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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/62679de44f8811599ef02315/bg1.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">第三章 图像数字水印的方案</div><div class="t m0 x2 h4 y3 ff2 fs1 fc0 sc1 ls0 ws0">3.1 <span class="ff1 sc0">图像数字水印的技术方案</span></div><div class="t m0 x3 h5 y4 ff1 fs2 fc0 sc1 ls0 ws0">在数<span class="_ _0"></span>据库<span class="_ _0"></span>中存<span class="_ _0"></span>储在<span class="_ _0"></span>国际<span class="_ _0"></span>互联<span class="_ _0"></span>网上<span class="_ _0"></span>传输<span class="_ _0"></span>的水<span class="_ _0"></span>印图<span class="_ _0"></span>像一<span class="_ _0"></span>般会<span class="_ _0"></span>被压<span class="_ _0"></span>缩，<span class="_ _0"></span>有时<span class="_ _0"></span>达到<span class="_ _0"></span>很高<span class="_ _0"></span>的</div><div class="t m0 x2 h5 y5 ff1 fs2 fc0 sc1 ls0 ws0">压<span class="_ _1"> </span>缩<span class="_ _1"> </span>比<span class="_ _1"> </span>。<span class="_ _1"> </span>因<span class="_ _1"> </span>此<span class="_ _2"> </span>，<span class="_ _1"> </span>数<span class="_ _2"> </span>字<span class="_ _1"> </span>水<span class="_ _1"> </span>印<span class="_ _1"> </span>算<span class="_ _1"> </span>法<span class="_ _1"> </span>所<span class="_ _2"> </span>面<span class="_ _1"> </span>临<span class="_ _1"> </span>的<span class="_ _1"> </span>第<span class="_ _1"> </span>一<span class="_ _1"> </span>个<span class="_ _2"> </span>考<span class="_ _1"> </span>验<span class="_ _1"> </span>就<span class="_ _1"> </span>是<span class="_ _1"> </span>压<span class="_ _1"> </span>缩<span class="_ _2"> </span>。<span class="_"> </span><span class="ff3">JPEG<span class="_ _3"> </span></span>和</div><div class="t m0 x2 h5 y6 ff3 fs2 fc0 sc1 ls0 ws0">EZW<span class="_ _0"></span><span class="ff1">（<span class="_ _0"></span></span>Embedded<span class="_ _0"></span> <span class="_ _0"></span>Zero-T<span class="_ _4"></span>ree W<span class="_ _4"></span>a<span class="_ _4"></span>velet<span class="_ _5"></span><span class="ff1">）<span class="_ _0"></span>压<span class="_ _0"></span>缩<span class="_ _0"></span>是<span class="_ _0"></span>最<span class="_ _0"></span>常<span class="_ _5"></span>见的<span class="_ _5"></span>两种<span class="_ _0"></span>压<span class="_ _0"></span>缩<span class="_ _5"></span>方法<span class="_ _0"></span>。<span class="_ _6"></span></span>JPEG<span class="_"> </span><span class="ff1">是基<span class="_ _5"></span>于离</span></div><div class="t m0 x2 h5 y7 ff1 fs2 fc0 sc1 ls0 ws0">散<span class="_ _0"></span>余<span class="_ _0"></span>弦<span class="_ _0"></span>变<span class="_ _0"></span>换<span class="_ _0"></span>域<span class="_ _0"></span>的<span class="_ _0"></span>压<span class="_ _0"></span>缩<span class="_ _0"></span>方<span class="_ _0"></span>法<span class="_ _0"></span>，<span class="_ _0"></span>而<span class="_ _1"> </span><span class="ff3">EZW<span class="_"> </span></span>是基<span class="_ _0"></span>于<span class="_ _0"></span>小<span class="_ _0"></span>波<span class="_ _0"></span>变<span class="_ _0"></span>换<span class="_ _0"></span>域<span class="_ _0"></span>的<span class="_ _0"></span>压<span class="_ _0"></span>缩<span class="_ _0"></span>方<span class="_ _0"></span>法<span class="_ _0"></span>。<span class="_ _0"></span>前<span class="_ _0"></span>人<span class="_ _0"></span>的<span class="_ _0"></span>研<span class="_ _0"></span>究<span class="_ _5"></span>证明</div><div class="t m0 x2 h5 y8 ff1 fs2 fc0 sc1 ls0 ws0">采用<span class="_ _0"></span>与压<span class="_ _0"></span>缩算<span class="_ _0"></span>法相<span class="_ _0"></span>同的<span class="_ _0"></span>变换<span class="_ _0"></span>域水<span class="_ _0"></span>印方<span class="_ _0"></span>法，<span class="_ _0"></span>对于<span class="_ _0"></span>压缩<span class="_ _0"></span>的稳<span class="_ _0"></span>健性<span class="_ _0"></span>较强<span class="_ _0"></span>。因<span class="_ _0"></span>此，<span class="_ _0"></span>我研<span class="_ _0"></span>究图<span class="_ _0"></span>像</div><div class="t m0 x2 h5 y9 ff1 fs2 fc0 sc1 ls0 ws0">文件水印算法主要集中在变换域算法及利用人眼视觉特性上。</div><div class="t m0 x3 h5 ya ff1 fs2 fc0 sc1 ls0 ws0">数字<span class="_ _0"></span>水印<span class="_ _0"></span>的嵌<span class="_ _0"></span>入要<span class="_ _0"></span>求即<span class="_ _0"></span>要考<span class="_ _0"></span>虑视<span class="_ _0"></span>觉透<span class="_ _0"></span>明性<span class="_ _0"></span>，又<span class="_ _0"></span>要保<span class="_ _0"></span>证嵌<span class="_ _0"></span>入水<span class="_ _0"></span>印后<span class="_ _0"></span>图像<span class="_ _0"></span>的稳<span class="_ _0"></span>健性<span class="_ _0"></span>，</div><div class="t m0 x2 h5 yb ff1 fs2 fc0 sc1 ls0 ws0">这两<span class="_ _0"></span>个方<span class="_ _0"></span>面存<span class="_ _0"></span>在着<span class="_ _0"></span>矛盾<span class="_ _0"></span>。保<span class="_ _0"></span>证视<span class="_ _0"></span>觉透<span class="_ _0"></span>明性<span class="_ _0"></span>，就<span class="_ _0"></span>要将<span class="_ _0"></span>水印<span class="_ _0"></span>嵌入<span class="_ _0"></span>到人<span class="_ _0"></span>眼不<span class="_ _0"></span>敏感<span class="_ _0"></span>区，<span class="_ _0"></span>也就<span class="_ _0"></span>是</div><div class="t m0 x2 h5 yc ff1 fs2 fc0 sc1 ls0 ws0">嵌入<span class="_ _0"></span>到图<span class="_ _0"></span>像的<span class="_ _0"></span>高频<span class="_ _0"></span>分量<span class="_ _0"></span>中。<span class="_ _0"></span>而多<span class="_ _0"></span>数图<span class="_ _0"></span>像处<span class="_ _0"></span>理方<span class="_ _0"></span>法对<span class="_ _0"></span>于图<span class="_ _0"></span>像高<span class="_ _0"></span>频部<span class="_ _0"></span>分的<span class="_ _0"></span>损坏<span class="_ _0"></span>程度<span class="_ _0"></span>较高<span class="_ _0"></span>，</div><div class="t m0 x2 h5 yd ff1 fs2 fc0 sc1 ls0 ws0">如有<span class="_ _0"></span>损压<span class="_ _0"></span>缩、<span class="_ _0"></span>高频<span class="_ _0"></span>滤波<span class="_ _0"></span>等。<span class="_ _0"></span>水印<span class="_ _0"></span>很容<span class="_ _0"></span>易在<span class="_ _0"></span>经历<span class="_ _0"></span>图像<span class="_ _0"></span>处理<span class="_ _0"></span>的过<span class="_ _0"></span>程中<span class="_ _0"></span>丢失<span class="_ _0"></span>。这<span class="_ _0"></span>样，<span class="_ _0"></span>则无<span class="_ _0"></span>法</div><div class="t m0 x2 h5 ye ff1 fs2 fc0 sc1 ls0 ws0">保证<span class="_ _0"></span>图像<span class="_ _0"></span>数字<span class="_ _0"></span>水印<span class="_ _0"></span>的稳<span class="_ _0"></span>健性<span class="_ _0"></span>。如<span class="_ _0"></span>果要<span class="_ _0"></span>获得<span class="_ _0"></span>很好<span class="_ _0"></span>的稳<span class="_ _0"></span>健性<span class="_ _0"></span>，数<span class="_ _0"></span>字水<span class="_ _0"></span>印应<span class="_ _0"></span>加在<span class="_ _0"></span>人眼<span class="_ _0"></span>敏感<span class="_ _0"></span>的</div><div class="t m0 x2 h5 yf ff1 fs2 fc0 sc1 ls0 ws0">低频<span class="_ _0"></span>部分<span class="_ _0"></span>，图<span class="_ _0"></span>像的<span class="_ _0"></span>大部<span class="_ _0"></span>分能<span class="_ _0"></span>量集<span class="_ _0"></span>中在<span class="_ _0"></span>低频<span class="_ _0"></span>部分<span class="_ _0"></span>，如<span class="_ _0"></span>果对<span class="_ _0"></span>于低<span class="_ _0"></span>频部<span class="_ _0"></span>分进<span class="_ _0"></span>行处<span class="_ _0"></span>理，<span class="_ _0"></span>水印<span class="_ _0"></span>固</div><div class="t m0 x2 h5 y10 ff1 fs2 fc0 sc1 ls0 ws0">然会<span class="_ _0"></span>失去<span class="_ _0"></span>，而<span class="_ _0"></span>图像<span class="_ _0"></span>也没<span class="_ _0"></span>有了<span class="_ _0"></span>利用<span class="_ _0"></span>价值<span class="_ _0"></span>，然<span class="_ _0"></span>而，<span class="_ _0"></span>水印<span class="_ _0"></span>的嵌<span class="_ _0"></span>入会<span class="_ _0"></span>对图<span class="_ _0"></span>像的<span class="_ _0"></span>质量<span class="_ _0"></span>有非<span class="_ _0"></span>常大<span class="_ _0"></span>的</div><div class="t m0 x2 h5 y11 ff1 fs2 fc0 sc1 ls0 ws0">影响，这又无法保证视觉透明性。</div><div class="t m0 x3 h5 y12 ff1 fs2 fc0 sc1 ls0 ws0">数字<span class="_ _0"></span>水印<span class="_ _0"></span>算法<span class="_ _0"></span>的实<span class="_ _0"></span>现基<span class="_ _0"></span>本分<span class="_ _0"></span>为三<span class="_ _0"></span>个部<span class="_ _0"></span>分：<span class="_ _0"></span>宿主<span class="_ _0"></span>图像<span class="_ _0"></span>的变<span class="_ _0"></span>换，<span class="_ _0"></span>水印<span class="_ _0"></span>的嵌<span class="_ _0"></span>入和<span class="_ _0"></span>水印<span class="_ _0"></span>的</div><div class="t m0 x2 h5 y13 ff1 fs2 fc0 sc1 ls0 ws0">检测，分别描述如下。</div><div class="t m0 x4 h4 y14 ff2 fs1 fc0 sc1 ls0 ws0">3.2 <span class="ff1 sc0">基于<span class="_ _2"> </span></span>DCT<span class="_ _2"> </span><span class="ff1 sc0">域的图像数字水印技术</span></div><div class="t m0 x5 h5 y15 ff1 fs2 fc0 sc1 ls0 ws0">离散余<span class="_ _0"></span>弦变换<span class="_ _0"></span>（<span class="ff3">Discrete Co<span class="_ _0"></span>sine T<span class="_ _4"></span>ransform<span class="ff1">）<span class="_ _0"></span>属于正<span class="_ _0"></span>交变换<span class="_ _0"></span>图像编<span class="_ _0"></span>码方法<span class="_ _0"></span>中的一<span class="_ _0"></span>种<span class="_ _0"></span>。</span></span></div><div class="t m0 x2 h5 y16 ff1 fs2 fc0 sc1 ls0 ws0">正交<span class="_ _0"></span>变换<span class="_ _0"></span>图像<span class="_ _0"></span>编码<span class="_ _0"></span>始于<span class="_ _1"> </span><span class="ff3">1968<span class="_ _2"> </span></span>年。当<span class="_ _0"></span>时安<span class="_ _0"></span>德鲁<span class="_ _0"></span>斯（<span class="_ _5"></span><span class="ff3">Andrews</span>）等<span class="_ _0"></span>人发<span class="_ _0"></span>现大<span class="_ _0"></span>多数<span class="_ _0"></span>自然<span class="_ _0"></span>图像</div><div class="t m0 x2 h5 y17 ff1 fs2 fc0 sc1 ls0 ws0">的高<span class="_ _0"></span>频分<span class="_ _0"></span>量相<span class="_ _0"></span>对幅<span class="_ _0"></span>度较<span class="_ _0"></span>低，<span class="_ _0"></span>可完<span class="_ _0"></span>全舍<span class="_ _0"></span>弃或<span class="_ _0"></span>者只<span class="_ _0"></span>用少<span class="_ _0"></span>数码<span class="_ _0"></span>字编<span class="_ _0"></span>码，<span class="_ _0"></span>提出<span class="_ _0"></span>不对<span class="_ _0"></span>图像<span class="_ _0"></span>本身<span class="_ _0"></span>编</div><div class="t m0 x2 h5 y18 ff1 fs2 fc0 sc1 ls0 ws0">码，只<span class="_ _0"></span>对其二<span class="_ _0"></span>维傅立<span class="_ _0"></span>叶（<span class="_ _0"></span><span class="ff3">DFT</span>）<span class="_ _0"></span>系数进<span class="_ _0"></span>行编码<span class="_ _0"></span>和传输<span class="_ _0"></span>。但<span class="_ _2"> </span><span class="ff3">DFT<span class="_"> </span></span>是一种正交变<span class="_ _0"></span>换，运<span class="_ _0"></span>算</div><div class="t m0 x2 h5 y19 ff1 fs2 fc0 sc1 ls0 ws0">量<span class="_ _0"></span>很<span class="_ _0"></span>大<span class="_ _0"></span>，<span class="_ _0"></span>常<span class="_ _0"></span>常<span class="_ _0"></span>使<span class="_ _0"></span>实<span class="_ _0"></span>时<span class="_ _0"></span>处<span class="_ _0"></span>理<span class="_ _0"></span>发<span class="_ _0"></span>生<span class="_ _0"></span>困<span class="_ _0"></span>难<span class="_ _0"></span>，<span class="_ _0"></span>第<span class="_ _0"></span>二<span class="_ _0"></span>年<span class="_ _0"></span>他<span class="_ _0"></span>们<span class="_ _0"></span>就<span class="_ _0"></span>用<span class="_ _7"> </span><span class="ff3">W<span class="_ _8"></span>alsh-Hadamard<span class="_"> </span><span class="ff1">变换<span class="_ _0"></span>（<span class="_ _0"></span></span>WHT<span class="_ _5"></span><span class="ff1">）</span></span></div><div class="t m0 x2 h5 y1a ff1 fs2 fc0 sc1 ls0 ws0">取代<span class="_ _2"> </span><span class="ff3">DFT<span class="_ _2"> </span></span>可以<span class="_ _0"></span>使运<span class="_ _0"></span>算量<span class="_ _0"></span>明显<span class="_ _0"></span>减少<span class="_ _0"></span>，这<span class="_ _0"></span>是因<span class="_ _0"></span>为<span class="_ _1"> </span><span class="ff3">WHT<span class="_"> </span></span>变换只<span class="_ _0"></span>有加<span class="_ _0"></span>减法<span class="_ _0"></span>而无<span class="_ _0"></span>需乘<span class="_ _0"></span>法。<span class="_ _0"></span>但是</div><div class="t m0 x2 h5 y1b ff1 fs2 fc0 sc1 ls0 ws0">更有<span class="_ _0"></span>意义<span class="_ _0"></span>的是<span class="_ _0"></span>离散<span class="_ _0"></span>余弦<span class="_ _0"></span>变换<span class="_ _0"></span>和离<span class="_ _0"></span>散正<span class="_ _0"></span>旋变<span class="_ _0"></span>换的<span class="_ _0"></span>出现<span class="_ _0"></span>，它<span class="_ _0"></span>们具<span class="_ _0"></span>有快<span class="_ _0"></span>速算<span class="_ _0"></span>法，<span class="_ _0"></span>精确<span class="_ _0"></span>度高<span class="_ _0"></span>。</div><div class="t m0 x2 h5 y1c ff1 fs2 fc0 sc1 ls0 ws0">其<span class="_ _0"></span>中<span class="_ _0"></span>最<span class="_ _0"></span>重<span class="_ _0"></span>要<span class="_ _0"></span>的<span class="_ _0"></span>是<span class="_ _2"> </span><span class="ff3">1974<span class="_"> </span></span>年提<span class="_ _0"></span>出<span class="_ _0"></span>的<span class="_ _2"> </span><span class="ff3">DCT<span class="_ _0"></span></span>，<span class="_ _0"></span>因<span class="_ _5"></span>为其<span class="_ _0"></span>变<span class="_ _0"></span>换<span class="_ _0"></span>矩<span class="_ _0"></span>阵<span class="_ _0"></span>的<span class="_ _0"></span>基<span class="_ _0"></span>向<span class="_ _0"></span>量<span class="_ _0"></span>很<span class="_ _0"></span>近<span class="_ _0"></span>似<span class="_ _0"></span>于<span class="_ _0"></span>托<span class="_ _0"></span>伯<span class="_ _0"></span>利<span class="_ _0"></span>兹<span class="_ _0"></span>矩</div><div class="t m0 x2 h5 y1d ff1 fs2 fc0 sc1 ls0 ws0">阵的<span class="_ _0"></span>特征<span class="_ _0"></span>向量<span class="_ _0"></span>，而<span class="_ _0"></span>托伯<span class="_ _0"></span>利兹<span class="_ _0"></span>矩阵<span class="_ _0"></span>又体<span class="_ _0"></span>现了<span class="_ _0"></span>人类<span class="_ _0"></span>语<span class="_ _0"></span><span class="ff4">言</span>及<span class="_ _0"></span>图像<span class="_ _0"></span><span class="ff4">信号<span class="_ _0"></span></span>的相<span class="_ _0"></span><span class="ff4">关</span>性<span class="_ _0"></span>。因<span class="_ _0"></span>此，<span class="_ _5"></span><span class="ff3">DCT</span></div><div class="t m0 x2 h5 y1e ff1 fs2 fc0 sc1 ls0 ws0">常常被<span class="ff4">认</span>为是语<span class="ff4">音</span>与图像<span class="ff4">信号</span>变换的<span class="ff4">准</span>最<span class="ff4">佳</span>变换。</div><div class="t m0 x5 h5 y1f ff1 fs2 fc0 sc1 ls0 ws0">图像是二维的，所以在研究时主要用到二维<span class="_ _1"> </span><span class="ff3">DCT</span>，以及二维<span class="_ _2"> </span><span class="ff3">IDCT<span class="_ _9"> </span><span class="ff4">来</span></span>对图像进行</div><div class="t m0 x2 h5 y20 ff1 fs2 fc0 sc1 ls0 ws0">处理。</div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
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<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62679de44f8811599ef02315/bg2.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x4 h4 y21 ff2 fs1 fc0 sc1 ls0 ws0">3.2.1 <span class="ff1 sc0">离散余弦变换（</span>DCT<span class="ff1 sc0">）的<span class="ff4">定</span>义</span></div><div class="t m0 x5 h5 y22 ff1 fs2 fc0 sc1 ls0 ws0">数字图像<span class="_ _9"> </span><span class="ff3">X</span>（<span class="_ _0"></span><span class="ff3">m,n</span>）是具有<span class="_ _9"> </span><span class="ff3">M<span class="_ _9"> </span></span>行<span class="_ _9"> </span><span class="ff3">N<span class="_ _9"> </span><span class="ff4">列</span></span>的<span class="_ _0"></span>一个矩阵。为<span class="_ _0"></span>了同时减<span class="_ _0"></span><span class="ff4">弱</span>或去<span class="ff4">除</span>图像<span class="_ _0"></span>数据</div><div class="t m0 x2 h5 y23 ff1 fs2 fc0 sc1 ls0 ws0">相<span class="ff4">关</span>性，可以运用二维<span class="_ _9"> </span><span class="ff3">DCT</span>，将图像<span class="ff4">从空间</span>域<span class="ff4">转</span>换到<span class="_ _9"> </span><span class="ff3">DCT<span class="_ _9"> </span></span>变换域。</div><div class="t m0 x2 h5 y24 ff4 fs2 fc0 sc1 ls0 ws0">根<span class="ff1">据</span>定<span class="ff1">义，二维离散余弦变换（<span class="ff3">DCT</span>）</span>定<span class="ff1">义如下：</span></div><div class="t m0 x6 h5 y25 ff4 fs2 fc0 sc1 ls0 ws0">式<span class="ff1">中：<span class="ff3">m</span>，<span class="ff3">k=0,1,…,M-1; n</span>，<span class="_ _a"> </span><span class="ff3"> <span class="_ _b"> </span>=0,1,…,N-1</span>。</span></div><div class="t m0 x7 h6 y26 ff3 fs2 fc0 sc1 ls0 ws0"> </div><div class="t m0 x2 h5 y27 ff1 fs2 fc0 sc1 ls0 ws0">二维<span class="ff4">逆</span>离散余弦变换（<span class="ff3">IDCT</span>）的<span class="ff4">定</span>义如下：</div><div class="t m0 x2 h5 y28 ff4 fs2 fc0 sc1 ls0 ws0">式<span class="ff1">中：<span class="ff3">m</span>，<span class="ff3">k=0,1,…,M-1; n</span>，<span class="_ _b"> </span><span class="ff3">=0,1,…N-1</span>。</span></div><div class="t m0 x2 h4 y29 ff2 fs1 fc0 sc1 ls0 ws0">3.2.2 <span class="ff1 sc0">离散余弦变换的特<span class="ff4">点</span></span></div><div class="t m0 x3 h5 y2a ff1 fs2 fc0 sc1 ls0 ws0">在基<span class="_ _0"></span>于<span class="_ _9"> </span><span class="ff3">DCT<span class="_"> </span></span>的变换编<span class="_ _0"></span>码中<span class="_ _0"></span>，图<span class="_ _0"></span>像是<span class="_ _0"></span><span class="ff4">先<span class="_ _0"></span></span>经分<span class="_ _0"></span><span class="ff4">块</span>（<span class="_ _0"></span><span class="ff3">8×8<span class="_ _9"> </span></span>或<span class="_ _2"> </span><span class="ff3">16×16</span>）<span class="_ _0"></span>后<span class="ff4">再<span class="_ _0"></span></span>经<span class="_ _9"> </span><span class="ff3">DCT<span class="_ _0"></span></span>，这<span class="_ _0"></span>种</div><div class="t m0 x2 h5 y2b ff1 fs2 fc0 sc1 ls0 ws0">变换<span class="_ _0"></span>是<span class="ff4">局<span class="_ _0"></span></span>部的<span class="_ _0"></span>，只<span class="_ _0"></span><span class="ff4">反<span class="_ _0"></span>映</span>了<span class="_ _0"></span>图像<span class="_ _0"></span><span class="ff4">某</span>一<span class="_ _0"></span>部分<span class="_ _0"></span>的<span class="ff4">信<span class="_ _0"></span>息</span>。<span class="_ _0"></span>当然<span class="_ _0"></span>也可<span class="_ _0"></span>以对<span class="_ _0"></span><span class="ff4">整</span>幅<span class="_ _0"></span>图像<span class="_ _0"></span>的特<span class="_ _0"></span><span class="ff4">点<span class="_ _0"></span></span>，但<span class="_ _0"></span>是</div><div class="t m0 x2 h5 y2c ff1 fs2 fc0 sc1 ls0 ws0">运算速度比分<span class="ff4">块<span class="_ _9"> </span><span class="ff3">DCT<span class="_ _9"> </span></span></span>要<span class="ff4">慢</span>。图像经<span class="_ _9"> </span><span class="ff3">DCT<span class="_ _9"> </span></span>后，得到的<span class="_ _9"> </span><span class="ff3">DCT<span class="_ _c"> </span></span>图像有三个特<span class="ff4">点</span>：</div><div class="t m0 x3 h5 y2d ff1 fs2 fc0 sc1 ls0 ws0">一是<span class="_ _0"></span>系<span class="_ _0"></span>数值<span class="_ _0"></span>全<span class="_ _0"></span>部集<span class="_ _0"></span>中<span class="_ _0"></span>到<span class="_ _9"> </span><span class="ff3">0<span class="_"> </span></span>值<span class="ff4">附<span class="_ _0"></span></span>近<span class="_ _0"></span>（<span class="ff4">从<span class="_ _0"></span>直<span class="_ _0"></span></span>方图<span class="_ _0"></span><span class="ff4">统<span class="_ _0"></span>计<span class="_ _0"></span></span>的意<span class="_ _0"></span>义<span class="_ _0"></span>上）<span class="_ _0"></span>，<span class="_ _0"></span><span class="ff4">动态<span class="_ _0"></span>范<span class="_ _0"></span>围<span class="_ _0"></span></span>很小<span class="_ _0"></span>，<span class="_ _0"></span>这</div><div class="t m0 x2 h5 y2e ff4 fs2 fc0 sc1 ls0 ws0">说<span class="ff1">明用较小的量</span>化<span class="ff1">比特数即可</span>表示<span class="_ _c"> </span><span class="ff3">DCT<span class="_ _9"> </span><span class="ff1">系数</span></span>；</div><div class="t m0 x3 h5 y2f ff1 fs2 fc0 sc1 ls0 ws0">二<span class="_ _0"></span>是<span class="_ _9"> </span><span class="ff3">DCT<span class="_"> </span></span>变换<span class="_ _0"></span>后<span class="_ _0"></span>图<span class="_ _0"></span>像<span class="_ _0"></span>能<span class="_ _0"></span>量集<span class="_ _0"></span>中<span class="_ _0"></span>在<span class="_ _0"></span>图<span class="_ _0"></span>像<span class="_ _0"></span>的低<span class="_ _0"></span>频<span class="_ _0"></span>部<span class="_ _0"></span>分<span class="_ _0"></span>，<span class="_ _0"></span>即<span class="_ _2"> </span><span class="ff3">DCT<span class="_"> </span></span>图像<span class="_ _0"></span>中<span class="_ _0"></span>不<span class="_ _0"></span>为<span class="_ _0"></span><span class="ff4">零<span class="_ _0"></span></span>的<span class="_ _0"></span>系<span class="_ _0"></span>数</div><div class="t m0 x2 h5 y30 ff1 fs2 fc0 sc1 ls0 ws0">大部分集中在一<span class="ff4">起</span>（<span class="ff4">左</span>上<span class="ff4">角</span>），因此编码<span class="ff4">效率</span>很高。</div><div class="t m0 x3 h5 y31 ff1 fs2 fc0 sc1 ls0 ws0">三是<span class="_ _0"></span>没有<span class="_ _0"></span>保<span class="ff4">留<span class="_ _0"></span>原</span>图<span class="_ _0"></span>像<span class="_ _0"></span><span class="ff4">块</span>的<span class="_ _0"></span>精<span class="ff4">细<span class="_ _0"></span>结构<span class="_ _0"></span></span>，<span class="ff4">从<span class="_ _0"></span></span>中<span class="ff4">反<span class="_ _0"></span>映</span>不<span class="_ _0"></span>了<span class="ff4">原<span class="_ _0"></span></span>图像<span class="_ _0"></span><span class="ff4">块</span>的<span class="_ _0"></span><span class="ff4">边缘<span class="_ _0"></span></span>、<span class="ff4">轮<span class="_ _0"></span>廓<span class="_ _0"></span></span>等<span class="ff4">信<span class="_ _0"></span>息<span class="_ _5"></span></span>，</div><div class="t m0 x2 h5 y32 ff1 fs2 fc0 sc1 ls0 ws0">这一特<span class="ff4">点</span>是<span class="ff4">由<span class="_ _c"> </span><span class="ff3">DCT<span class="_ _9"> </span></span>缺乏</span>时<span class="ff4">局</span>域性<span class="ff4">造成</span>的。</div><div class="t m0 x3 h5 y33 ff1 fs2 fc0 sc1 ls0 ws0">如下<span class="_ _0"></span><span class="ff4">左</span>图<span class="_ _2"> </span><span class="ff3">3<span class="ff5">—</span>1<span class="_"> </span></span>是<span class="ff4">原</span>始<span class="_ _0"></span>图像<span class="_ _0"></span>经过<span class="_ _1"> </span><span class="ff3">DCT<span class="_ _9"> </span></span>变<span class="_ _0"></span>换后<span class="_ _0"></span>的系<span class="_ _0"></span>数图<span class="_ _0"></span>像为<span class="_ _0"></span>图<span class="_ _1"> </span><span class="ff3">3<span class="ff5">—</span>2</span>。<span class="_ _0"></span>两<span class="ff4">条<span class="_ _0"></span>线划<span class="_ _0"></span></span>分出</div><div class="t m0 x2 h5 y34 ff1 fs2 fc0 sc1 ls0 ws0">图像的低频、中频和高频分别所在的矩<span class="ff4">形</span>区域。可以<span class="ff4">看</span>出，图像<span class="_ _d"> </span><span class="ff3">DCT<span class="_ _c"> </span></span>变换后大部分<span class="ff4">参</span></div><div class="t m0 x2 h5 y35 ff1 fs2 fc0 sc1 ls0 ws0">数<span class="ff4">接<span class="_ _0"></span></span>近于<span class="_ _0"></span><span class="ff4">零</span>，<span class="_ _0"></span>只有<span class="_ _0"></span><span class="ff4">左<span class="_ _0"></span></span>上<span class="ff4">角<span class="_ _0"></span></span>的低<span class="_ _0"></span>频部<span class="_ _0"></span>分有<span class="_ _0"></span>较大<span class="_ _0"></span>的数<span class="_ _0"></span>值，<span class="_ _0"></span>中频<span class="_ _0"></span>部分<span class="_ _0"></span><span class="ff4">参</span>数<span class="_ _0"></span>值相<span class="_ _0"></span>对较<span class="_ _0"></span>小，<span class="_ _0"></span>而大</div><div class="t m0 x8 h5 y36 ff1 fs2 fc0 sc1 ls0 ws0">部分高频<span class="ff4">参</span>数值非常小，<span class="ff4">接</span>近于<span class="ff4">零</span>。</div><div class="t m0 x8 h5 y37 ff3 fs2 fc0 sc1 ls0 ws0"> <span class="fc1 sc1"> </span><span class="fc1 sc1"> </span><span class="fc1 sc1"> </span><span class="fc1 sc1"> </span><span class="fc1 sc1"> </span><span class="fc1 sc1"> </span><span class="fc1 sc1"> </span><span class="ff1"><span class="fc1 sc1">图</span></span><span class="fc1 sc1"> </span><span class="fc1 sc1">3</span><span class="ff5"><span class="fc1 sc1">—</span></span><span class="fc1 sc1">1</span><span class="ff1"><span class="fc1 sc1">：</span><span class="ff4"><span class="fc1 sc1">原</span></span><span class="fc1 sc1">图像</span><span class="_ _e"> </span>图<span class="_ _5"></span></span> <span class="_ _5"></span>3<span class="ff5">—</span>2<span class="_ _5"></span><span class="ff1">：<span class="_ _5"></span>变</span></div><div class="t m0 x8 h5 y38 ff1 fs2 fc0 sc1 ls0 ws0">换<span class="fc1 sc1">后的系数图像</span></div><div class="t m0 x8 h4 y39 ff2 fs1 fc0 sc1 ls0 ws0">3<span class="fc1 sc1">.</span><span class="fc1 sc1">2</span><span class="fc1 sc1">.</span><span class="fc1 sc1">3</span><span class="fc1 sc1"> </span><span class="ff1 sc0"><span class="fc1 sc1">离散余弦变换的数字水</span>印算法</span></div><div class="t m0 x9 h5 y3a ff4 fs2 fc0 sc1 ls0 ws0"><span class="fc1 sc1">根</span><span class="ff1"><span class="fc1 sc1">据</span><span class="fc1 sc1">离</span><span class="_ _0"></span><span class="fc1 sc1">散</span><span class="fc1 sc1">余</span><span class="fc1 sc1">弦</span><span class="_ _0"></span><span class="fc1 sc1">变</span><span class="fc1 sc1">换</span><span class="fc1 sc1">后</span><span class="_ _0"></span><span class="fc1 sc1">的</span></span><span class="fc1 sc1">参</span><span class="ff1"><span class="fc1 sc1">数</span><span class="_ _0"></span><span class="fc1 sc1">性</span>质，<span class="_ _0"></span>本文采<span class="_ _0"></span>用了</span></div><div class="t m0 x8 h5 y3b ff1 fs2 fc0 sc1 ls0 ws0">以<span class="_ _2"> </span><span class="ff3"><span class="fc1 sc1">Zi</span><span class="fc1 sc1">g</span><span class="fc1 sc1">Z</span><span class="fc1 sc1">a</span><span class="fc1 sc1">g</span><span class="_"> </span></span><span class="fc1 sc1">方</span><span class="_ _5"></span><span class="ff4"><span class="fc1 sc1">式</span></span><span class="fc1 sc1">重</span><span class="_ _5"></span><span class="ff4"><span class="fc1 sc1">排</span><span class="_ _0"></span></span><span class="fc1 sc1">变</span><span class="_ _5"></span><span class="fc1 sc1">换</span><span class="fc1 sc1">域</span><span class="_ _5"></span><span class="fc1 sc1">系</span><span class="_ _0"></span><span class="fc1 sc1">数</span><span class="_ _0"></span><span class="fc1 sc1">的</span><span class="_ _5"></span>方<span class="_ _0"></span>法<span class="_ _0"></span>，<span class="_ _5"></span><span class="ff4">选<span class="_ _0"></span></span>出<span class="_ _5"></span>中频</div></div><div class="c xa y3c w3 h7"><div class="t m1 x0 h8 y3d ff6 fs3 fc0 sc1 ls0 ws0"><span class="_ _f"></span></div></div><div class="t m0 xb h6 y3e ff3 fs2 fc0 sc1 ls0 ws0"> </div><div class="c xc y3f w4 h7"><div class="t m2 x0 h8 y40 ff6 fs3 fc0 sc1 ls0 ws0"><span class="fc1 sc1"></span><span class="_ _f"></span><span class="fc1 sc1"></span><span class="_ _f"></span><span class="fc1 sc1"></span></div></div><div class="c xa y3f w3 h7"><div class="t m1 x0 h8 y40 ff6 fs3 fc0 sc1 ls0 ws0"><span class="_ _f"></span></div></div><div class="t m0 xb h6 y41 ff3 fs2 fc0 sc1 ls0 ws0"> </div><div class="c xd y42 w3 h7"><div class="t m1 x0 h8 y40 ff6 fs3 fc0 sc1 ls0 ws0"><span class="_ _f"></span></div></div><div class="c xe y42 w3 h7"><div class="t m1 x0 h8 y40 ff6 fs3 fc0 sc1 ls0 ws0"><span class="_ _f"></span></div></div><div class="t m0 xc h6 y43 ff3 fs2 fc0 sc1 ls0 ws0"> </div><div class="c xf y42 w3 h7"><div class="t m1 x0 h8 y40 ff6 fs3 fc0 sc1 ls0 ws0"><span class="_ _f"></span></div></div><div class="t m0 x10 h6 y43 ff3 fs2 fc0 sc1 ls0 ws0"> </div><div class="c xd y3c w4 h7"><div class="t m2 x0 h8 y3d ff6 fs3 fc0 sc1 ls0 ws0"><span class="_ _f"></span><span class="_ _f"></span></div></div><div class="c x11 y3c w4 h7"><div class="t m2 x0 h8 y3d ff6 fs3 fc0 sc1 ls0 ws0"><span class="_ _f"></span><span class="_ _f"></span></div></div><div class="c xd y3f w4 h7"><div class="t m2 x0 h8 y40 ff6 fs3 fc0 sc1 ls0 ws0"><span class="_ _f"></span><span class="_ _f"></span></div></div><div class="c x11 y3f w4 h7"><div class="t m2 x0 h8 y40 ff6 fs3 fc0 sc1 ls0 ws0"><span class="_ _f"></span><span class="_ _f"></span></div></div><div class="c x12 y44 w5 h9"><div class="t m0 x13 h6 y45 ff3 fs2 fc0 sc1 ls0 ws0">…</div></div><div class="c x9 y46 w4 ha"><div class="t m2 x0 h8 y47 ff6 fs3 fc0 sc1 ls0 ws0"><span class="_ _f"></span><span class="_ _f"></span></div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62679de44f8811599ef02315/bg3.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x2 h5 y48 ff1 fs2 fc0 sc1 ls0 ws0">分量<span class="_ _0"></span>，用<span class="_ _0"></span>数字<span class="_ _0"></span>水印<span class="_ _0"></span><span class="ff4">序<span class="_ _0"></span>列</span>对<span class="_ _0"></span>其进<span class="_ _0"></span>行非<span class="_ _0"></span><span class="ff4">线</span>性<span class="_ _0"></span><span class="ff4">调制<span class="_ _0"></span></span>。水<span class="_ _0"></span>印检<span class="_ _0"></span>测时<span class="_ _0"></span>，<span class="ff4">待<span class="_ _0"></span></span>检测<span class="_ _0"></span>图像<span class="_ _0"></span><span class="ff4">仍<span class="_ _0"></span>按</span>比<span class="_ _0"></span>方<span class="ff4">式<span class="_ _0"></span>选</span></div><div class="t m0 x2 h5 y49 ff4 fs2 fc0 sc1 ls0 ws0">择<span class="ff1">变换域系数，与</span>待<span class="ff1">水印进行相</span>关<span class="ff1">运算，与</span>阈<span class="ff1">值比较</span>来判断<span class="ff1">是</span>否<span class="ff1">所</span>含<span class="ff1">水印。</span></div><div class="t m0 x3 h5 y4a ff1 fs2 fc0 sc1 ls0 ws0">离散<span class="_ _0"></span>余弦<span class="_ _0"></span>域的<span class="_ _0"></span>数字<span class="_ _0"></span>水印<span class="_ _0"></span>算法<span class="_ _0"></span>的具<span class="_ _0"></span>体实<span class="_ _0"></span>现分<span class="_ _0"></span>为三<span class="_ _0"></span><span class="ff4">步<span class="_ _0"></span></span>：宿<span class="_ _0"></span>主图<span class="_ _0"></span>像的<span class="_ _0"></span>变换<span class="_ _0"></span>，数<span class="_ _0"></span>字水<span class="_ _0"></span>印的</div><div class="t m0 x2 h5 y4b ff1 fs2 fc0 sc1 ls0 ws0">嵌入，数字水印的检测。</div><div class="t m0 x2 h4 y4c ff2 fs1 fc0 sc1 ls0 ws0">3.2.3.1 <span class="ff1 sc0">宿主图像的<span class="_ _2"> </span></span>DCT<span class="_ _2"> </span><span class="ff1 sc0">变换</span></div><div class="t m0 x3 h5 y4d ff1 fs2 fc0 sc1 ls0 ws0">对于<span class="_ _c"> </span><span class="ff3">N×<span class="_ _0"></span>N<span class="_ _c"> </span></span>大小的<span class="_ _9"> </span><span class="ff3">256<span class="_ _9"> </span><span class="ff4">灰</span></span>度<span class="ff4">级</span>的宿主图像<span class="_ _9"> </span><span class="ff3">I<span class="_ _c"> </span></span>进行<span class="_ _9"> </span><span class="ff3">N×<span class="_ _0"></span>N<span class="_ _c"> </span></span>二维离散余弦变换（<span class="ff3">DCT<span class="_ _0"></span></span>）。</div><div class="t m0 x2 h5 y4e ff1 fs2 fc0 sc1 ls0 ws0">以<span class="_ _c"> </span><span class="ff3">ZigZag<span class="_ _9"> </span></span>方<span class="ff4">式</span>对于<span class="_ _9"> </span><span class="ff3">DCT<span class="_ _9"> </span></span>变换后的图像频<span class="ff4">率</span>系数重<span class="ff4">新排列成</span>一维向量<span class="_ _9"> </span><span class="ff3">Y={y</span></div><div class="t m0 x14 hb y4f ff3 fs4 fc0 sc1 ls0 ws0">1</div><div class="t m0 x15 h6 y4e ff3 fs2 fc0 sc1 ls0 ws0">, y</div><div class="t m0 x16 hb y4f ff3 fs4 fc0 sc1 ls0 ws0">2</div><div class="t m0 x17 h6 y4e ff3 fs2 fc0 sc1 ls0 ws0">,…y</div><div class="t m0 x18 hb y4f ff3 fs4 fc0 sc1 ls0 ws0">N×N</div><div class="t m0 x19 h6 y4e ff3 fs2 fc0 sc1 ls0 ws0">}.</div><div class="t m0 x3 h5 y50 ff4 fs2 fc0 sc1 ls0 ws0">并<span class="ff1">取出</span>序列<span class="ff1">中第<span class="_ _c"> </span><span class="ff3">L+1<span class="_ _9"> </span></span>到<span class="_ _9"> </span><span class="ff3">L+M<span class="_ _9"> </span></span>的中频系数部分<span class="ff3">,</span>得到<span class="_ _9"> </span><span class="ff3">Y</span></span></div><div class="t m0 x1a hb y51 ff3 fs4 fc0 sc1 ls0 ws0">L</div><div class="t m0 x1b h6 y50 ff3 fs2 fc0 sc1 ls0 ws0">={ <span class="_ _4"></span>Y</div><div class="t m0 x1c hb y51 ff3 fs4 fc0 sc1 ls0 ws0">L+1</div><div class="t m0 x1d h6 y50 ff3 fs2 fc0 sc1 ls0 ws0">, <span class="_ _4"></span>Y</div><div class="t m0 x1e hb y51 ff3 fs4 fc0 sc1 ls0 ws0">L+2</div><div class="t m0 x1f h6 y50 ff3 fs2 fc0 sc1 ls0 ws0">,…, <span class="_ _4"></span>Y</div><div class="t m0 x20 hb y51 ff3 fs4 fc0 sc1 ls0 ws0">L+M</div><div class="t m0 x17 h6 y50 ff3 fs2 fc0 sc1 ls0 ws0">} </div><div class="t m0 x2 h4 y52 ff2 fs1 fc0 sc1 ls0 ws0">3.2.3.2 <span class="ff1 sc0">数字水印的嵌入</span></div><div class="t m0 x3 h5 y53 ff4 fs2 fc0 sc1 ls0 ws0">假<span class="_ _5"></span>设<span class="_ _5"></span><span class="ff1">数<span class="_ _5"></span>字<span class="_ _0"></span>水<span class="_ _5"></span>印<span class="_"> </span><span class="ff3">W<span class="_"> </span></span>为<span class="_ _5"></span>一<span class="_ _5"></span></span>服<span class="_ _5"></span>从<span class="_ _5"></span>标<span class="_ _5"></span>准<span class="_ _5"></span><span class="ff1">正<span class="_ _0"></span></span>态<span class="_ _5"></span><span class="ff1">分<span class="_ _5"></span></span>布<span class="_ _5"></span><span class="ff1">的<span class="_ _5"></span></span>随<span class="_ _5"></span>机<span class="_ _5"></span><span class="ff1">实<span class="_ _0"></span>数<span class="_ _5"></span></span>序<span class="_ _5"></span>列<span class="_ _5"></span><span class="ff1">，<span class="_ _5"></span>用<span class="_ _5"></span>数<span class="_ _5"></span>字<span class="_ _0"></span></span>序<span class="_ _5"></span>列<span class="_ _5"></span>表<span class="_ _5"></span>示<span class="_ _5"></span><span class="ff1">为</span></div><div class="t m0 x2 h6 y54 ff3 fs2 fc0 sc1 ls0 ws0">W={W</div><div class="t m0 x21 hb y55 ff3 fs4 fc0 sc1 ls0 ws0">1</div><div class="t m0 x22 h5 y54 ff3 fs2 fc0 sc1 ls0 ws0"> <span class="_ _0"></span><span class="ff1">，</span>W</div><div class="t m0 x23 hb y55 ff3 fs4 fc0 sc1 ls0 ws0">2</div><div class="t m0 x24 h5 y54 ff3 fs2 fc0 sc1 ls0 ws0"> <span class="_ _0"></span><span class="ff1">，<span class="ff4">…</span></span>W</div><div class="t m0 x25 hb y55 ff3 fs4 fc0 sc1 ls0 ws0">M</div><div class="t m0 x26 h5 y54 ff3 fs2 fc0 sc1 ls0 ws0"> }<span class="ff1">。<span class="_ _0"></span>用<span class="_ _9"> </span></span>W<span class="_"> </span><span class="ff1">对<span class="_ _c"> </span></span>Y<span class="_ _9"> </span><span class="ff4">序列<span class="_ _0"></span><span class="ff1">中第<span class="_ _2"> </span></span></span>L+1<span class="_ _9"> </span><span class="ff1">到<span class="_ _9"> </span></span>L+M<span class="_"> </span><span class="ff1">的中频系数<span class="_ _0"></span>部分的<span class="_ _0"></span>值进行<span class="_ _0"></span><span class="ff4">修</span></span></div><div class="t m0 x2 h5 y56 ff4 fs2 fc0 sc1 ls0 ws0">改<span class="ff1">，</span>按<span class="ff1">以下</span>公式<span class="ff1">进行：</span></div><div class="t m0 x3 h6 y57 ff3 fs2 fc0 sc1 ls0 ws0"> </div></div><div class="c x5 y58 w6 hc"><div class="t m0 x27 hd y59 ff3 fs5 fc0 sc1 ls0 ws0">'</div><div class="t m0 x28 hd y5a ff3 fs5 fc0 sc1 ls0 ws0">'<span class="_ _10"> </span>2</div><div class="t m3 x29 he y5b ff3 fs6 fc0 sc1 ls0 ws0">,<span class="_ _11"> </span>0</div><div class="t m0 x2a hf y5c ff7 fs5 fc0 sc1 ls0 ws0">i<span class="_ _12"> </span>i</div><div class="t m0 x2b hf y5d ff7 fs5 fc0 sc1 ls0 ws0">i<span class="_ _12"> </span>i<span class="_ _13"> </span>i<span class="_ _b"> </span>i</div><div class="t m3 x2b h10 y5e ff7 fs6 fc0 sc1 ls0 ws0">y<span class="_ _14"> </span>y<span class="_ _15"> </span>i<span class="_ _16"> </span>L<span class="_ _17"> </span>i<span class="_ _16"> </span>L<span class="_ _18"> </span>m</div><div class="t m3 x2c h10 y5b ff7 fs6 fc0 sc1 ls0 ws0">y<span class="_ _14"> </span>y<span class="_ _19"> </span>y<span class="_ _1a"> </span>w<span class="_ _11"> </span>L<span class="_ _17"> </span>i<span class="_ _16"> </span>L<span class="_ _1b"> </span>M</div><div class="t m4 x2d h11 y5b ff6 fs7 fc0 sc1 ls0 ws0"><span class="_ _1c"> </span></div><div class="t m3 x2e h12 y5f ff6 fs6 fc0 sc1 ls0 ws0"></div><div class="t m3 x2f h12 y5e ff6 fs6 fc0 sc1 ls0 ws0"><span class="_ _1d"> </span><span class="_ _1e"> </span><span class="_ _1f"> </span></div><div class="t m3 x2e h12 y60 ff6 fs6 fc0 sc1 ls0 ws0"></div><div class="t m3 x27 h12 y5b ff6 fs6 fc0 sc1 ls0 ws0"><span class="_ _17"> </span><span class="_ _20"> </span><span class="_ _21"> </span><span class="_ _1f"> </span><span class="_ _22"> </span></div><div class="t m3 x2e h12 y61 ff6 fs6 fc0 sc1 ls0 ws0"></div><div class="t m3 x30 h13 y5e ff1 fs6 fc0 sc1 ls0 ws0">或</div></div><div class="c x0 y1 w2 h2"><div class="t m0 x31 h6 y57 ff3 fs2 fc0 sc1 ls0 ws0"> </div><div class="t m0 x3 h5 y62 ff1 fs2 fc0 sc1 ls0 ws0">经过<span class="_ _0"></span><span class="ff4">修改<span class="_ _0"></span></span>的系<span class="_ _0"></span>数<span class="ff4">序<span class="_ _0"></span>列<span class="_ _2"> </span><span class="ff5">Y′ ={ <span class="_ _0"></span>Y</span></span></div><div class="t m0 x32 h14 y63 ff5 fs4 fc0 sc1 ls0 ws0">1</div><div class="t m0 x33 h15 y62 ff5 fs2 fc0 sc1 ls0 ws0">′, Y</div><div class="t m0 x34 h14 y63 ff5 fs4 fc0 sc1 ls0 ws0">2</div><div class="t m0 xe h15 y62 ff5 fs2 fc0 sc1 ls0 ws0">′,... <span class="_ _0"></span><span class="ff3">Y</span>′</div><div class="t m0 x35 hb y64 ff3 fs4 fc0 sc1 ls0 ws0">N×N</div><div class="t m0 x31 h5 y62 ff5 fs2 fc0 sc1 ls0 ws0">}<span class="ff3"> <span class="_ _0"></span><span class="ff1">以<span class="_ _9"> </span></span>ZigZag<span class="_"> </span><span class="ff4">逆<span class="ff1">变换<span class="_ _0"></span></span>形式<span class="_ _0"></span><span class="ff1">重</span>组<span class="_ _0"></span><span class="ff1">，</span>再<span class="_ _0"></span><span class="ff1">进行</span></span></span></div><div class="t m0 x2 h5 y65 ff3 fs2 fc0 sc1 ls0 ws0">N×N DCT<span class="_ _9"> </span><span class="ff4">逆<span class="ff1">变换，得到嵌有数字水印的图像<span class="_ _9"> </span></span></span>I<span class="ff5">′<span class="ff1">。</span></span></div><div class="t m0 x2 h4 y66 ff2 fs1 fc0 sc1 ls0 ws0">3.2.3.3 <span class="ff1 sc0">数字水印的检测</span></div><div class="t m0 x3 h5 y67 ff4 fs2 fc0 sc1 ls0 ws0">待<span class="ff1">检测的可能</span>含<span class="ff1">有水印的图像<span class="_ _c"> </span><span class="ff3">I<span class="ff5">"</span></span></span></div><div class="t m0 x36 h14 y68 ff5 fs4 fc0 sc1 ls0 ws0"> </div><div class="t m0 x37 h5 y67 ff1 fs2 fc0 sc1 ls0 ws0">。<span class="ff4">假设<span class="_ _c"> </span><span class="ff3">I<span class="ff5">"<span class="_ _0"></span></span></span>未</span>损失大量<span class="ff4">信息</span>，可以近似<span class="ff4">认</span>为<span class="_ _c"> </span><span class="ff3">I<span class="ff5">"</span>=<span class="_ _0"></span> I<span class="ff5">′</span></span>。</div><div class="t m0 x2 h5 y69 ff1 fs2 fc0 sc1 ls0 ws0">在此<span class="ff4">假设</span>下可以运用<span class="ff4">统计</span>的方法<span class="ff4">来</span>检测水印。</div><div class="t m0 x2 h5 y6a ff1 fs2 fc0 sc1 ls0 ws0">（<span class="ff3">1</span>）<span class="ff4">待</span>检水印域<span class="ff4">待</span>检图像中频系数相<span class="ff4">关</span>性的测<span class="ff4">定</span></div><div class="t m0 x3 h5 y6b ff1 fs2 fc0 sc1 ls0 ws0">同<span class="_ _0"></span>样<span class="_ _0"></span>对<span class="_ _2"> </span><span class="ff3">I<span class="ff5">′<span class="_ _0"></span></span></span>进<span class="_ _0"></span>行<span class="_ _2"> </span><span class="ff3">DCT<span class="_"> </span></span>变<span class="_ _0"></span>换<span class="_ _0"></span>，<span class="_ _0"></span>以<span class="_ _2"> </span><span class="ff3">ZigZag<span class="_"> </span></span>方<span class="ff4">式<span class="_ _0"></span></span>将<span class="_ _1"> </span><span class="ff3">DCT<span class="_"> </span></span>系数<span class="_ _0"></span><span class="ff4">排<span class="_ _0"></span>成<span class="_ _0"></span></span>一<span class="_ _0"></span>维<span class="_ _0"></span>向<span class="_ _0"></span>量<span class="_ _1"> </span><span class="ff5">Y <span class="_ _0"></span>"=<span class="_ _0"></span> {<span class="_ _0"></span> Y</span></div><div class="t m0 x38 h14 y6c ff5 fs4 fc0 sc1 ls0 ws0">1</div><div class="t m0 x39 h15 y6b ff5 fs2 fc0 sc1 ls0 ws0"> <span class="_ _0"></span>",</div><div class="t m0 x2 h15 y6d ff5 fs2 fc0 sc1 ls0 ws0">Y</div><div class="t m0 x3a h14 y6e ff5 fs4 fc0 sc1 ls0 ws0">2</div><div class="t m0 x3b h15 y6d ff5 fs2 fc0 sc1 ls0 ws0"> ",... <span class="ff3">Y</span></div><div class="t m0 x3c hb y6f ff3 fs4 fc0 sc1 ls0 ws0">N×N</div><div class="t m0 x3d h5 y6d ff5 fs2 fc0 sc1 ls0 ws0">"}<span class="ff1">。<span class="ff4">由</span>于<span class="ff4">假设<span class="_ _c"> </span><span class="ff3">I</span></span></span>"<span class="_ _0"></span><span class="ff3">=I</span>′<span class="ff1">，则<span class="_ _c"> </span><span class="ff3">Y</span></span>"<span class="_ _0"></span><span class="ff3">=</span> Y ′<span class="ff1">。</span></div><div class="t m0 x3 h5 y70 ff1 fs2 fc0 sc1 ls0 ws0">取<span class="_ _5"></span>出<span class="_"> </span><span class="ff3">Y<span class="ff5">"<span class="_ _5"></span></span></span>（<span class="_ _5"></span>等<span class="_ _5"></span>于<span class="_"> </span><span class="ff5">Y′<span class="_ _5"></span></span>）<span class="_ _5"></span>中<span class="_ _6"></span>第<span class="_ _1"> </span><span class="ff3">L+1<span class="_ _23"> </span></span>到<span class="_"> </span><span class="ff3">L+M<span class="_"> </span></span>的<span class="_ _5"></span>中<span class="_ _6"></span>频<span class="_ _5"></span>系<span class="_ _5"></span>数<span class="_ _5"></span>部<span class="_ _5"></span>分<span class="_"> </span><span class="ff5">Y</span></div><div class="t m0 x3e h14 y71 ff5 fs4 fc0 sc1 ls0 ws0">L</div><div class="t m0 x3f h15 y70 ff5 fs2 fc0 sc1 ls0 ws0"> <span class="_ _5"></span>"={<span class="_ _0"></span> <span class="_ _5"></span>Y</div><div class="t m0 x40 h14 y71 ff5 fs4 fc0 sc1 ls0 ws0">L+1</div><div class="t m0 x14 h15 y70 ff5 fs2 fc0 sc1 ls0 ws0"> <span class="_ _5"></span>",<span class="_ _0"></span> <span class="_ _5"></span>Y</div><div class="t m0 x41 h14 y71 ff5 fs4 fc0 sc1 ls0 ws0">L+2</div><div class="t m0 x42 h15 y70 ff5 fs2 fc0 sc1 ls0 ws0">"</div><div class="t m0 x38 h14 y72 ff5 fs4 fc0 sc1 ls0 ws0">’</div><div class="t m0 x43 h15 y70 ff5 fs2 fc0 sc1 ls0 ws0">,...</div><div class="t m0 x2 h6 y73 ff3 fs2 fc0 sc1 ls0 ws0">Y</div><div class="t m0 x44 hb y74 ff3 fs4 fc0 sc1 ls0 ws0">L+M</div><div class="t m0 x45 h5 y73 ff5 fs2 fc0 sc1 ls0 ws0">"}<span class="_ _0"></span><span class="ff1">。<span class="_ _0"></span><span class="ff4">假<span class="_ _0"></span>设<span class="_ _0"></span>待<span class="_ _0"></span></span>检<span class="_ _0"></span>测<span class="_ _0"></span>的<span class="_ _0"></span>数<span class="_ _0"></span>字<span class="_ _0"></span>水<span class="_ _0"></span>印<span class="_"> </span></span>X={X</div><div class="t m0 x46 h14 y75 ff5 fs4 fc0 sc1 ls0 ws0">1</div><div class="t m0 x47 h5 y73 ff1 fs2 fc0 sc1 ls0 ws0">，<span class="_ _0"></span><span class="ff5">X</span></div><div class="t m0 x48 h14 y75 ff5 fs4 fc0 sc1 ls0 ws0">2</div><div class="t m0 x35 h5 y73 ff1 fs2 fc0 sc1 ls0 ws0">，<span class="_ _0"></span><span class="ff5">... <span class="_ _0"></span>X</span></div><div class="t m0 x49 h14 y75 ff5 fs4 fc0 sc1 ls0 ws0">M</div><div class="t m0 x4a h5 y73 ff5 fs2 fc0 sc1 ls0 ws0">}<span class="_ _0"></span><span class="ff1">为<span class="_ _0"></span>一<span class="_ _0"></span><span class="ff4">符<span class="_ _0"></span>合<span class="_ _0"></span>标<span class="_ _0"></span>准<span class="_ _0"></span></span>正<span class="_ _0"></span><span class="ff4">态<span class="_ _0"></span></span>分<span class="_ _0"></span><span class="ff4">布<span class="_ _0"></span></span>的<span class="_ _0"></span>实<span class="_ _0"></span>数</span></div><div class="t m0 x2 h5 y76 ff4 fs2 fc0 sc1 ls0 ws0">伪随<span class="_ _0"></span>机序<span class="_ _0"></span>列<span class="ff1">。<span class="_ _0"></span>则可<span class="_ _0"></span>以<span class="_ _0"></span></span>通<span class="ff1">过<span class="_ _0"></span></span>待<span class="ff1">检<span class="_ _0"></span>水印<span class="_ _0"></span>与图<span class="_ _0"></span>像中<span class="_ _0"></span>频系<span class="_ _0"></span>数</span>作<span class="_ _0"></span><span class="ff1">相</span>关<span class="_ _0"></span><span class="ff1">运算<span class="_ _0"></span></span>来判<span class="_ _0"></span>断<span class="ff1">是<span class="_ _0"></span></span>否<span class="_ _0"></span><span class="ff1">所加<span class="_ _0"></span>入了<span class="_ _0"></span>水</span></div><div class="t m0 x2 h5 y77 ff1 fs2 fc0 sc1 ls0 ws0">印。<span class="_ _0"></span>只有<span class="_ _0"></span>在<span class="ff4">待<span class="_ _0"></span></span>检水<span class="_ _0"></span>印为<span class="_ _0"></span>所加<span class="_ _0"></span>入的<span class="_ _0"></span>水印<span class="_ _0"></span>时，<span class="_ _0"></span><span class="ff4">才<span class="_ _0"></span></span>能得<span class="_ _0"></span>到较<span class="_ _0"></span>大的<span class="_ _0"></span>相<span class="ff4">关<span class="_ _0"></span></span>值。<span class="_ _0"></span><span class="ff4">否</span>则<span class="_ _0"></span>相<span class="_ _0"></span><span class="ff4">关</span>值<span class="_ _0"></span>很小<span class="_ _0"></span>，</div><div class="t m0 x2 h5 y78 ff4 fs2 fc0 sc1 ls0 ws0">接<span class="ff1">近于</span>零<span class="ff1">。</span></div><div class="t m0 x2 h5 y79 ff1 fs2 fc0 sc1 ls0 ws0">用<span class="ff4">符号<span class="_ _c"> </span><span class="ff3">E<span class="_ _9"> </span></span>表示</span>数<span class="ff4">学期望</span>，得到：</div><div class="t m0 x3 h6 y7a ff3 fs2 fc0 sc1 ls0 ws0"> </div></div><div class="c x30 y7b w7 h16"><div class="t m5 x4b h17 y7c ff3 fs8 fc0 sc1 ls0 ws0">2</div><div class="t m6 x27 h18 y7d ff3 fs1 fc0 sc1 ls0 ws0">(<span class="_ _24"> </span>)<span class="_ _25"> </span>(<span class="_ _16"> </span>)</div><div class="t m6 x2a h18 y7e ff3 fs1 fc0 sc1 ls0 ws0">(<span class="_ _24"> </span>)<span class="_ _26"> </span>0</div><div class="t m6 x4c h18 y7f ff3 fs1 fc0 sc1 ls0 ws0">(<span class="_ _24"> </span>)<span class="_ _26"> </span>0</div><div class="t m6 x4d h19 y7d ff7 fs1 fc0 sc1 ls0 ws0">E<span class="_ _a"> </span>z<span class="_ _1e"> </span>E<span class="_ _27"> </span>Y<span class="_ _28"> </span>X<span class="_ _16"> </span>W</div><div class="t m6 x4e h19 y7e ff7 fs1 fc0 sc1 ls0 ws0">E<span class="_ _a"> </span>z<span class="_ _29"> </span>X<span class="_ _16"> </span>W</div><div class="t m6 x13 h19 y7f ff7 fs1 fc0 sc1 ls0 ws0">E<span class="_ _2a"> </span>z</div><div class="t m7 x4f h1a y7d ff6 fs9 fc0 sc1 ls0 ws0"></div><div class="t m6 x2e h1b y80 ff6 fs1 fc0 sc1 ls0 ws0"></div><div class="t m6 x50 h1b y7d ff6 fs1 fc0 sc1 ls0 ws0"><span class="_ _2b"> </span></div><div class="t m6 x2e h1b y81 ff6 fs1 fc0 sc1 ls0 ws0"></div><div class="t m6 x51 h1b y7e ff6 fs1 fc0 sc1 ls0 ws0"><span class="_ _2c"> </span></div><div class="t m6 x2e h1b y82 ff6 fs1 fc0 sc1 ls0 ws0"></div><div class="t m6 x2e h1b y83 ff6 fs1 fc0 sc1 ls0 ws0"></div><div class="t m6 x52 h1b y7f ff6 fs1 fc0 sc1 ls0 ws0"></div><div class="t m6 x2e h1b y84 ff6 fs1 fc0 sc1 ls0 ws0"></div><div class="t m6 x53 h4 y7f ff1 fs1 fc0 sc1 ls0 ws0">没有水印存在</div></div><div class="c x0 y1 w2 h2"><div class="t m0 x12 h6 y7a ff3 fs2 fc0 sc1 ls0 ws0"> </div><div class="t m0 x2 h5 y85 ff1 fs2 fc0 sc1 ls0 ws0">（<span class="ff5">2</span>）<span class="ff4">阈</span>值的确<span class="ff4">定</span></div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
<div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62679de44f8811599ef02315/bg4.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x3 h5 y86 ff4 fs2 fc0 sc1 ls0 ws0">根<span class="ff1">据中</span>心极限定<span class="ff1">理，</span>参照<span class="ff1">水印</span>匹配<span class="ff1">与不</span>匹配<span class="ff1">两种</span>情况<span class="ff1">得到</span>阈<span class="ff1">值为</span></div><div class="t m0 x2 h5 y87 ff4 fs2 fc0 sc1 ls0 ws0">由<span class="ff1">于</span>原<span class="ff1">始图像难以得到，因此</span>从<span class="ff1">实用性出发，</span>阈<span class="ff1">值</span>定<span class="ff1">义为： </span></div><div class="t m0 x12 h15 y88 ff5 fs2 fc0 sc1 ls0 ws0"> <span class="_ _0"></span> </div><div class="t m0 x3 h5 y89 ff4 fs2 fc0 sc1 ls0 ws0">综<span class="_ _0"></span><span class="ff1">上所<span class="_ _0"></span>述<span class="_ _0"></span>，<span class="_ _0"></span></span>满<span class="_ _0"></span>足<span class="_ _2d"> </span><span class="ff1">时，<span class="_ _0"></span>则<span class="_ _0"></span></span>表<span class="_ _0"></span><span class="ff1">明<span class="_ _0"></span>检<span class="_ _0"></span>测<span class="_ _0"></span>到<span class="_ _0"></span></span>匹配<span class="_ _0"></span><span class="ff1">水<span class="_ _0"></span>印<span class="_ _0"></span>。<span class="_ _0"></span></span>否<span class="_ _0"></span><span class="ff1">则<span class="_ _0"></span>，<span class="_ _0"></span></span>未</div><div class="t m0 x2 h5 y8a ff1 fs2 fc0 sc1 ls0 ws0">检测到<span class="ff4">匹配</span>的水印。</div><div class="t m0 x4 h4 y8b ff2 fs1 fc0 sc1 ls0 ws0">3.3 MA<span class="_ _8"></span>TLAB<span class="_ _9"> </span><span class="ff4 sc0">工<span class="ff1">具</span>简介</span></div><div class="t m0 x4 h1c y8c ff2 fs1 fc0 sc1 ls0 ws0">3.3.1. <span class="ff4 sc0">简介</span></div><div class="t m0 x3 h5 y8d ff3 fs2 fc0 sc1 ls0 ws0">Matlab<span class="_"> </span><span class="ff1">是当前<span class="_ _0"></span>在国<span class="_ _0"></span><span class="ff4">内<span class="_ _0"></span>外<span class="_ _0"></span>十</span>分<span class="_ _0"></span><span class="ff4">流<span class="_ _0"></span></span>行<span class="_ _0"></span>的<span class="ff4">工<span class="_ _0"></span></span>程<span class="_ _0"></span><span class="ff4">设计<span class="_ _0"></span></span>和<span class="_ _0"></span>系<span class="_ _0"></span><span class="ff4">统仿<span class="_ _0"></span>真<span class="_ _0"></span>软</span>件<span class="_ _0"></span><span class="ff4">包<span class="_ _0"></span></span>。它<span class="_ _0"></span>是<span class="_"> </span></span>Math<span class="_ _0"></span>W<span class="_ _8"></span>orks</div><div class="t m0 x2 h5 y8e ff4 fs2 fc0 sc1 ls0 ws0">公司<span class="ff1">于<span class="_ _9"> </span><span class="ff3">1982<span class="_ _c"> </span></span>年</span>推<span class="ff1">出的一</span>套<span class="ff1">高性能的数值</span>计<span class="ff1">算和可视</span>化软<span class="ff1">件，它集数值分</span>析<span class="ff1">、矩阵运算<span class="_ _c"> </span>、</span></div><div class="t m0 x2 h5 y8f ff4 fs2 fc0 sc1 ls0 ws0">信号<span class="ff1">处理和图</span>形<span class="ff1">显</span>示<span class="ff1">于一体，</span>构成<span class="ff1">了一人方</span>便<span class="ff1">的、</span>界<span class="ff1">面</span>友<span class="ff1">好的用</span>户环境<span class="ff1">。</span></div><div class="t m0 x2 h5 y90 ff3 fs2 fc0 sc1 ls0 ws0">Matlab<span class="_ _9"> </span><span class="ff1">的<span class="_ _0"></span><span class="ff4">推</span>出<span class="_ _0"></span>得到<span class="_ _0"></span>了<span class="ff4">各<span class="_ _0"></span></span>个<span class="ff4">领<span class="_ _0"></span></span>域<span class="ff4">专<span class="_ _0"></span>家</span>、<span class="_ _0"></span><span class="ff4">学<span class="_ _0"></span></span>者的<span class="_ _0"></span><span class="ff4">广泛<span class="_ _0"></span>关注<span class="_ _0"></span></span>，其<span class="_ _0"></span>强大<span class="_ _0"></span>的<span class="_ _0"></span><span class="ff4">扩展<span class="_ _0"></span>功</span>能<span class="_ _0"></span>为<span class="ff4">各<span class="_ _0"></span></span>个<span class="ff4">领<span class="_ _0"></span></span>域</span></div><div class="t m0 x2 h5 y91 ff1 fs2 fc0 sc1 ls0 ws0">的<span class="_ _0"></span>应<span class="_ _0"></span>用<span class="_ _0"></span>提<span class="_ _0"></span><span class="ff4">供<span class="_ _0"></span></span>了<span class="_ _0"></span>基<span class="_ _0"></span><span class="ff4">础<span class="_ _0"></span></span>。<span class="_ _0"></span><span class="ff4">由<span class="_ _0"></span>各<span class="_ _0"></span></span>个<span class="_ _0"></span><span class="ff4">专<span class="_ _0"></span>家<span class="_ _0"></span>学<span class="_ _0"></span></span>者<span class="_ _5"></span>相<span class="ff4">继<span class="_ _0"></span>推<span class="_ _0"></span></span>出<span class="_ _0"></span>了<span class="_ _d"> </span><span class="ff3">MA<span class="_ _2e"></span>TLAB<span class="_"> </span><span class="ff4">工<span class="ff1">具<span class="_ _0"></span></span>箱<span class="_ _0"></span><span class="ff1">，<span class="_ _0"></span>其<span class="_ _0"></span>中<span class="_ _0"></span>的<span class="_ _5"></span></span>信号<span class="_ _0"></span><span class="ff1">处<span class="_ _0"></span>理</span></span></span></div><div class="t m0 x2 h5 y92 ff3 fs2 fc0 sc1 ls0 ws0">(signal<span class="_ _0"></span> <span class="_ _5"></span>processin<span class="_ _4"></span>g)<span class="_ _6"> </span><span class="ff1">、<span class="_ _5"></span><span class="ff4">控<span class="_ _5"></span>制<span class="_ _6"></span></span>系<span class="_ _5"></span><span class="ff4">统<span class="_ _6"></span></span></span>(control<span class="_ _0"></span> <span class="_ _0"></span>system)<span class="_ _6"></span><span class="ff1">、<span class="_ _5"></span><span class="ff4">神<span class="_ _5"></span></span>经<span class="_ _6"></span>网<span class="_ _5"></span><span class="ff4">络<span class="_ _6"></span></span></span>(<span class="_ _4"></span>neural<span class="_ _5"></span> <span class="_ _0"></span>network)<span class="_ _5"></span><span class="ff1">、<span class="_ _6"></span>图<span class="_ _5"></span>像<span class="_ _5"></span>处<span class="_ _5"></span>理</span></div><div class="t m0 x2 h5 y93 ff3 fs2 fc0 sc1 ls0 ws0">(image<span class="_ _0"></span> <span class="_ _5"></span>pr<span class="_ _4"></span>ocessing)<span class="_ _6"></span><span class="ff1">、<span class="_ _5"></span>鲁<span class="_ _5"></span><span class="ff4">棒<span class="_ _5"></span>控<span class="_ _5"></span>制<span class="_ _5"></span></span></span>(robust<span class="_ _0"></span> <span class="_ _0"></span>control)<span class="_ _6"></span><span class="ff1">、<span class="_ _5"></span>非<span class="_ _5"></span><span class="ff4">线<span class="_ _5"></span></span>性<span class="_ _5"></span>系<span class="_ _5"></span><span class="ff4">统<span class="_ _5"></span>控<span class="_ _5"></span>制<span class="_ _5"></span>设<span class="_ _5"></span>计<span class="_ _5"></span></span></span>(nonlinear<span class="_ _5"></span> <span class="_ _0"></span>system</div><div class="t m0 x2 h5 y94 ff3 fs2 fc0 sc1 ls0 ws0">control design)<span class="_ _0"></span><span class="ff1">、系<span class="_ _0"></span><span class="ff4">统辨识<span class="_ _0"></span></span></span>(system identification)<span class="_ _0"></span><span class="ff1">、<span class="_ _0"></span>最<span class="ff4">优化<span class="_ _0"></span></span></span>(optimization)<span class="ff1">、<span class="_ _0"></span><span class="ff4">模糊逻<span class="_ _0"></span>辑</span></span>(fuzzy</div><div class="t m0 x2 h5 y95 ff3 fs2 fc0 sc1 ls0 ws0">logic)<span class="ff1">、<span class="_ _0"></span>小<span class="_ _0"></span>波<span class="_ _0"></span></span>(wavelet)<span class="_ _0"></span><span class="ff1">、<span class="ff4">通<span class="_ _0"></span>信<span class="_ _0"></span></span></span>(communication)<span class="_ _0"></span><span class="ff1">、<span class="ff4">统<span class="_ _0"></span>计<span class="_ _0"></span></span></span>(statistics)<span class="_ _0"></span><span class="ff1">等<span class="ff4">工<span class="_ _0"></span></span>具<span class="_ _0"></span><span class="ff4">箱</span>，<span class="_ _0"></span>这<span class="_ _0"></span><span class="ff4">些工<span class="_ _0"></span></span>具<span class="_ _0"></span><span class="ff4">箱<span class="_ _0"></span>给</span></span></div><div class="t m0 x2 h5 y96 ff4 fs2 fc0 sc1 ls0 ws0">各<span class="ff1">个</span>领<span class="ff1">域的研究和</span>工<span class="ff1">程应用提</span>供<span class="ff1">了有</span>力<span class="ff1">的</span>工<span class="ff1">具，</span>借助<span class="ff1">于这</span>些<span class="_ _0"></span>“巨<span class="ff1">人</span>肩<span class="ff1">上的</span>工<span class="ff1">具</span>”<span class="_ _2f"></span><span class="ff1">，<span class="ff4">各</span>个<span class="ff4">层</span></span></div><div class="t m0 x2 h5 y97 ff4 fs2 fc0 sc1 ls0 ws0">次<span class="ff1">的研究人</span>员<span class="ff1">可</span>直观<span class="ff1">、方</span>便地<span class="ff1">进行分</span>析<span class="ff1">、</span>计<span class="ff1">算及</span>设计工作<span class="ff1">，</span>从<span class="ff1">而大大</span>地节省<span class="ff1">了时</span>间<span class="ff1">。</span></div><div class="t m0 x4 h4 y98 ff2 fs1 fc0 sc1 ls0 ws0">3.3.2. MA<span class="_ _8"></span>TLAB<span class="_ _9"> </span><span class="ff1 sc0">研究数字水印的<span class="ff4">优点</span></span></div><div class="t m0 x2 h5 y99 ff3 fs2 fc0 sc1 ls0 ws0">1<span class="_ _16"> </span><span class="ff1">集<span class="ff4">成</span>了<span class="_ _9"> </span></span>DCT<span class="ff1">、<span class="_ _0"></span></span>DWT<span class="_ _c"> </span><span class="ff1">等<span class="_ _0"></span><span class="ff4">函</span>数有<span class="ff4">丰富</span>的<span class="_ _0"></span>小波<span class="ff4">函</span>数和处<span class="_ _0"></span>理<span class="ff4">函</span>数，<span class="_ _0"></span>这不<span class="ff4">仅</span>方<span class="ff4">便</span>了<span class="_ _0"></span>研究人<span class="ff4">员</span>，</span></div><div class="t m0 x54 h5 y9a ff1 fs2 fc0 sc1 ls0 ws0">而<span class="ff4">且</span>使<span class="ff4">源</span>程<span class="ff4">序简洁</span>明了、易实现。</div><div class="t m0 x2 h5 y9b ff3 fs2 fc0 sc1 ls0 ws0">2<span class="_ _16"> </span><span class="ff1">强大的数<span class="ff4">学</span>运算<span class="ff4">功</span>能。能<span class="ff4">够</span>方<span class="ff4">便</span>、高<span class="ff4">效地</span>实现<span class="ff4">音</span>频、视频中的大量矩阵运算。</span></div><div class="t m0 x2 h5 y9c ff3 fs2 fc0 sc1 ls0 ws0">3<span class="_ _16"> </span><span class="ff1">提<span class="_ _0"></span><span class="ff4">供</span>了<span class="_ _0"></span>图<span class="_ _0"></span>像<span class="_ _0"></span>处<span class="_ _0"></span>理<span class="_ _0"></span><span class="ff4">工<span class="_ _0"></span></span>具<span class="_ _0"></span><span class="ff4">箱</span>、<span class="_ _5"></span>小波分<span class="_ _0"></span><span class="ff4">析<span class="_ _0"></span>工<span class="_ _0"></span></span>具<span class="_ _0"></span><span class="ff4">箱<span class="_ _0"></span></span>、<span class="_ _0"></span>数<span class="_ _0"></span>字<span class="_ _0"></span><span class="ff4">信号<span class="_ _0"></span></span>处<span class="_ _0"></span>理<span class="_ _0"></span><span class="ff4">工<span class="_ _0"></span></span>具<span class="_ _0"></span><span class="ff4">箱<span class="_ _0"></span></span>。<span class="_ _0"></span>用<span class="ff4">来<span class="_ _0"></span></span>编<span class="_ _0"></span><span class="ff4">制<span class="_ _0"></span>跨<span class="_ _0"></span></span>数</span></div><div class="t m0 x54 h5 y9d ff1 fs2 fc0 sc1 ls0 ws0">字图像处理技术、数字<span class="ff4">信号</span>处理等多<span class="ff4">学科</span>的数字水印技术是非常好的<span class="ff4">选择</span>。</div><div class="t m0 x2 h5 y9e ff3 fs2 fc0 sc1 ls0 ws0">4<span class="_ _16"> </span>MA<span class="_ _2e"></span>TLAB<span class="_ _9"> </span><span class="ff1">与<span class="ff4">目</span>前最强大的编程<span class="ff4">工</span>具<span class="ff4">——</span></span>V<span class="_ _8"></span>isual C++<span class="ff1">具有<span class="ff4">良</span>好的<span class="ff4">接口</span>。</span></div><div class="t m0 x4 h4 y9f ff2 fs1 fc0 sc1 ls0 ws0">3.3.3. MA<span class="_ _8"></span>TLAB<span class="_ _9"> </span><span class="ff4 sc0">函<span class="ff1">数</span>介绍</span></div><div class="t m0 x3 h5 ya0 ff1 fs2 fc0 sc1 ls0 ws0">在<span class="ff4">介<span class="_ _0"></span>绍函<span class="_ _0"></span></span>数<span class="ff4">之<span class="_ _0"></span></span>前，<span class="_ _0"></span>我们<span class="_ _0"></span><span class="ff4">必<span class="_ _0"></span>须</span>明<span class="_ _0"></span>确一<span class="_ _0"></span><span class="ff4">点</span>：<span class="_ _0"></span><span class="ff4">作</span>水<span class="_ _0"></span>印程<span class="_ _0"></span><span class="ff4">序</span>时<span class="_ _0"></span>，处<span class="_ _0"></span>理的<span class="_ _0"></span>图像<span class="_ _0"></span>数据<span class="_ _0"></span>是二<span class="_ _0"></span>维<span class="_ _0"></span><span class="ff4">信</span></div><div class="t m0 x2 h5 ya1 ff4 fs2 fc0 sc1 ls0 ws0">号<span class="ff1">，而</span>声音信号<span class="ff1">是一维</span>信号<span class="ff1">。这</span>里<span class="ff1">，我们</span>仅仅简单介绍<span class="ff1">与水印有</span>关<span class="ff1">的</span>函<span class="ff1">数。</span></div><div class="t m0 x3 h5 ya2 ff3 fs2 fc0 sc1 ls0 ws0">1<span class="_ _30"> </span><span class="ff1">数据输入输出<span class="ff4">函</span>数</span></div><div class="t m0 x2 h5 ya3 ff3 fs2 fc0 sc1 ls0 ws0">imread<span class="_ _0"></span><span class="ff1">（<span class="_ _5"></span>）和<span class="_ _1"> </span></span>imwrite<span class="_ _0"></span><span class="ff1">（<span class="_ _5"></span>）<span class="_ _0"></span>：<span class="_ _0"></span>可<span class="_ _0"></span>以<span class="_ _5"></span><span class="ff4">读写<span class="_ _1"> </span></span></span>bmp,jpg/jpeg,<span class="_ _0"></span> <span class="_ _0"></span>tif/tiff, png,<span class="_ _0"></span> <span class="_ _0"></span>hdf, <span class="_ _0"></span>pcx,<span class="_ _0"></span> wxd<span class="_ _23"> </span><span class="ff4">格<span class="_ _0"></span>式<span class="_ _0"></span><span class="ff1">文<span class="_ _0"></span>件<span class="_ _5"></span>。</span></span></div><div class="t m0 x2 h5 ya4 ff4 fs2 fc0 sc1 ls0 ws0">读索引<span class="ff1">文件时，</span>还<span class="ff1">可以得到相应的</span>调色板<span class="ff1">数据。</span></div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
