2 fc0 sc1 ls0 ws0">=</div></div><div class="c x3a y5a w7 h17"><div class="t m0 x24 h10 y62 ffa fs2 fc0 sc1 ls0 ws0">{</div></div><div class="c x3b y5a w3 h18"><div class="t m0 x24 ha y63 ff8 fs2 fc0 sc1 ls0 ws0">e</div></div><div class="c x5 y5a wa h19"><div class="t m2 x2f h16 y64 ff8 fs6 fc0 sc1 ls0 ws0">ij</div></div><div class="c x3c y5a w7 h17"><div class="t m0 x24 h10 y62 ffa fs2 fc0 sc1 ls0 ws0">}</div></div><div class="t m0 x9 ha y65 ff7 fs2 fc0 sc1 ls0 ws0">为边集，其中</div><div class="c x3d y5a w3 h1a"><div class="t m0 x24 ha y66 ff8 fs2 fc0 sc1 ls0 ws0">e</div></div><div class="c x3e y5a wa h1b"><div class="t m2 x2f h16 y67 ff8 fs6 fc0 sc1 ls0 ws0">ij</div></div><div class="c x4 y5a w4 h1c"><div class="t m0 x24 h10 y68 ffa fs2 fc0 sc1 ls0 ws0">=</div></div><div class="c x3f y5a w3 h1d"><div class="t m0 x24 ha y69 ff8 fs2 fc0 sc1 ls0 ws0">(</div></div><div class="c x40 y5a w3 h1e"><div class="t m0 x24 ha y6a ff8 fs2 fc0 sc1 ls0 ws0">v</div></div><div class="c x41 y5a w8 h1f"><div class="t m2 x2f h16 y6b ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c x42 y5a w3 h20"><div class="t m0 x24 ha y6c ff8 fs2 fc0 sc1 ls0 ws0">,</div></div><div class="c x43 y5a w3 h1a"><div class="t m0 x24 ha y66 ff8 fs2 fc0 sc1 ls0 ws0">v</div></div><div class="c x44 y5a w8 h1b"><div class="t m2 x2f h16 y67 ff8 fs6 fc0 sc1 ls0 ws0">j</div></div><div class="c x45 y5a wb h1d"><div class="t m0 x24 ha y69 ff8 fs2 fc0 sc1 ls0 ws0">)(i</div></div><div class="c x46 y5a w4 h1c"><div class="t m0 x24 h10 y68 ffb fs2 fc0 sc1 ls0 ws0">≠</div></div><div class="c x47 y5a wc h1d"><div class="t m0 x24 ha y69 ff8 fs2 fc0 sc1 ls0 ws0">j)</div></div><div class="t m0 x48 ha y65 ff7 fs2 fc0 sc1 ls0 ws0">，无向图中</div><div class="c x14 y5a w3 h1a"><div class="t m0 x24 ha y66 ff8 fs2 fc0 sc1 ls0 ws0">e</div></div><div class="c x28 y5a wa h1b"><div class="t m2 x2f h16 y67 ff8 fs6 fc0 sc1 ls0 ws0">ij</div></div><div class="c x49 y5a w4 h1c"><div class="t m0 x24 h10 y68 ffa fs2 fc0 sc1 ls0 ws0">=</div></div><div class="c x4a y5a w3 h1a"><div class="t m0 x24 ha y66 ff8 fs2 fc0 sc1 ls0 ws0">e</div></div><div class="c x4b y5a wa h1b"><div class="t m2 x2f h16 y67 ff8 fs6 fc0 sc1 ls0 ws0">ji</div></div><div class="t m0 x4c ha y65 ff7 fs2 fc0 sc1 ls0 ws0">，</div><div class="c x4d y5a w3 h1d"><div class="t m0 x24 ha y69 ff8 fs2 fc0 sc1 ls0 ws0">A</div></div><div class="c x31 y5a wd h1c"><div class="t m0 x24 h10 y68 ffb fs2 fc0 sc1 ls0 ws0">∈</div></div><div class="c x33 y5a w3 h21"><div class="t m0 x24 ha y6d ff8 fs2 fc0 sc1 ls0 ws0">R</div></div><div class="c x4e y5a w8 h22"><div class="t m2 x2f h16 y6e ff8 fs6 fc0 sc1 ls0 ws0">N</div></div><div class="c x4f y5a we h23"><div class="t m2 x2f h24 y6f ffa fs6 fc0 sc1 ls0 ws0">×</div></div><div class="c x50 y5a w8 h22"><div class="t m2 x2f h16 y6e ff8 fs6 fc0 sc1 ls0 ws0">N</div></div><div class="t m0 x36 ha y65 ff7 fs2 fc0 sc1 ls0 ws0">为图的权值邻接<span class="_ _1"></span>矩</div><div class="t m0 x1 ha y70 ff7 fs2 fc0 sc1 ls0 ws0">阵<span class="_ _1"></span>，</div><div class="c x51 y5a w3 h25"><div class="t m0 x24 ha y71 ff8 fs2 fc0 sc1 ls0 ws0">w</div></div><div class="c x52 y5a wa h26"><div class="t m2 x2f h16 y72 ff8 fs6 fc0 sc1 ls0 ws0">ij</div></div><div class="c xc y5a wd h27"><div class="t m0 x24 h10 y73 ffb fs2 fc0 sc1 ls0 ws0">∈</div></div><div class="c x53 y5a w3 h28"><div class="t m0 x24 ha y74 ff8 fs2 fc0 sc1 ls0 ws0">A</div></div><div class="t m0 x54 ha y70 ff7 fs2 fc0 sc1 ls0 ws0">表<span class="_ _1"></span>示边</div><div class="c x55 y5a w3 h25"><div class="t m0 x24 ha y71 ff8 fs2 fc0 sc1 ls0 ws0">e</div></div><div class="c x56 y5a wa h26"><div class="t m2 x2f h16 y72 ff8 fs6 fc0 sc1 ls0 ws0">ij</div></div><div class="t m0 x57 ha y70 ff7 fs2 fc0 sc1 ls0 ws0">上<span class="_ _1"></span>的权<span class="_ _1"></span>值<span class="_ _1"></span>。<span class="_ _1"></span>定<span class="_ _1"></span>义<span class="_ _1"></span>图<span class="_ _1"></span>上<span class="_ _1"></span>的<span class="_ _1"></span>信<span class="_ _1"></span>号<span class="_ _1"></span>为</div><div class="c x58 y5a w3 h29"><div class="t m0 x24 ha y75 ff8 fs2 fc0 sc1 ls0 ws0">x</div></div><div class="t m0 x59 ha y70 ff7 fs2 fc0 sc1 ls0 ws0">，<span class="_ _1"></span>图的<span class="_ _1"></span>节<span class="_ _1"></span>点<span class="_ _1"></span>特<span class="_ _1"></span>征<span class="_ _1"></span>矩<span class="_ _1"></span>阵<span class="_ _1"></span>用</div><div class="c x5a y5a w3 h28"><div class="t m0 x24 ha y74 ff8 fs2 fc0 sc1 ls0 ws0">X</div></div><div class="c xa y5a wd h27"><div class="t m0 x24 h10 y73 ffb fs2 fc0 sc1 ls0 ws0">∈</div></div><div class="c x5b y5a w3 h2a"><div class="t m0 x24 ha y76 ff8 fs2 fc0 sc1 ls0 ws0">R</div></div><div class="c x19 y5a w8 h2b"><div class="t m2 x2f h16 y77 ff8 fs6 fc0 sc1 ls0 ws0">N</div></div><div class="c x5c y5a we h2c"><div class="t m2 x2f h24 y78 ffa fs6 fc0 sc1 ls0 ws0">×</div></div><div class="c x5d y5a w8 h2b"><div class="t m2 x2f h16 y77 ff8 fs6 fc0 sc1 ls0 ws0">C</div></div><div class="t m0 x5e ha y70 ff7 fs2 fc0 sc1 ls0 ws0">表<span class="_ _1"></span>示，</div><div class="t m0 x1 ha y79 ff7 fs2 fc0 sc1 ls0 ws0">定义</div><div class="c x51 y5a w3 h2d"><div class="t m0 x24 ha y7a ff8 fs2 fc0 sc1 ls0 ws0">x</div></div><div class="c x9 y5a w8 h2e"><div class="t m2 x2f h16 y7b ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c x5f y5a wd h2f"><div class="t m0 x24 h10 y7c ffb fs2 fc0 sc1 ls0 ws0">∈</div></div><div class="c x60 y5a w3 h2d"><div class="t m0 x24 ha y7a ff8 fs2 fc0 sc1 ls0 ws0">R</div></div><div class="c xd y5a w8 h30"><div class="t m2 x2f h16 y7d ff8 fs6 fc0 sc1 ls0 ws0">c</div></div><div class="t m0 x61 ha y79 ff7 fs2 fc0 sc1 ls0 ws0">为第</div><div class="c x62 y5a w3 h31"><div class="t m0 x24 ha y7e ff8 fs2 fc0 sc1 ls0 ws0">i</div></div><div class="t m0 x1c ha y79 ff7 fs2 fc0 sc1 ls0 ws0">个节点的特征向量，</div><div class="c x63 y5a w3 h31"><div class="t m0 x24 ha y7e ff8 fs2 fc0 sc1 ls0 ws0">C</div></div><div class="t m0 x64 ha y79 ff7 fs2 fc0 sc1 ls0 ws0">为节点特征的维度大小。<span class="_ _f"></span>构建指静脉加权图操作包括</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/89551058/bg3.jpg"><div class="t m0 x1 ha y25 ff7 fs2 fc0 sc1 ls0 ws0">节点集的构建、节点特征的计算、边集的构建以及权值的计算。</div><div class="t m1 x1 h5 y7f ff6 fs2 fc0 sc1 ls0 ws0">1.<span class="_ _1"></span>1<span class="_ _1"></span> <span class="_ _8"> </span><span class="ff1 sc0">节<span class="_ _1"></span>点<span class="_ _1"></span>集<span class="_ _a"></span>的<span class="_ _a"></span>构<span class="_ _1"></span>建<span class="_ _a"></span>、<span class="_ _a"></span>节<span class="_ _1"></span>点<span class="_ _a"></span>特<span class="_ _1"></span>征<span class="_ _a"></span>的<span class="_ _a"></span>计<span class="_ _1"></span>算</span></div><div class="t m0 x9 ha y80 ff8 fs2 fc0 sc1 ls0 ws0">SLIC</div><div class="t m0 xd hb y81 ff8 fs4 fc0 sc1 ls0 ws0">[14]</div><div class="t m0 x6 ha y80 ff7 fs2 fc0 sc1 ls0 ws0">是一种基<span class="_ _1"></span>于改进的<span class="_ _9"> </span><span class="ff8">K<span class="_ _2"> </span></span>均值<span class="_ _1"></span>聚类算法<span class="_ _1"></span>来生成超<span class="_ _1"></span>像素，<span class="_ _1"></span>输入一张<span class="_ _1"></span>指静脉原<span class="_ _1"></span>始图像，</div><div class="t m0 x1 ha y82 ff7 fs2 fc0 sc1 ls0 ws0">设定一<span class="_ _1"></span>个分割<span class="_ _1"></span>数<span class="_ _2"> </span><span class="ff8">k</span>，<span class="_ _1"></span>算法首<span class="_ _1"></span>先将<span class="_ _1"></span>图像转<span class="_ _1"></span>至<span class="_ _2"> </span><span class="ff8">CIELAB<span class="_ _9"> </span></span>颜色空间<span class="_ _1"></span>，并<span class="_ _1"></span>将每个<span class="_ _1"></span>像素的<span class="_ _1"></span>亮度、<span class="_ _1"></span>颜色值</div><div class="c x3a y5a w5 h32"><div class="t m0 x24 h10 y83 ffa fs2 fc0 sc1 ls0 ws0">(</div></div><div class="c x3b y5a w6 h33"><div class="t m0 x24 ha y84 ff8 fs2 fc0 sc1 ls0 ws0">L,a,b</div></div><div class="c x65 y5a w5 h32"><div class="t m0 x24 h10 y83 ffa fs2 fc0 sc1 ls0 ws0">)</div></div><div class="t m0 x60 ha y85 ff7 fs2 fc0 sc1 ls0 ws0">和空间坐标</div><div class="c x66 y5a w5 h32"><div class="t m0 x24 h10 y83 ffa fs2 fc0 sc1 ls0 ws0">(</div></div><div class="c x3e y5a wb h33"><div class="t m0 x24 ha y84 ff8 fs2 fc0 sc1 ls0 ws0">x,y</div></div><div class="c x67 y5a w5 h32"><div class="t m0 x24 h10 y83 ffa fs2 fc0 sc1 ls0 ws0">)</div></div><div class="t m0 x68 ha y85 ff7 fs2 fc0 sc1 ls0 ws0">结合成一个五维向量</div><div class="c x69 y5a w5 h32"><div class="t m0 x24 h10 y83 ffa fs2 fc0 sc1 ls0 ws0">(</div></div><div class="c x6a y5a wf h33"><div class="t m0 x24 ha y84 ff8 fs2 fc0 sc1 ls0 ws0">L,a,b,x,y</div></div><div class="c x6b y5a w5 h32"><div class="t m0 x24 h10 y83 ffa fs2 fc0 sc1 ls0 ws0">)</div></div><div class="t m0 xe ha y85 ff7 fs2 fc0 sc1 ls0 ws0">，<span class="_ _e"></span>在图像中设定<span class="_ _2"> </span><span class="ff8">k<span class="_ _2"> </span></span>个初始聚类中心</div><div class="c x3a y5a w3 h34"><div class="t m0 x24 ha y86 ff8 fs2 fc0 sc1 ls0 ws0">C</div></div><div class="c x1 y87 w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c x6c y5a w4 h36"><div class="t m0 x24 h10 y89 ffa fs2 fc0 sc1 ls0 ws0">=</div></div><div class="c x51 y5a w10 h37"><div class="t m0 x24 h10 y8a ffa fs2 fc0 sc1 ls0 ws0">[</div></div><div class="c x6d y5a w3 h38"><div class="t m0 x24 ha y8b ff8 fs2 fc0 sc1 ls0 ws0">l</div></div><div class="c x5f y8c w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c x6e y5a w3 h38"><div class="t m0 x24 ha y8b ff8 fs2 fc0 sc1 ls0 ws0">,</div></div><div class="c x6f y5a w3 h38"><div class="t m0 x24 ha y8b ff8 fs2 fc0 sc1 ls0 ws0">a</div></div><div class="c x70 y8c w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c x20 y5a w3 h38"><div class="t m0 x24 ha y8b ff8 fs2 fc0 sc1 ls0 ws0">,</div></div><div class="c x71 y5a w3 h38"><div class="t m0 x24 ha y8b ff8 fs2 fc0 sc1 ls0 ws0">b</div></div><div class="c x6 y8c w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c x72 y5a w3 h38"><div class="t m0 x24 ha y8b ff8 fs2 fc0 sc1 ls0 ws0">,</div></div><div class="c x1b y5a w3 h38"><div class="t m0 x24 ha y8b ff8 fs2 fc0 sc1 ls0 ws0">x</div></div><div class="c x73 y8c w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c x74 y5a w3 h38"><div class="t m0 x24 ha y8b ff8 fs2 fc0 sc1 ls0 ws0">,</div></div><div class="c x3d y5a w3 h38"><div class="t m0 x24 ha y8b ff8 fs2 fc0 sc1 ls0 ws0">y</div></div><div class="c x3e y8c w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c x75 y5a w10 h37"><div class="t m0 x24 h10 y8a ffa fs2 fc0 sc1 ls0 ws0">]</div></div><div class="c x76 y8d w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">T</div></div><div class="t m0 x67 ha y8e ff8 fs2 fc0 sc1 ls0 ws0">,<span class="ff7">然后在间隔</span></div><div class="c x77 y5a w3 h39"><div class="t m0 x24 ha y8f ff8 fs2 fc0 sc1 ls0 ws0">S</div></div><div class="c x78 y5a w4 h36"><div class="t m0 x24 h10 y89 ffa fs2 fc0 sc1 ls0 ws0">=</div></div><div class="c x79 y5a wb h3a"><div class="t m0 x24 ha y90 ff8 fs2 fc0 sc1 ls0 ws0">N/k</div></div><div class="t m0 x7a ha y8e ff7 fs2 fc0 sc1 ls0 ws0">个像素的网格上采样，</div><div class="c x7b y5a w3 h3b"><div class="t m0 x24 ha y91 ff8 fs2 fc0 sc1 ls0 ws0">N</div></div><div class="t m0 x7c ha y8e ff7 fs2 fc0 sc1 ls0 ws0">为总像素数，<span class="_ _f"></span>为避免聚</div><div class="t m0 x1 ha y92 ff7 fs2 fc0 sc1 ls0 ws0">类中心落在梯度较大的轮廓边界，将聚类<span class="_ _1"></span>中心移动到<span class="_ _2"> </span><span class="ff8">3×3<span class="_ _2"> </span></span>邻域内梯度最<span class="_ _1"></span>小的位置，在聚类</div><div class="t m0 x1 ha y93 ff7 fs2 fc0 sc1 ls0 ws0">中心搜<span class="_ _1"></span>索邻域<span class="_ _1"></span>内为每<span class="_ _1"></span>个像素<span class="_ _1"></span>点分配<span class="_ _1"></span>标签。<span class="_ _1"></span>和标准<span class="_ _1"></span>的<span class="_ _2"> </span><span class="ff8">K<span class="_ _9"> </span></span>均值聚类<span class="_ _1"></span>在整张<span class="_ _1"></span>图中搜<span class="_ _1"></span>索不同<span class="_ _1"></span>，<span class="ff8">SLIC</span></div><div class="t m0 x1 ha y94 ff7 fs2 fc0 sc1 ls0 ws0">的搜索范围限制为</div><div class="c x3d y5a wc h3c"><div class="t m0 x24 ha y95 ff8 fs2 fc0 sc1 ls0 ws0">2S</div></div><div class="c x7d y5a w11 h3d"><div class="t m0 x24 h10 y96 ffa fs2 fc0 sc1 ls0 ws0">×</div></div><div class="c x7e y5a wc h3c"><div class="t m0 x24 ha y95 ff8 fs2 fc0 sc1 ls0 ws0">2S</div></div><div class="t m0 x7f ha y94 ff7 fs2 fc0 sc1 ls0 ws0">，减少了距离计算<span class="_ _1"></span>，从而能加速算<span class="_ _1"></span>法的收敛。对搜<span class="_ _1"></span>索到的每个像</div><div class="t m0 x1 ha y97 ff7 fs2 fc0 sc1 ls0 ws0">素<span class="_ _1"></span>点分<span class="_ _1"></span>别<span class="_ _1"></span>计<span class="_ _1"></span>算<span class="_ _1"></span>它<span class="_ _1"></span>和<span class="_ _1"></span>聚<span class="_ _1"></span>类<span class="_ _1"></span>中<span class="_ _1"></span>心<span class="_ _1"></span>的<span class="_ _1"></span>颜<span class="_ _1"></span>色<span class="_ _1"></span>距<span class="_ _1"></span>离</div><div class="c x64 y5a w3 h3e"><div class="t m0 x24 ha y98 ff8 fs2 fc0 sc1 ls0 ws0">d</div></div><div class="c x80 y99 w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">c</div></div><div class="t m0 x81 ha y97 ff7 fs2 fc0 sc1 ls0 ws0">和<span class="_ _1"></span>空间<span class="_ _1"></span>距<span class="_ _1"></span>离</div><div class="c x82 y5a w3 h3e"><div class="t m0 x24 ha y98 ff8 fs2 fc0 sc1 ls0 ws0">d</div></div><div class="c x49 y99 w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">s</div></div><div class="t m0 x83 ha y97 ff7 fs2 fc0 sc1 ls0 ws0">，<span class="_ _1"></span>并归<span class="_ _1"></span>一<span class="_ _1"></span>化<span class="_ _1"></span>得<span class="_ _1"></span>到<span class="_ _1"></span>最<span class="_ _1"></span>终<span class="_ _1"></span>的<span class="_ _1"></span>距<span class="_ _1"></span>离<span class="_ _1"></span>度<span class="_ _1"></span>量</div><div class="c x84 y5a w3 h3f"><div class="t m0 x24 ha y9a ff8 fs2 fc0 sc1 ls0 ws0">D</div></div><div class="c x85 y9b w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">'</div></div><div class="t m0 x86 ha y97 ff7 fs2 fc0 sc1 ls0 ws0">：</div><div class="c x77 y5a w3 h40"><div class="t m0 x24 ha y9c ff8 fs2 fc0 sc1 ls0 ws0">d</div></div><div class="c x78 y9d w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">c</div></div><div class="c x63 y5a w4 h41"><div class="t m0 x24 h10 y9e ffa fs2 fc0 sc1 ls0 ws0">=</div></div><div class="c x87 y5a w5 h42"><div class="t m0 x24 h10 y9f ffa fs2 fc0 sc1 ls0 ws0">(</div></div><div class="c x88 y5a w3 h43"><div class="t m0 x24 ha ya0 ff8 fs2 fc0 sc1 ls0 ws0">l</div></div><div class="c x25 ya1 w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">j</div></div><div class="c x69 y5a w12 h44"><div class="t m0 x24 h45 ya2 ffc fs2 fc0 sc1 ls0 ws0">−</div></div><div class="c x89 y5a w3 h43"><div class="t m0 x24 ha ya0 ff8 fs2 fc0 sc1 ls0 ws0">l</div></div><div class="c x8a ya1 w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c x8b y5a w5 h42"><div class="t m0 x24 h10 y9f ffa fs2 fc0 sc1 ls0 ws0">)</div></div><div class="c x8c ya3 w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">2</div></div><div class="c x8d y5a w4 h42"><div class="t m0 x24 h10 y9f ffa fs2 fc0 sc1 ls0 ws0">+</div></div><div class="c x8e y5a w5 h42"><div class="t m0 x24 h10 y9f ffa fs2 fc0 sc1 ls0 ws0">(</div></div><div class="c x8f y5a w3 h43"><div class="t m0 x24 ha ya0 ff8 fs2 fc0 sc1 ls0 ws0">a</div></div><div class="c x90 ya1 w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">j</div></div><div class="c x91 y5a w12 h44"><div class="t m0 x24 h45 ya2 ffc fs2 fc0 sc1 ls0 ws0">−</div></div><div class="c x4a y5a w3 h43"><div class="t m0 x24 ha ya0 ff8 fs2 fc0 sc1 ls0 ws0">a</div></div><div class="c x4b ya1 w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c x92 y5a w5 h42"><div class="t m0 x24 h10 y9f ffa fs2 fc0 sc1 ls0 ws0">)</div></div><div class="c x2c ya3 w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">2</div></div><div class="c x4c y5a w4 h42"><div class="t m0 x24 h10 y9f ffa fs2 fc0 sc1 ls0 ws0">+</div></div><div class="c x93 y5a w5 h42"><div class="t m0 x24 h10 y9f ffa fs2 fc0 sc1 ls0 ws0">(</div></div><div class="c x94 y5a w3 h43"><div class="t m0 x24 ha ya0 ff8 fs2 fc0 sc1 ls0 ws0">b</div></div><div class="c x95 ya1 w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">j</div></div><div class="c x96 y5a w12 h44"><div class="t m0 x24 h45 ya2 ffc fs2 fc0 sc1 ls0 ws0">−</div></div><div class="c x4e y5a w3 h43"><div class="t m0 x24 ha ya0 ff8 fs2 fc0 sc1 ls0 ws0">b</div></div><div class="c x7c ya1 w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c x97 y5a w5 h42"><div class="t m0 x24 h10 y9f ffa fs2 fc0 sc1 ls0 ws0">)</div></div><div class="c x50 ya3 w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">2</div></div><div class="t m0 x98 ha ya4 ff8 fs2 fc0 sc1 ls0 ws0"> <span class="ff7">（</span>1<span class="ff7">）</span></div><div class="t m0 x99 h46 ya5 ffd fs2 fc0 sc1 ls0 ws0"> </div><div class="c x9a y5a w3 h47"><div class="t m0 x24 ha ya6 ff8 fs2 fc0 sc1 ls0 ws0">d</div></div><div class="c x9b ya7 w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">s</div></div><div class="c x9c y5a w4 h48"><div class="t m0 x24 h10 ya8 ffa fs2 fc0 sc1 ls0 ws0">=</div></div><div class="c x48 y5a w5 h49"><div class="t m0 x24 h10 ya9 ffa fs2 fc0 sc1 ls0 ws0">(</div></div><div class="c x9d y5a w3 h4a"><div class="t m0 x24 ha yaa ff8 fs2 fc0 sc1 ls0 ws0">x</div></div><div class="c x9e yab w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">j</div></div><div class="c x25 y5a w12 h4b"><div class="t m0 x24 h45 yac ffc fs2 fc0 sc1 ls0 ws0">−</div></div><div class="c x6a y5a w3 h4a"><div class="t m0 x24 ha yaa ff8 fs2 fc0 sc1 ls0 ws0">x</div></div><div class="c x9f yab w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c xa0 y5a w5 h49"><div class="t m0 x24 h10 ya9 ffa fs2 fc0 sc1 ls0 ws0">)</div></div><div class="c xa1 yad w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">2</div></div><div class="c xa2 y5a w4 h49"><div class="t m0 x24 h10 ya9 ffa fs2 fc0 sc1 ls0 ws0">+</div></div><div class="c xa3 y5a w5 h49"><div class="t m0 x24 h10 ya9 ffa fs2 fc0 sc1 ls0 ws0">(</div></div><div class="c x28 y5a w3 h4a"><div class="t m0 x24 ha yaa ff8 fs2 fc0 sc1 ls0 ws0">y</div></div><div class="c xa4 yab w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">j</div></div><div class="c x29 y5a w12 h4b"><div class="t m0 x24 h45 yac ffc fs2 fc0 sc1 ls0 ws0">−</div></div><div class="c x2a y5a w3 h4a"><div class="t m0 x24 ha yaa ff8 fs2 fc0 sc1 ls0 ws0">y</div></div><div class="c x2b yab w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c x4b y5a w5 h49"><div class="t m0 x24 h10 ya9 ffa fs2 fc0 sc1 ls0 ws0">)</div></div><div class="c xa5 yad w8 h35"><div class="t m2 x2f h16 y88 ff8 fs6 fc0 sc1 ls0 ws0">2</div></div><div class="t m0 xa6 ha ya5 ff8 fs2 fc0 sc1 ls0 ws0"> <span class="ff7">（</span>2<span class="ff7">）</span></div><div class="c xa7 y5a w3 h4c"><div class="t m0 x24 ha yae ff8 fs2 fc0 sc1 ls0 ws0">D</div></div><div class="c x99 y5a w8 h4d"><div class="t m2 x2f h16 yaf ff8 fs6 fc0 sc1 ls0 ws0">'</div></div><div class="c xa8 y5a w4 h4e"><div class="t m0 x24 h10 yb0 ffa fs2 fc0 sc1 ls0 ws0">=</div></div><div class="c x80 y5a w3 h4f"><div class="t m0 x24 ha yb1 ff8 fs2 fc0 sc1 ls0 ws0">d</div></div><div class="c xa9 y5a w8 h50"><div class="t m2 x2f h16 yb2 ff8 fs6 fc0 sc1 ls0 ws0">c</div></div><div class="c xaa y5a w3 h4f"><div class="t m0 x24 ha yb1 ff8 fs2 fc0 sc1 ls0 ws0">N</div></div><div class="c x6a y5a w8 h50"><div class="t m2 x2f h16 yb2 ff8 fs6 fc0 sc1 ls0 ws0">c</div></div><div class="c xa0 y5a w8 h51"><div class="t m2 x2f h16 yb3 ff8 fs6 fc0 sc1 ls0 ws0">2</div></div><div class="c xa1 y5a w4 h52"><div class="t m0 x24 h10 yb4 ffa fs2 fc0 sc1 ls0 ws0">+</div></div><div class="c x58 y5a w3 h4f"><div class="t m0 x24 ha yb1 ff8 fs2 fc0 sc1 ls0 ws0">d</div></div><div class="c x82 y5a w8 h50"><div class="t m2 x2f h16 yb2 ff8 fs6 fc0 sc1 ls0 ws0">s</div></div><div class="c x29 y5a w3 h4f"><div class="t m0 x24 ha yb1 ff8 fs2 fc0 sc1 ls0 ws0">N</div></div><div class="c x83 y5a w8 h50"><div class="t m2 x2f h16 yb2 ff8 fs6 fc0 sc1 ls0 ws0">s</div></div><div class="c xab y5a w8 h51"><div class="t m2 x2f h16 yb3 ff8 fs6 fc0 sc1 ls0 ws0">2</div></div><div class="t m0 xac ha yb5 ff8 fs2 fc0 sc1 ls0 ws0"> <span class="ff7">（</span>3<span class="ff7">）</span></div><div class="t m0 x1 ha yb6 ff7 fs2 fc0 sc1 ls0 ws0">式中</div><div class="c x51 y5a w3 h53"><div class="t m0 x24 ha yb7 ff8 fs2 fc0 sc1 ls0 ws0">N</div></div><div class="c x52 y5a w8 h54"><div class="t m2 x2f h16 yb8 ff8 fs6 fc0 sc1 ls0 ws0">s</div></div><div class="c x5f y5a w4 h55"><div class="t m0 x24 h10 yb9 ffa fs2 fc0 sc1 ls0 ws0">=</div></div><div class="c xad y5a w3 h56"><div class="t m0 x24 ha yba ff8 fs2 fc0 sc1 ls0 ws0">S</div></div><div class="t m0 x61 ha yb6 ff7 fs2 fc0 sc1 ls0 ws0">为类内最大空间距离，</div><div class="c xae y5a w3 h53"><div class="t m0 x24 ha yb7 ff8 fs2 fc0 sc1 ls0 ws0">N</div></div><div class="c xaf y5a w8 h54"><div class="t m2 x2f h16 yb8 ff8 fs6 fc0 sc1 ls0 ws0">c</div></div><div class="t m0 x63 ha yb6 ff7 fs2 fc0 sc1 ls0 ws0">为最大颜色距离，一般<span class="_ _1"></span>在</div><div class="c x2d y5a w10 h57"><div class="t m0 x24 h10 ybb ffa fs2 fc0 sc1 ls0 ws0">[</div></div><div class="c xa6 y5a w9 h58"><div class="t m0 x24 ha ybc ff8 fs2 fc0 sc1 ls0 ws0">1,40</div></div><div class="c x33 y5a w10 h57"><div class="t m0 x24 h10 ybb ffa fs2 fc0 sc1 ls0 ws0">]</div></div><div class="t m0 xb0 ha yb6 ff7 fs2 fc0 sc1 ls0 ws0">区间内取一个固定的常</div><div class="t m0 x1 ha ybd ff7 fs2 fc0 sc1 ls0 ws0">数值</div><div class="t m3 xb1 h59 ybd ffe fs7 fc0 sc1 ls0 ws0">q</div><div class="t m0 x6e ha ybd ff7 fs2 fc0 sc1 ls0 ws0">，<span class="_ _11"></span>权衡颜色相似性和空间邻近度之间的相对重要性。<span class="_ _11"></span>不断迭代上述步骤直到误差收敛，</div><div class="t m0 x1 ha ybe ff7 fs2 fc0 sc1 ls0 ws0">最后使用连通分量算法将不连续的、<span class="_ _b"></span>尺寸过小的超像素重新分配给邻近的超像素区域，<span class="_ _b"></span>算法</div><div class="t m0 x1 ha ybf ff7 fs2 fc0 sc1 ls0 ws0">具体流程（伪代码）如下表<span class="_ _2"> </span><span class="ff8">1<span class="_ _2"> </span></span>所示。</div><div class="c x1 yc0 w13 h5a"><div class="t m0 xb2 ha yc1 fff fs2 fc0 sc0 ls0 ws0">表<span class="_ _2"> </span><span class="ff10">1 SLI<span class="_ _1"></span>C<span class="_ _2"> </span></span>超像素分<span class="_ _1"></span>割算法</div></div><div class="c x1 yc2 w13 h5b"><div class="t m0 xb3 ha yc3 ff7 fs2 fc0 sc1 ls0 ws0">在图像中设定<span class="_ _2"> </span><span class="ff8">k<span class="_ _2"> </span></span>个初始聚类中心</div></div><div class="c xa7 yc2 w3 h5c"><div class="t m0 x24 ha yc4 ff8 fs2 fc0 sc1 ls0 ws0">C</div></div><div class="c x99 yc2 w8 h5d"><div class="t m2 x2f h16 yc5 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c xa8 yc2 w4 h5e"><div class="t m0 x24 h10 yc6 ffa fs2 fc0 sc1 ls0 ws0">=</div></div><div class="c x47 yc2 w10 h5f"><div class="t m0 x24 h10 yc7 ffa fs2 fc0 sc1 ls0 ws0">[</div></div><div class="c xb4 yc2 w3 h60"><div class="t m0 x24 ha yc8 ff8 fs2 fc0 sc1 ls0 ws0">l</div></div><div class="c xb5 yc2 w8 h61"><div class="t m2 x2f h16 yc9 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c x79 yc2 w3 h60"><div class="t m0 x24 ha yc8 ff8 fs2 fc0 sc1 ls0 ws0">,</div></div><div class="c x87 yc2 w3 h60"><div class="t m0 x24 ha yc8 ff8 fs2 fc0 sc1 ls0 ws0">a</div></div><div class="c xb6 yc2 w8 h61"><div class="t m2 x2f h16 yc9 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c xb7 yc2 w3 h60"><div class="t m0 x24 ha yc8 ff8 fs2 fc0 sc1 ls0 ws0">,</div></div><div class="c xb8 yc2 w3 h60"><div class="t m0 x24 ha yc8 ff8 fs2 fc0 sc1 ls0 ws0">b</div></div><div class="c x26 yc2 w8 h61"><div class="t m2 x2f h16 yc9 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c x9f yc2 w3 h60"><div class="t m0 x24 ha yc8 ff8 fs2 fc0 sc1 ls0 ws0">,</div></div><div class="c x8b yc2 w3 h60"><div class="t m0 x24 ha yc8 ff8 fs2 fc0 sc1 ls0 ws0">x</div></div><div class="c xb9 yc2 w8 h61"><div class="t m2 x2f h16 yc9 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c xba yc2 w3 h60"><div class="t m0 x24 ha yc8 ff8 fs2 fc0 sc1 ls0 ws0">,</div></div><div class="c x14 yc2 w3 h60"><div class="t m0 x24 ha yc8 ff8 fs2 fc0 sc1 ls0 ws0">y</div></div><div class="c xbb yc2 w8 h61"><div class="t m2 x2f h16 yc9 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c x82 yc2 w10 h5f"><div class="t m0 x24 h10 yc7 ffa fs2 fc0 sc1 ls0 ws0">]</div></div><div class="c x59 yc2 w8 h5b"><div class="t m2 x2f h16 yca ff8 fs6 fc0 sc1 ls0 ws0">T</div></div><div class="c x1 yc2 w13 h5b"><div class="t m0 xb3 ha ycb ff7 fs2 fc0 sc1 ls0 ws0">对于每一个像素点</div></div><div class="c xbc ycc w14 h62"><div class="t m4 xbd h63 ycd ff9 fs8 fc0 sc1 ls0 ws0">p</div></div><div class="c x1 yc2 w13 h5b"><div class="t m0 x3c ha ycb ff7 fs2 fc0 sc1 ls0 ws0">，设置其标签为</div></div><div class="c xbe yce w15 h64"><div class="t m5 xbf h65 ycd ff5 fs9 fc0 sc1 ls0 ws0">1<span class="_ _12"></span>)<span class="_ _13"></span>(<span class="_ _14"> </span><span class="ff11">�<span class="_ _15"></span>�<span class="_ _16"></span><span class="ff9">p<span class="_ _13"></span>l</span></span></div></div><div class="c x1 yc2 w13 h5b"><div class="t m0 xc0 ha ycb ff8 fs2 fc0 sc1 ls0 ws0">;<span class="ff7">设置距离为</span></div></div><div class="c x4d yce w16 h64"><div class="t m6 xc1 h65 ycd ff11 fs9 fc0 sc1 ls0 ws0">�<span class="_ _15"></span>�<span class="_ _17"></span><span class="ff5">)<span class="_ _13"></span>(<span class="_ _7"> </span><span class="ff9">p<span class="_ _18"></span>d</span></span></div></div><div class="c x1 yc2 w13 h5b"><div class="t m0 xb3 h46 ycf ff12 fs2 fc0 sc1 ls0 ws0">循环</div><div class="t m0 xb3 h46 yd0 ffd fs2 fc0 sc1 ls0 ws0"> <span class="_ _19"> </span>for <span class="_ _0"> </span><span class="ff12">每一个聚类中心</span></div></div><div class="c xc2 yd1 w2 h66"><div class="t m7 xc3 h67 yd2 ff9 fs4 fc0 sc1 ls0 ws0">i</div><div class="t m7 xc4 h63 yd3 ff9 fs3 fc0 sc1 ls0 ws0">C</div></div><div class="c x1 yc2 w13 h5b"><div class="t m0 xd h46 yd0 ffd fs2 fc0 sc1 ls0 ws0"> <span class="_ _0"> </span>do</div><div class="t m0 xb3 h46 yd4 ffd fs2 fc0 sc1 ls0 ws0"> <span class="_ _1a"> </span>for <span class="_ _0"> </span><span class="ff12">聚类中心</span></div></div><div class="c x67 yd5 w2 h66"><div class="t m7 xc3 h67 yd2 ff9 fs4 fc0 sc1 ls0 ws0">i</div><div class="t m7 xc4 h63 yd3 ff9 fs3 fc0 sc1 ls0 ws0">C</div></div><div class="c x1 yc2 w13 h5b"><div class="t m0 xc5 h46 yd4 ff12 fs2 fc0 sc1 ls0 ws0">周围</div></div><div class="c xc6 yc2 w17 h68"><div class="t m0 x24 h10 yd6 ffa fs2 fc0 sc1 ls0 ws0">2</div></div><div class="c x45 yc2 w18 h68"><div class="t m0 x24 h10 yd6 ffb fs2 fc0 sc1 ls0 ws0">𝑆</div></div><div class="c xc7 yc2 w11 h68"><div class="t m0 x24 h10 yd6 ffa fs2 fc0 sc1 ls0 ws0">×</div></div><div class="c xc8 yc2 w17 h68"><div class="t m0 x24 h10 yd6 ffa fs2 fc0 sc1 ls0 ws0">2</div></div><div class="c xc9 yc2 w18 h68"><div class="t m0 x24 h10 yd6 ffb fs2 fc0 sc1 ls0 ws0">𝑆</div></div><div class="c x1 yc2 w13 h5b"><div class="t m0 x66 h46 yd4 ff12 fs2 fc0 sc1 ls0 ws0">的区域内每一个像素点</div></div><div class="c x4c yd7 w14 h62"><div class="t m4 xbd h63 ycd ff9 fs8 fc0 sc1 ls0 ws0">p</div></div><div class="c x1 yc2 w13 h5b"><div class="t m0 xaa h46 yd4 ffd fs2 fc0 sc1 ls0 ws0"> <span class="_ _0"> </span>do</div><div class="t m0 xb3 h46 yd8 ffd fs2 fc0 sc1 ls0 ws0"> <span class="_ _1b"> </span><span class="ff12">计算像素点</span></div></div><div class="c xca yd9 w14 h62"><div class="t m4 xbd h63 ycd ff9 fs8 fc0 sc1 ls0 ws0">p</div></div><div class="c x1 yc2 w13 h5b"><div class="t m0 xcb h46 yd8 ff12 fs2 fc0 sc1 ls0 ws0">到聚类中心</div></div><div class="c xcc yda w2 h66"><div class="t m7 xc3 h67 yd2 ff9 fs4 fc0 sc1 ls0 ws0">i</div><div class="t m7 xc4 h63 yd3 ff9 fs3 fc0 sc1 ls0 ws0">C</div></div><div class="c x1 yc2 w13 h5b"><div class="t m0 x7e h46 yd8 ff12 fs2 fc0 sc1 ls0 ws0">的距离</div></div><div class="c xa1 yc2 w19 h69"><div class="t m0 x24 h10 ydb ffb fs2 fc0 sc1 ls0 ws0">𝐷</div></div><div class="c xcd yc2 w1a h6a"><div class="t m2 x2f h24 ydc ffb fs6 fc0 sc1 ls0 ws0">′</div></div><div class="c x1 yc2 w13 h5b"><div class="t m0 xb3 h46 ydd ffd fs2 fc0 sc1 ls0 ws0"> <span class="_ _1b"> </span>If </div></div><div class="c xce yde w1b h66"><div class="t m8 xcf h6b ycd ff5 fs3 fc0 sc1 ls0 ws0">)<span class="_ _13"></span>(</div><div class="t m8 xd0 h6c ydf ff5 fs4 fc0 sc1 ls0 ws0">'</div><div class="t m8 xd1 h65 ycd ff9 fs3 fc0 sc1 ls0 ws0">p<span class="_ _18"></span>d<span class="_ _1c"></span>D<span class="_ _1d"> </span><span class="ff11">�</span></div></div><div class="c x1 yc2 w13 h5b"><div class="t m0 xcb h46 ydd ffd fs2 fc0 sc1 ls0 ws0"> <span class="_ _0"> </span>then</div><div class="t m0 xb3 h46 ye0 ffd fs2 fc0 sc1 ls0 ws0"> </div></div><div class="c x12 ye1 w1c h64"><div class="t m9 xd2 h65 ycd ff9 fs9 fc0 sc1 ls0 ws0">i<span class="_ _1e"></span>p<span class="_ _13"></span>l<span class="_ _1f"> </span><span class="ff11">�<span class="_ _17"></span><span class="ff5">)<span class="_ _13"></span>(</span></span></div></div><div class="c x1 yc2 w13 h5b"><div class="t m0 xb3 h46 ye2 ffd fs2 fc0 sc1 ls0 ws0"> </div></div><div class="c x12 ye3 w1d h66"><div class="t ma xd3 h6c ydf ff5 fs4 fc0 sc1 ls0 ws0">'</div><div class="t ma xd4 h65 ycd ff5 fs3 fc0 sc1 ls0 ws0">)<span class="_ _13"></span>(<span class="_ _20"> </span><span class="ff9">D<span class="_ _21"></span>p<span class="_ _18"></span>d<span class="_ _22"> </span><span class="ff11">�</span></span></div></div><div class="c x1 yc2 w13 h5b"><div class="t m0 xb3 h46 ye4 ffd fs2 fc0 sc1 ls0 ws0"> <span class="_ _1b"> </span>end if</div><div class="t m0 xb3 h46 ye5 ffd fs2 fc0 sc1 ls0 ws0"> <span class="_ _1a"> </span>end for</div><div class="t m0 xd5 h46 ye6 ffd fs2 fc0 sc1 ls0 ws0">end for</div><div class="t m0 xd5 h46 ye7 ffd fs2 fc0 sc1 ls0 ws0">/*<span class="ff12">更新</span>*/</div><div class="t m0 xd5 h46 ye8 ff12 fs2 fc0 sc1 ls0 ws0">更新新的聚类中心</div><div class="t m0 xd5 h46 ye9 ff12 fs2 fc0 sc1 ls0 ws0">计算误差</div></div><div class="c xd6 yea w14 h62"><div class="t m4 x21 h63 yeb ff9 fs8 fc0 sc1 ls0 ws0">E</div></div><div class="c x1 yc2 w13 h5b"><div class="t m0 xb3 h46 yec ff12 fs2 fc0 sc1 ls0 ws0">若误差</div></div><div class="c xd7 yed w1e hc"><div class="t mb xd8 h6d y59 ff9 fs5 fc0 sc1 ls0 ws0">threshold<span class="_ _23"></span>E<span class="_ _24"> </span><span class="ff11">�</span></div></div><div class="c x1 yc2 w13 h5b"><div class="t m0 xd9 h46 yec ff12 fs2 fc0 sc1 ls0 ws0">结束整个算法；反之则继续</div></div><div class="t m0 x9 ha yee ff7 fs2 fc0 sc1 ls0 ws0">通过<span class="_ _2"> </span><span class="ff8">SLIC<span class="_ _2"> </span></span>算法得到指静脉超像素图后，将一个超像素块构成加权图的一个节点。由于</div><div class="t m0 x1 ha yef ff7 fs2 fc0 sc1 ls0 ws0">不同手指个体的表皮和皮下组织厚度不同，对应指静脉成像中灰度特征不同，同一静脉图</div><div class="t m0 x1 ha yf0 ff7 fs2 fc0 sc1 ls0 ws0">像中静脉与非静脉部分区域的灰度也存在差异，并且每块超像素具有不同的空间位置特征<span class="ff8">,</span></div><div class="t m0 x1 ha yf1 ff7 fs2 fc0 sc1 ls0 ws0">因此通过计算每个超像素块的像素强度值</div><div class="c x80 y5a w3 h6e"><div class="t m0 x24 ha yf2 ff8 fs2 fc0 sc1 ls0 ws0">M</div></div><div class="c xa9 y5a wa h6f"><div class="t m2 x2f h16 yf3 ff8 fs6 fc0 sc1 ls0 ws0">sp</div></div><div class="c xaa y5a w4 h70"><div class="t m0 x24 h10 yf4 ffa fs2 fc0 sc1 ls0 ws0">=</div></div><div class="c xda y5a w1f h71"><div class="t m0 x24 h10 yf5 ffb fs2 fc0 sc1 ls0 ws0">∑</div></div><div class="c xdb y5a w8 h72"><div class="t m2 x2f h16 yf6 ff8 fs6 fc0 sc1 ls0 ws0">N</div></div><div class="c xb9 y5a w20 h73"><div class="t mc xbd h74 yf7 ff8 fsa fc0 sc1 ls0 ws0">i</div></div><div class="c xdb y5a w21 h75"><div class="t m2 x2f h16 yf8 ff8 fs6 fc0 sc1 ls0 ws0">n<span class="ffc">−</span>1</div></div><div class="c x14 y5a w3 h76"><div class="t m0 x24 ha yf9 ff8 fs2 fc0 sc1 ls0 ws0">p</div></div><div class="c xbb y5a w8 h77"><div class="t m2 x2f h16 yfa ff8 fs6 fc0 sc1 ls0 ws0">n</div></div><div class="c x82 y5a w9 h76"><div class="t m0 x24 ha yf9 ff8 fs2 fc0 sc1 ls0 ws0">/255</div></div><div class="c x2b y5a w3 h76"><div class="t m0 x24 ha yf9 ff8 fs2 fc0 sc1 ls0 ws0">N</div></div><div class="c x1f y5a w8 h77"><div class="t m2 x2f h16 yfa ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="t m0 x4c ha yf1 ff7 fs2 fc0 sc1 ls0 ws0">和质心坐标</div><div class="c x15 y5a w3 h6e"><div class="t m0 x24 ha yf2 ff8 fs2 fc0 sc1 ls0 ws0">C</div></div><div class="c xdc y5a wa h6f"><div class="t m2 x2f h16 yf3 ff8 fs6 fc0 sc1 ls0 ws0">sp</div></div><div class="c xdd y5a w4 h70"><div class="t m0 x24 h10 yf4 ffa fs2 fc0 sc1 ls0 ws0">=</div></div><div class="c xde y5a w5 h78"><div class="t m0 x24 h10 yfb ffa fs2 fc0 sc1 ls0 ws0">(</div></div><div class="c xa y5a w3 h79"><div class="t m0 x24 ha yfc ff8 fs2 fc0 sc1 ls0 ws0">x</div></div><div class="c xdf y5a w8 h7a"><div class="t m2 x2f h16 yfd ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c x5b y5a w3 h79"><div class="t m0 x24 ha yfc ff8 fs2 fc0 sc1 ls0 ws0">,</div></div><div class="c xe0 y5a w3 h79"><div class="t m0 x24 ha yfc ff8 fs2 fc0 sc1 ls0 ws0">y</div></div><div class="c x5c y5a w8 h7a"><div class="t m2 x2f h16 yfd ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c x11 y5a w5 h78"><div class="t m0 x24 h10 yfb ffa fs2 fc0 sc1 ls0 ws0">)</div></div><div class="c xe1 y5a w3 h7b"><div class="t m0 x24 ha yfe ff8 fs2 fc0 sc1 ls0 ws0">/</div></div><div class="c xe2 y5a w3 h6e"><div class="t m0 x24 ha yf2 ff8 fs2 fc0 sc1 ls0 ws0">S</div></div><div class="c x5e y5a w22 h6f"><div class="t m2 x2f h16 yf3 ff8 fs6 fc0 sc1 ls0 ws0">max</div></div><div class="t m0 x1 ha yff ff7 fs2 fc0 sc1 ls0 ws0">得到节点的灰度特征和空间特征，其中</div><div class="c xb4 y5a w3 h7c"><div class="t m0 x24 ha y100 ff8 fs2 fc0 sc1 ls0 ws0">N</div></div><div class="c xb5 y5a w8 h7d"><div class="t m2 x2f h16 y101 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="t m0 x23 ha yff ff7 fs2 fc0 sc1 ls0 ws0">表示第</div><div class="c x8a y5a w3 h7e"><div class="t m0 x24 ha y102 ff8 fs2 fc0 sc1 ls0 ws0">i</div></div><div class="t m0 xa2 ha yff ff7 fs2 fc0 sc1 ls0 ws0">个超像素内像素的总数，</div><div class="c x16 y5a w3 h7c"><div class="t m0 x24 ha y100 ff8 fs2 fc0 sc1 ls0 ws0">p</div></div><div class="c x37 y5a w8 h7d"><div class="t m2 x2f h16 y101 ff8 fs6 fc0 sc1 ls0 ws0">n</div></div><div class="t m0 xde ha yff ff7 fs2 fc0 sc1 ls0 ws0">为每个像素的</div><div class="t m0 x1 ha y103 ff7 fs2 fc0 sc1 ls0 ws0">像素值，</div><div class="c x60 y5a w3 h7f"><div class="t m0 x24 ha y104 ff8 fs2 fc0 sc1 ls0 ws0">S</div></div><div class="c xd y5a w22 h80"><div class="t m2 x2f h16 y105 ff8 fs6 fc0 sc1 ls0 ws0">max</div></div><div class="t m0 xe3 ha y103 ff7 fs2 fc0 sc1 ls0 ws0">是图像尺寸的最大值。由于两特征尺度不同，进行<span class="_ _2"> </span><span class="ff8">z-score(zero-mean)</span>标准</div><div class="t m0 x1 ha y106 ff7 fs2 fc0 sc1 ls0 ws0">化处理得到最终指静脉加权图的节点特征</div><div class="c x80 y5a w3 h81"><div class="t m0 x24 ha y107 ff8 fs2 fc0 sc1 ls0 ws0">x</div></div><div class="c xa9 y5a w8 h82"><div class="t m2 x2f h16 y108 ff8 fs6 fc0 sc1 ls0 ws0">i</div></div><div class="c xe4 y5a w4 h83"><div class="t m0 x24 h10 y109 ffa fs2 fc0 sc1 ls0 ws0">=</div></div><div class="c x6a y5a w10 h84"><div class="t m0 x24 h10 y10a ffa fs2 fc0 sc1 ls0 ws0">[</div></div><div class="c xda y5a w3 h85"><div class="t m0 x24 ha y10b ff8 fs2 fc0 sc1 ls0 ws0">M</div></div><div class="c x8b y5a wa h86"><div class="t m2 x2f h16 y10c ff8 fs6 fc0 sc1 ls0 ws0">sp</div></div><div class="c x8c y5a w3 h85"><div class="t m0 x24 ha y10b ff8 fs2 fc0 sc1 ls0 ws0">,</div></div><div class="c x8d y5a w3 h85"><div class="t m0 x24 ha y10b ff8 fs2 fc0 sc1 ls0 ws0">C</div></div><div class="c x58 y5a wa h86"><div class="t m2 x2f h16 y10c ff8 fs6 fc0 sc1 ls0 ws0">sp</div></div><div class="c x8f y5a w10 h84"><div class="t m0 x24 h10 y10a ffa fs2 fc0 sc1 ls0 ws0">]</div></div><div class="t m0 x91 ha y106 ff7 fs2 fc0 sc1 ls0 ws0">，所有节点特征构成特征矩阵</div><div class="c xe5 y5a w3 h87"><div class="t m0 x24 ha y10d ff8 fs2 fc0 sc1 ls0 ws0">X</div></div><div class="t m0 xe6 ha y106 ff7 fs2 fc0 sc1 ls0 ws0">。</div></div><div class="pi" data-data='{"ctm":[1.611830,0.000000,0.000000,1.611830,0.000000,0.000000]}'></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="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89551058/bg4.jpg"><div class="t m0 x1 ha y10e ff7 fs2 fc0 sc1 ls0 ws0">图<span class="_ _2"> </span><span class="ff8">1<span class="_ _2"> </span></span>所示为<span class="_ _2"> </span><span class="ff8">k<span class="_ _2"> </span></span>取<span class="_ _2"> </span><span class="ff8">100</span>，即超像素分割数为<span class="_ _2"> </span><span class="ff8">100</span>，</div><div class="t m3 x8b h59 y10e ffe fs7 fc0 sc1 ls0 ws0">q</div><div class="t m0 xb9 ha y10e ff7 fs2 fc0 sc1 ls0 ws0">取<span class="_ _2"> </span><span class="ff8">10<span class="_ _2"> </span></span>时，经过高斯平滑、归一化后的指</div><div class="t m0 x1 ha y10f ff7 fs2 fc0 sc1 ls0 ws0">静脉<span class="_ _2"> </span><span class="ff8">ROI<span class="_ _2"> </span></span>图像通过<span class="_ _2"> </span><span class="ff8">SLIC<span class="_ _2"> </span></span>算法构建节点集的示意图。<span class="ff8"> </span></div><div class="t m0 xbe h46 y110 ff12 fs2 fc0 sc1 ls0 ws0">图<span class="_ _2"> </span><span class="ffd">1 <span class="_ _0"> </span></span>节点集的构建</div><div class="t m1 x1 h5 y111 ff6 fs2 fc0 sc1 ls0 ws0">1.<span class="_ _1"></span>2<span class="_ _1"></span> <span class="_ _8"> </span><span class="ff1 sc0">构<span class="_ _1"></span>建<span class="_ _1"></span>边<span class="_ _a"></span>集<span class="_ _a"></span>、<span class="_ _1"></span>计<span class="_ _a"></span>算<span class="_ _a"></span>权<span class="_ _1"></span>重</span></div><div class="t m0 x9 ha y112 ff7 fs2 fc0 sc1 ls0 ws0">图的<span class="_ _1"></span>边描<span class="_ _1"></span>述<span class="_ _1"></span>的是<span class="_ _1"></span>节点<span class="_ _1"></span>之<span class="_ _1"></span>间的<span class="_ _1"></span>连<span class="_ _1"></span>接关<span class="_ _1"></span>系，<span class="_ _1"></span>边<span class="_ _1"></span>上的<span class="_ _1"></span>权<span class="_ _1"></span>值则<span class="_ _1"></span>描述<span class="_ _1"></span>了<span class="_ _1"></span>节点<span class="_ _1"></span>之间<span class="_ _1"></span>连<span class="_ _1"></span>接关<span class="_ _1"></span>系<span class="_ _1"></span>的强<span class="_ _1"></span>弱。</div><div class="t m0 x1 ha y113 ff7 fs2 fc0 sc1 ls0 ws0">典型<span class="_ _1"></span>的边<span class="_ _1"></span>集表<span class="_ _1"></span>示构<span class="_ _1"></span>成的<span class="_ _1"></span>图有<span class="_ _1"></span>区域<span class="_ _1"></span>邻接<span class="_ _1"></span>图，<span class="_ _1"></span><span class="ff8">K<span class="_ _2"> </span></span>近<span class="_ _1"></span>邻图<span class="_ _1"></span>和三<span class="_ _1"></span>角剖<span class="_ _1"></span>分图<span class="_ _1"></span>等</div><div class="t m0 xe7 hb y114 ff8 fs4 fc0 sc1 ls0 ws0">[15]</div><div class="t m0 xe8 ha y113 ff7 fs2 fc0 sc1 ls0 ws0">，这<span class="_ _1"></span>些都<span class="_ _1"></span>是局<span class="_ _1"></span>部连<span class="_ _1"></span>接</div><div class="t m0 x1 ha y115 ff7 fs2 fc0 sc1 ls0 ws0">的图结构，<span class="_ _f"></span>构成的图高度稀疏，<span class="_ _f"></span>图卷积提取的感知信息较少，<span class="_ _f"></span>因而本文提出构建无向完全图，</div><div class="t m0 x1 ha y116 ff7 fs2 fc0 sc1 ls0 ws0">每对不同的顶点之间都只存在一条边，如图<span class="_ _2"> </span><span class="ff8">2<span class="_ _2"> </span></span>所示。</div><div class="t m0 x47 h46 y117 ff12 fs2 fc0 sc1 ls0 ws0">图<span class="_ _2"> </span><span class="ffd">2 <span class="_ _0"> </span></span>边集的构建</div><div class="t m0 x9 ha y118 ff7 fs2 fc0 sc1 ls0 ws0">在加权图中，<span class="_ _b"></span>节点间的权重被定义为它们之间的空间亲密度，<span class="_ _b"></span>通过超像素质心坐标的空</div><div class="t m0 x1 ha y119 ff7 fs2 fc0 sc1 ls0 ws0">间距离来计算。<span class="_ _d"></span>权值越小，<span class="_ _d"></span>意味着两个超像素质心之间的距离越远，<span class="_ _d"></span>那么相应的节点间的空</div><div class="t m0 x1 ha y11a ff7 fs2 fc0 sc1 ls0 ws0">间亲密度就越低，连接关系也就越弱。权值的计算方法如下<span class="ff8">:</span></div><div class="c xc0 y11b w23 h88"><div class="t md x66 h89 y11c ff5 fsb fc0 sc1 ls0 ws0">)<span class="_ _25"></span>/<span class="_ _26"></span>)<span class="_ _16"></span>,<span class="_ _27"></span>(<span class="_ _18"></span>)<span class="_ _18"></span>,<span class="_ _15"></span>(<span class="_ _28"></span>exp(</div><div class="t md x1c h8a y11d ff5 fsc fc0 sc1 ls0 ws0">2</div><div class="t md xe9 h8a y11e ff5 fsc fc0 sc1 ls0 ws0">2</div><div class="t md xe9 h8a y11f ff5 fsc fc0 sc1 ls0 ws0">2</div><div class="t me xea h8b y11c ff13 fsd fc0 sc1 ls0 ws0">�</div><div class="t md x53 h8c y120 ff9 fsc fc0 sc1 ls0 ws0">j<span class="_ _29"></span>j<span class="_ _2a"></span>i<span class="_ _15"></span>i<span class="_ _2b"></span>ij</div><div class="t md x60 h8d y11c ff9 fsb fc0 sc1 ls0 ws0">y<span class="_ _2c"></span>x<span class="_ _2d"></span>y<span class="_ _2e"></span>x<span class="_ _2f"></span>w<span class="_ _30"> </span><span class="ff11">�<span class="_ _31"></span>�<span class="_ _32"></span>�</span></div></div><div class="t m0 xb0 ha y121 ff8 fs2 fc0 sc1 ls0 ws0"> <span class="ff7">（</span>4<span class="ff7">）</span></div><div class="t m0 x1 ha y122 ff7 fs2 fc0 sc1 ls0 ws0">其<span class="_ _a"></span>中</div><div class="c x52 y123 w24 h66"><div class="t mf xeb h6b yd3 ff5 fs3 fc0 sc1 ls0 ws0">)<span class="_ _18"></span>,<span class="_ _33"></span>(</div><div class="t mf xec h67 yd2 ff9 fs4 fc0 sc1 ls0 ws0">i<span class="_ _33"></span>i</div><div class="t mf xd4 h63 yd3 ff9 fs3 fc0 sc1 ls0 ws0">y<span class="_ _2e"></span>x</div></div><div class="t m0 xe3 ha y122 ff7 fs2 fc0 sc1 ls0 ws0">和</div><div class="c x73 y124 w1c h8e"><div class="t m10 xd2 h8f y125 ff5 fse fc0 sc1 ls0 ws0">)<span class="_ _16"></span>,<span class="_ _18"></span>(</div><div class="t m10 xed h90 y126 ff9 fsf fc0 sc1 ls0 ws0">j<span class="_ _29"></span>j</div><div class="t m10 xd8 h91 y125 ff9 fse fc0 sc1 ls0 ws0">y<span class="_ _2c"></span>x</div></div><div class="t m0 xee ha y122 ff7 fs2 fc0 sc1 ls0 ws0">为<span class="_ _a"></span>两<span class="_ _5"></span>超<span class="_ _5"></span>像<span class="_ _5"></span>素<span class="_ _5"></span>块<span class="_ _5"></span>的<span class="_ _a"></span>质<span class="_ _5"></span>心<span class="_ _5"></span>坐<span class="_ _5"></span>标<span class="_ _5"></span>，</div><div class="c xa4 y127 w14 h92"><div class="t m11 xc4 h93 yd2 ff13 fs10 fc0 sc1 ls0 ws0">�</div></div><div class="t m0 xef ha y122 ff7 fs2 fc0 sc1 ls0 ws0">为<span class="_ _a"></span>取<span class="_ _5"></span>值</div><div class="c x94 y128 w25 h64"><div class="t m12 xf0 h6b ycd ff5 fs9 fc0 sc1 ls0 ws0">]<span class="_ _34"></span>1<span class="_ _35"></span>,<span class="_ _34"></span>0<span class="_ _36"></span>[</div></div><div class="t m0 xf1 ha y122 ff7 fs2 fc0 sc1 ls0 ws0">的<span class="_ _a"></span>常<span class="_ _5"></span>数<span class="_ _5"></span>值<span class="_ _5"></span>，<span class="_ _5"></span>实<span class="_ _5"></span>验<span class="_ _a"></span>中<span class="_ _5"></span>取</div><div class="c x1 y129 w26 hc"><div class="t m13 xf2 h94 y59 ff13 fs11 fc0 sc1 ls0 ws0">�</div><div class="t m14 xf0 h6d y59 ff11 fs5 fc0 sc1 ls0 ws0">�<span class="_ _37"></span><span class="ff5">1<span class="_ _34"></span>.<span class="_ _34"></span>0</span></div></div><div class="t m0 x60 ha y12a ff7 fs2 fc0 sc1 ls0 ws0">能够获得较好的权值分布。</div><div class="t m1 x1 h9 y12b ff6 fs3 fc0 sc1 ls0 ws0">2 <span class="_ _24"> </span><span class="ff1 sc0">双<span class="_ _a"></span>分<span class="_ _1"></span>支<span class="_ _a"></span>多<span class="_ _1"></span>交<span class="_ _a"></span>互<span class="_ _a"></span>的<span class="_ _1"></span>深<span class="_ _a"></span>度<span class="_ _a"></span>图<span class="_ _1"></span>卷<span class="_ _a"></span>积<span class="_ _1"></span>网<span class="_ _a"></span>络<span class="_ _a"></span>构<span class="_ _1"></span>建</span></div><div class="t m1 x1 h5 y12c ff6 fs2 fc0 sc1 ls0 ws0">2.<span class="_ _1"></span>1<span class="_ _1"></span> <span class="_ _8"> </span><span class="ff1 sc0">图<span class="_ _1"></span>卷<span class="_ _1"></span>积<span class="_ _a"></span>神<span class="_ _a"></span>经<span class="_ _1"></span>网<span class="_ _a"></span>络</span></div><div class="t m0 x9 ha y12d ff7 fs2 fc0 sc1 ls0 ws0">图卷积网<span class="_ _1"></span>络可以分<span class="_ _1"></span>为基于频<span class="_ _1"></span>域和基于<span class="_ _1"></span>空域两种<span class="_ _1"></span>类型</div><div class="t m0 x1e hb y12e ff8 fs4 fc0 sc1 ls0 ws0">[16]</div><div class="t m0 x1f ha y12d ff7 fs2 fc0 sc1 ls0 ws0">。基于频<span class="_ _1"></span>域的方法<span class="_ _1"></span>通过引入<span class="_ _1"></span>滤波</div><div class="t m0 x1 ha y12f ff7 fs2 fc0 sc1 ls0 ws0">器，<span class="_ _1"></span>并利<span class="_ _1"></span>用图<span class="_ _1"></span>谱<span class="_ _1"></span>的理<span class="_ _1"></span>论来<span class="_ _1"></span>实<span class="_ _1"></span>现拓<span class="_ _1"></span>扑图<span class="_ _1"></span>上<span class="_ _1"></span>的卷<span class="_ _1"></span>积操<span class="_ _1"></span>作，<span class="_ _1"></span>从<span class="_ _1"></span>图信<span class="_ _1"></span>号处<span class="_ _1"></span>理<span class="_ _1"></span>的视<span class="_ _1"></span>角定<span class="_ _1"></span>义图<span class="_ _1"></span>卷<span class="_ _1"></span>积运<span class="_ _1"></span>算。</div><div class="t m0 x1 ha y130 ff7 fs2 fc0 sc1 ls0 ws0">而基于空域的图卷积通过定义一个聚合函数来聚合节点及它们的一阶邻域特征信息。<span class="_ _e"></span>在本文</div><div class="t m0 x1 ha y131 ff7 fs2 fc0 sc1 ls0 ws0">中，<span class="_ _b"></span>构建的指静脉权重图是一个非稀疏图。<span class="_ _b"></span>与基于空域的方法仅聚集一阶邻域信息和堆叠层</div><div class="t m0 x1 ha y132 ff7 fs2 fc0 sc1 ls0 ws0">数相比，基于频域的图卷积能够通过其卷积核的感受野扩张来捕获图中的更高阶信息。</div><div class="t m0 x9 ha y133 ff7 fs2 fc0 sc1 ls0 ws0">对<span class="_ _38"> </span>于<span class="_ _38"> </span>一<span class="_ _38"> </span>个<span class="_ _38"> </span>无<span class="_ _38"> </span>向<span class="_ _38"> </span>图</div><div class="c xf3 y5a w27 h95"><div class="t m0 x24 h10 y134 ffb fs2 fc0 sc1 ls0 ws0">𝐺</div></div><div class="c xf4 y5a w4 h95"><div class="t m0 x24 h10 y134 ffa fs2 fc0 sc1 ls0 ws0">=</div></div><div class="c xa7 y5a w5 h96"><div class="t m0 x24 h10 y135 ffa fs2 fc0 sc1 ls0 ws0">(</div></div><div class="c xae y5a w28 h96"><div class="t m0 x24 h10 y135 ffb fs2 fc0 sc1 ls0 ws0">𝑉</div></div><div class="c x9b y5a w29 h96"><div class="t m0 x24 h10 y135 ffa fs2 fc0 sc1 ls0 ws0">,</div></div><div class="c x78 y5a w2a h96"><div class="t m0 x24 h10 y135 ffb fs2 fc0 sc1 ls0 ws0">𝐸</div></div><div class="c xf5 y5a w29 h96"><div class="t m0 x24 h10 y135 ffa fs2 fc0 sc1 ls0 ws0">,</div></div><div class="c xb4 y5a w2b h96"><div class="t m0 x24 h10 y135 ffb fs2 fc0 sc1 ls0 ws0">𝐴</div></div><div class="c xb5 y5a w5 h96"><div class="t m0 x24 h10 y135 ffa fs2 fc0 sc1 ls0 ws0">)</div></div><div class="t m0 x9d h46 y136 ff12 fs2 fc0 sc1 ls0 ws0">，</div><div class="c xaa y5a w28 h95"><div class="t m0 x24 h10 y134 ffb fs2 fc0 sc1 ls0 ws0">𝑉</div></div><div class="c x26 y5a w4 h95"><div class="t m0 x24 h10 y134 ffa fs2 fc0 sc1 ls0 ws0">=</div></div><div class="c xdb y5a w7 h97"><div class="t m0 x24 h10 y137 ffa fs2 fc0 sc1 ls0 ws0">{</div></div><div class="c x8c y5a w2c h97"><div class="t m0 x24 h10 y137 ffb fs2 fc0 sc1 ls0 ws0">𝑣</div></div><div class="c xcd y5a w2d h98"><div class="t m2 x2f h24 y138 ffa fs6 fc0 sc1 ls0 ws0">1</div></div><div class="c xf6 y5a w29 h97"><div class="t m0 x24 h10 y137 ffa fs2 fc0 sc1 ls0 ws0">,</div></div><div class="c xa3 y5a w2c h97"><div class="t m0 x24 h10 y137 ffb fs2 fc0 sc1 ls0 ws0">𝑣</div></div><div class="c xf7 y5a w2d h98"><div class="t m2 x2f h24 y138 ffa fs6 fc0 sc1 ls0 ws0">2</div></div><div class="c x59 y5a w2e h97"><div class="t m0 x24 h10 y137 ffa fs2 fc0 sc1 ls0 ws0">,…,</div></div><div class="c x4a y5a w2c h97"><div class="t m0 x24 h10 y137 ffb fs2 fc0 sc1 ls0 ws0">𝑣</div></div><div class="c x4b y5a w2f h98"><div class="t m2 x2f h24 y138 ffb fs6 fc0 sc1 ls0 ws0">𝑁</div></div><div class="c xf8 y5a w7 h97"><div class="t m0 x24 h10 y137 ffa fs2 fc0 sc1 ls0 ws0">}</div></div><div class="t m0 xa6 ha y133 ff7 fs2 fc0 sc1 ls0 ws0">是</div><div class="c xf9 y139 w2 hc"><div class="t m0 x21 hd y59 ff9 fs5 fc0 sc1 ls0 ws0">N</div></div><div class="t m0 xfa ha y133 ff7 fs2 fc0 sc1 ls0 ws0">个<span class="_ _38"> </span>节<span class="_ _38"> </span>点<span class="_ _38"> </span>的<span class="_ _38"> </span>集<span class="_ _38"> </span>合<span class="_ _38"> </span>，</div><div class="c x1 y13a w30 h66"><div class="t m15 xfb h6b yd3 ff5 fs3 fc0 sc1 ls0 ws0">}<span class="_ _39"></span>,...,<span class="_ _3a"></span>,<span class="_ _3b"></span>{</div><div class="t m15 xcf h6c yd2 ff5 fs4 fc0 sc1 ls0 ws0">2<span class="_ _3c"></span>1<span class="_ _3d"> </span><span class="ff9">m</span></div><div class="t m15 xfc h65 yd3 ff9 fs3 fc0 sc1 ls0 ws0">e<span class="_ _21"></span>e<span class="_ _27"></span>e<span class="_ _3e"></span>E<span class="_ _24"> </span><span class="ff11">�</span></div></div><div class="t m0 x3e ha y13b ff7 fs2 fc0 sc1 ls0 ws0">为</div><div class="t m3 xfd h59 y13b ffe fs7 fc0 sc1 ls0 ws0">m</div><div class="t m0 x3f ha y13b ff7 fs2 fc0 sc1 ls0 ws0">条边<span class="_ _1"></span>的集<span class="_ _1"></span>合，</div><div class="c x3 y13c w31 h8e"><div class="t m16 xfe h90 y13d ff9 fsf fc0 sc1 ls0 ws0">d<span class="_ _3f"></span>N</div><div class="t m16 xff h90 y13e ff9 fsf fc0 sc1 ls0 ws0">N</div><div class="t m16 x100 h91 yd3 ff9 fse fc0 sc1 ls0 ws0">R<span class="_ _40"></span>x<span class="_ _41"></span>x<span class="_ _42"></span>x<span class="_ _21"></span>X</div><div class="t m16 xc5 h99 y13d ff11 fsf fc0 sc1 ls0 ws0">�</div><div class="t m16 x101 h9a yd3 ff11 fse fc0 sc1 ls0 ws0">�<span class="_ _43"></span>�<span class="_ _44"> </span><span class="ff5">}<span class="_ _28"></span>,...,<span class="_ _45"></span>,<span class="_ _29"></span>{</span></div><div class="t m16 x102 h9b y13e ff5 fsf fc0 sc1 ls0 ws0">2<span class="_ _27"></span>1</div></div><div class="t m0 x95 ha y13b ff7 fs2 fc0 sc1 ls0 ws0">为节<span class="_ _1"></span>点特<span class="_ _1"></span>征矩<span class="_ _1"></span>阵，</div><div class="c x1a y13f w32 hc"><div class="t m17 xc4 hd y59 ff9 fs5 fc0 sc1 ls0 ws0">d</div></div><div class="t m0 x5e ha y13b ff7 fs2 fc0 sc1 ls0 ws0">为每</div><div class="t m0 x1 ha y140 ff7 fs2 fc0 sc1 ls0 ws0">个节点的特征维数，</div><div class="c x4 y141 w33 h66"><div class="t m18 x103 h67 ydf ff9 fs4 fc0 sc1 ls0 ws0">N<span class="_ _17"></span>N</div><div class="t m18 x21 h63 ycd ff9 fs3 fc0 sc1 ls0 ws0">A</div><div class="t m18 x102 h9c ydf ff11 fs4 fc0 sc1 ls0 ws0">�</div><div class="t m18 xd0 h65 ycd ff11 fs3 fc0 sc1 ls0 ws0">�<span class="_ _46"> </span><span class="ff5">}<span class="_ _36"></span>1<span class="_ _35"></span>,<span class="_ _34"></span>0<span class="_ _47"></span>{</span></div></div><div class="t m0 xaf ha y140 ff7 fs2 fc0 sc1 ls0 ws0">为大小为</div><div class="c xaa y142 w34 hc"><div class="t m19 xd8 h6d y59 ff9 fs5 fc0 sc1 ls0 ws0">N<span class="_ _48"></span>N<span class="_"> </span><span class="ff11">�</span></div></div><div class="t m0 xf6 ha y140 ff7 fs2 fc0 sc1 ls0 ws0">的邻接矩阵，</div><div class="c xf9 y143 w35 h62"><div class="t m0 x21 h63 yeb ff9 fs8 fc0 sc1 ls0 ws0">D</div></div><div class="t m0 xfa ha y140 ff7 fs2 fc0 sc1 ls0 ws0">为</div><div class="c x104 y143 w14 h62"><div class="t m4 x21 h63 yeb ff9 fs8 fc0 sc1 ls0 ws0">A</div></div><div class="t m0 x36 ha y140 ff7 fs2 fc0 sc1 ls0 ws0">的对角度矩阵。</div><div class="c x9d y144 w36 h88"><div class="t m1a xd3 h8c y145 ff9 fsc fc0 sc1 ls0 ws0">n</div><div class="t m1a x105 h8d y120 ff9 fsb fc0 sc1 ls0 ws0">I<span class="_ _49"></span>A<span class="_ _48"></span>A<span class="_ _4a"> </span><span class="ff11">�<span class="_ _4b"></span>�</span></div><div class="t m1a xbd h8a y146 ff5 fsc fc0 sc1 ls0 ws0">~</div></div><div class="t m0 x106 h46 y147 ffd fs2 fc0 sc1 ls0 ws0"> </div><div class="t m0 x1 h46 y148 ff12 fs2 fc0 sc1 ls0 ws0">为添加自连接的邻接矩阵，</div><div class="c xf3 y149 w35 h66"><div class="t m1b x107 h67 yd2 ff9 fs4 fc0 sc1 ls0 ws0">n</div><div class="t m1b x21 h63 yd3 ff9 fs3 fc0 sc1 ls0 ws0">I</div></div><div class="t m0 x108 h46 y148 ff12 fs2 fc0 sc1 ls0 ws0">为<span class="_ _2"> </span><span class="ffd">n<span class="_"> </span></span>阶单位矩阵，</div><div class="c x9d y14a w37 h88"><div class="t m1c x102 h8c y145 ff9 fsc fc0 sc1 ls0 ws0">n</div><div class="t m1c x109 h8d y120 ff9 fsb fc0 sc1 ls0 ws0">I<span class="_ _4c"></span>D<span class="_ _1c"></span>D<span class="_ _14"> </span><span class="ff11">�<span class="_ _4d"></span>�</span></div><div class="t m1c x2f h8a y146 ff5 fsc fc0 sc1 ls0 ws0">~</div></div><div class="t m0 x1 h46 y14b ff12 fs2 fc0 sc1 ls0 ws0">节点标签表示为一组<span class="_ _2"> </span><span class="ffd">one-hot<span class="_"> </span></span>向量。</div><div class="t m0 x9 ha y14c ff8 fs2 fc0 sc1 ls0 ws0">Kipf<span class="_ _2"> </span><span class="ff7">等提出用于半监督节点分类的<span class="_ _2"> </span></span>GCN<span class="ff7">，<span class="_ _c"></span>只考虑一阶邻居，<span class="_ _4e"></span><span class="ff8">GCN<span class="_ _2"> </span><span class="ff7">的特征提取过程可表示</span></span></span></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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