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src="https://cdn.wpsshop.cn/public/wpsshopindex/js/mid_detail_last.js?v=33890"></script><style type="text/css"></style><script type="text/javascript"></script><div class="interactive_info" id="body-data-0098" attrv="46230"></div><div class="article_box" style="overflow: hidden;"><div class="article_channel"><div class="channel_top_line"><div class="cn_t_l"></div><div class="cn_t_r"></div></div><div class="article_channel_info">当前位置: <a href="/article/list/1">article</a> > 正文 </div></div><div class="article_title"><h1>相机标定（张正友标定算法）解读与实战三_张正友标定法实战</h1></div><div class="article_info"><div class="article_c_info"> 作者：Cpp五条 | 2024-05-30 09:07:56</div><div class="article_click" style="width: 140px;"><p class="operation-b-img operation-b-img-active"><i class="img-up txclick" attc="upclick" attn="0"></i><span class="num"> 赞</span></p><p class="operation-b-img operation-b-img-active"><i class="img-down txclick" attc="downclick" attn="0"></i><span class="num">踩</span></p></div></div><div class="article_intro">张正友标定法实战</div><div class="article_content article_contentheight"> <link rel="stylesheet" href="https://csdnimg.cn/release/blogv2/dist/mdeditor/css/editerView/kdoc_html_views-1a98987dfd.css"> <link rel="stylesheet" href="https://csdnimg.cn/release/blogv2/dist/mdeditor/css/editerView/ck_htmledit_views-044f2cf1dc.css"> <div id="content_views" class="markdown_views prism-atom-one-dark"> <svg xmlns="http://www.w3.org/2000/svg" style="display: none;"> <path stroke-linecap="round" d="M5,0 0,2.5 5,5z" id="raphael-marker-block" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0);"></path> </svg> <p><a href="https://so.csdn.net/so/search?q=%E7%9B%B8%E6%9C%BA%E6%A0%87%E5%AE%9A&spm=1001.2101.3001.7020" target="_blank" class="hl hl-1" data-report-click="{"spm":"1001.2101.3001.7020","dest":"https://so.csdn.net/so/search?q=%E7%9B%B8%E6%9C%BA%E6%A0%87%E5%AE%9A&spm=1001.2101.3001.7020","extra":"{\"searchword\":\"相机标定\"}"}" data-tit="相机标定" data-pretit="相机标定">相机标定</a>系列</p> <ol><li><a href="https://blog.csdn.net/zhaitianyong/article/details/104816946">相机标定（张正友标定算法）解读与实战一</a></li><li><a href="https://blog.csdn.net/zhaitianyong/article/details/110871030">相机标定（张正友标定算法）解读与实战二</a></li></ol> <p>前两篇文章偏重理论，介绍了针孔相机模型、镜头畸变模型和张氏标定的原理。今天主要讲解代码实现，虽然很多成熟视觉框架已经包含了相机标定，<a href="https://so.csdn.net/so/search?q=opencv&spm=1001.2101.3001.7020" target="_blank" class="hl hl-1" data-report-click="{"spm":"1001.2101.3001.7020","dest":"https://so.csdn.net/so/search?q=opencv&spm=1001.2101.3001.7020","extra":"{\"searchword\":\"opencv\"}"}" data-tit="opencv" data-pretit="opencv">opencv</a> 、matlab、halcon、ros，为了更深入的结合原理，还是有必要自己码一遍。</p> <p><img src="https://img-blog.csdnimg.cn/20201212150646576.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3poYWl0aWFueW9uZw==,size_16,color_FFFFFF,t_70" alt="在这里插入图片描述"></p> <p>这里数据采用OpenCV data 中提供的left 和right标定版图像，我这里用left的，共有13张，棋盘格BorderSize是 9x6，单元格大小SquareSize是 25x25。<br> 用到的库：<br> OpenCV （图像库）<br> Eigen3 （矩阵库）<br> Ceres （算法优化库）<br> 算法实现步骤：</p> <ol><li>提取图像的棋盘格角点 imagePoints</li><li>设置棋盘格角点对应的世界坐标点（z=0) objectPoints</li><li>计算imagePoints 与 objectPoints 对应的单应性矩阵共有13个H</li><li>对H进行分解，构建Vb = 0, 计算B矩阵和内参矩阵K</li><li>根据K计算，每张棋盘格的外参R和t</li><li>把畸变系数也考虑进去构建最优化算法，求出最优K 和畸变系数 k1、k2、k3、p1、p2。</li></ol> <h5><a id="1__29"></a>1. 提取图像的棋盘格角点</h5> <pre data-index="0" class="set-code-hide prettyprint"><code class="prism language-cpp has-numbering" onclick="mdcp.signin(event)" style="position: unset;"><span class="token comment">// 准备数据 13张</span> std<span class="token operator">::</span>vector<span class="token operator"><</span>std<span class="token operator">::</span>string<span class="token operator">></span> files <span class="token operator">=</span> <span class="token punctuation">{</span> <span class="token string">"../data/images/left01.jpg"</span><span class="token punctuation">,</span> <span class="token string">"../data/images/left02.jpg"</span><span class="token punctuation">,</span> <span class="token string">"../data/images/left03.jpg"</span><span class="token punctuation">,</span> <span class="token string">"../data/images/left04.jpg"</span><span class="token punctuation">,</span> <span class="token string">"../data/images/left05.jpg"</span><span class="token punctuation">,</span> <span class="token string">"../data/images/left06.jpg"</span><span class="token punctuation">,</span> <span class="token string">"../data/images/left07.jpg"</span><span class="token punctuation">,</span> <span class="token string">"../data/images/left08.jpg"</span><span class="token punctuation">,</span> <span class="token string">"../data/images/left09.jpg"</span><span class="token punctuation">,</span> <span class="token string">"../data/images/left11.jpg"</span><span class="token punctuation">,</span> <span class="token string">"../data/images/left12.jpg"</span><span class="token punctuation">,</span> <span class="token string">"../data/images/left13.jpg"</span><span class="token punctuation">,</span> <span class="token string">"../data/images/left14.jpg"</span><span class="token punctuation">,</span> <span class="token punctuation">}</span><span class="token punctuation">;</span> <span class="token comment">// 2. 提取棋盘格角点</span> std<span class="token operator">::</span>vector<span class="token operator"><</span>std<span class="token operator">::</span>vector<span class="token operator"><</span>Eigen<span class="token operator">::</span>Vector2d<span class="token operator">>></span> imagePoints<span class="token punctuation">;</span> std<span class="token operator">::</span>vector<span class="token operator"><</span>std<span class="token operator">::</span>vector<span class="token operator"><</span>Eigen<span class="token operator">::</span>Vector3d<span class="token operator">>></span> objectPoints<span class="token punctuation">;</span> cv<span class="token operator">::</span>Size <span class="token function">boardSize</span><span class="token punctuation">(</span><span class="token number">9</span><span class="token punctuation">,</span> <span class="token number">6</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token comment">// 棋盘格大小</span> cv<span class="token operator">::</span>Size2f <span class="token function">squareSize</span><span class="token punctuation">(</span><span class="token number">25.</span><span class="token punctuation">,</span> <span class="token number">25.</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token comment">// 单元格大小，单位mm</span> <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span> i<span class="token operator"><</span>files<span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token operator">++</span>i<span class="token punctuation">)</span> <span class="token punctuation">{</span> cv<span class="token operator">::</span>Mat img <span class="token operator">=</span> cv<span class="token operator">::</span><span class="token function">imread</span><span class="token punctuation">(</span>files<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span> std<span class="token operator">::</span>vector<span class="token operator"><</span>cv<span class="token operator">::</span>Point2f<span class="token operator">></span> corners<span class="token punctuation">;</span> <span class="token keyword">bool</span> ok <span class="token operator">=</span> cv<span class="token operator">::</span><span class="token function">findChessboardCorners</span><span class="token punctuation">(</span>img<span class="token punctuation">,</span> boardSize<span class="token punctuation">,</span> corners<span class="token punctuation">,</span> cv<span class="token operator">::</span>CALIB_CB_ADAPTIVE_THRESH <span class="token operator">|</span> cv<span class="token operator">::</span>CALIB_CB_FAST_CHECK <span class="token operator">|</span> cv<span class="token operator">::</span>CALIB_CB_NORMALIZE_IMAGE<span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token keyword">if</span><span class="token punctuation">(</span>ok<span class="token punctuation">)</span> <span class="token punctuation">{</span> cv<span class="token operator">::</span>Mat gray<span class="token punctuation">;</span> cv<span class="token operator">::</span><span class="token function">cvtColor</span><span class="token punctuation">(</span>img<span class="token punctuation">,</span> gray<span class="token punctuation">,</span> CV_BGR2GRAY<span class="token punctuation">)</span><span class="token punctuation">;</span> cv<span class="token operator">::</span><span class="token function">cornerSubPix</span><span class="token punctuation">(</span>gray<span class="token punctuation">,</span> corners<span class="token punctuation">,</span> cv<span class="token operator">::</span><span class="token function">Size</span><span class="token punctuation">(</span><span class="token number">11</span><span class="token punctuation">,</span> <span class="token number">11</span><span class="token punctuation">)</span><span class="token punctuation">,</span> cv<span class="token operator">::</span><span class="token function">Size</span><span class="token punctuation">(</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">,</span> <span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">,</span> cv<span class="token operator">::</span><span class="token function">TermCriteria</span><span class="token punctuation">(</span>cv<span class="token operator">::</span>TermCriteria<span class="token operator">::</span>EPS <span class="token operator">+</span> cv<span class="token operator">::</span>TermCriteria<span class="token operator">::</span>MAX_ITER<span class="token punctuation">,</span> <span class="token number">30</span><span class="token punctuation">,</span> <span class="token number">0.001</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span> cv<span class="token operator">::</span><span class="token function">drawChessboardCorners</span><span class="token punctuation">(</span>img<span class="token punctuation">,</span> boardSize<span class="token punctuation">,</span> cv<span class="token operator">::</span><span class="token function">Mat</span><span class="token punctuation">(</span>corners<span class="token punctuation">)</span><span class="token punctuation">,</span> ok<span class="token punctuation">)</span><span class="token punctuation">;</span> cv<span class="token operator">::</span><span class="token function">imshow</span><span class="token punctuation">(</span><span class="token string">"corners"</span><span class="token punctuation">,</span> img<span class="token punctuation">)</span><span class="token punctuation">;</span> cv<span class="token operator">::</span><span class="token function">waitKey</span><span class="token punctuation">(</span><span class="token number">100</span><span class="token punctuation">)</span><span class="token punctuation">;</span> std<span class="token operator">::</span>vector<span class="token operator"><</span>Eigen<span class="token operator">::</span>Vector2d<span class="token operator">></span> _corners<span class="token punctuation">;</span> <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">auto</span><span class="token operator">&</span> pt<span class="token operator">:</span> corners<span class="token punctuation">)</span><span class="token punctuation">{</span> _corners<span class="token punctuation">.</span><span class="token function">push_back</span><span class="token punctuation">(</span>Eigen<span class="token operator">::</span><span class="token function">Vector2d</span><span class="token punctuation">(</span>pt<span class="token punctuation">.</span>x<span class="token punctuation">,</span> pt<span class="token punctuation">.</span>y<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token punctuation">}</span> imagePoints<span class="token punctuation">.</span><span class="token function">push_back</span><span class="token punctuation">(</span>_corners<span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> <div class="hljs-button signin active" data-title="登录复制" data-report-click="{"spm":"1001.2101.3001.4334"}"></div></code><div class="hide-preCode-box"><span class="hide-preCode-bt" data-report-view="{"spm":"1001.2101.3001.7365"}"><img class="look-more-preCode contentImg-no-view" src="https://csdnimg.cn/release/blogv2/dist/pc/img/newCodeMoreWhite.png" alt="" title=""></span></div><ul class="pre-numbering" style=""><li style="color: rgb(153, 153, 153);">1</li><li style="color: rgb(153, 153, 153);">2</li><li style="color: rgb(153, 153, 153);">3</li><li style="color: rgb(153, 153, 153);">4</li><li style="color: rgb(153, 153, 153);">5</li><li style="color: rgb(153, 153, 153);">6</li><li style="color: rgb(153, 153, 153);">7</li><li style="color: rgb(153, 153, 153);">8</li><li style="color: rgb(153, 153, 153);">9</li><li style="color: rgb(153, 153, 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operator"><</span>imagePoints<span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token operator">++</span>i<span class="token punctuation">)</span><span class="token punctuation">{</span> std<span class="token operator">::</span>vector<span class="token operator"><</span>Eigen<span class="token operator">::</span>Vector3d<span class="token operator">></span> corners<span class="token punctuation">;</span> <span class="token function">getObjectPoints</span><span class="token punctuation">(</span>boardSize<span class="token punctuation">,</span> squareSize<span class="token punctuation">,</span> corners<span class="token punctuation">)</span><span class="token punctuation">;</span> objectPoints<span class="token punctuation">.</span><span class="token function">push_back</span><span class="token punctuation">(</span>corners<span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token keyword">void</span> <span class="token function">getObjectPoints</span><span class="token punctuation">(</span><span class="token keyword">const</span> cv<span class="token operator">::</span>Size<span class="token operator">&</span> borderSize<span class="token punctuation">,</span> <span class="token keyword">const</span> cv<span class="token operator">::</span>Size2f<span class="token operator">&</span> squareSize<span class="token punctuation">,</span> std<span class="token operator">::</span>vector<span class="token operator"><</span>Eigen<span class="token operator">::</span>Vector3d<span class="token operator">></span><span class="token operator">&</span> objectPoints<span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> r<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span> r<span class="token operator"><</span>borderSize<span class="token punctuation">.</span>height<span class="token punctuation">;</span> <span class="token operator">++</span>r<span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> c<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span> c<span class="token operator"><</span>borderSize<span class="token punctuation">.</span>width<span class="token punctuation">;</span> <span class="token operator">++</span>c<span class="token punctuation">)</span> <span class="token punctuation">{</span> objectPoints<span class="token punctuation">.</span><span class="token function">push_back</span><span class="token punctuation">(</span>Eigen<span class="token operator">::</span><span class="token function">Vector3d</span><span class="token punctuation">(</span>c<span class="token operator">*</span>squareSize<span class="token punctuation">.</span>width<span class="token punctuation">,</span> r<span class="token operator">*</span>squareSize<span class="token punctuation">.</span>height<span class="token punctuation">,</span> <span class="token number">0.</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> <div class="hljs-button signin active" data-title="登录复制" data-report-click="{"spm":"1001.2101.3001.4334"}"></div></code><ul class="pre-numbering" style=""><li style="color: rgb(153, 153, 153);">1</li><li style="color: rgb(153, 153, 153);">2</li><li style="color: rgb(153, 153, 153);">3</li><li style="color: rgb(153, 153, 153);">4</li><li style="color: rgb(153, 153, 153);">5</li><li style="color: rgb(153, 153, 153);">6</li><li style="color: rgb(153, 153, 153);">7</li><li style="color: rgb(153, 153, 153);">8</li><li style="color: rgb(153, 153, 153);">9</li><li style="color: rgb(153, 153, 153);">10</li><li style="color: rgb(153, 153, 153);">11</li><li style="color: rgb(153, 153, 153);">12</li><li style="color: rgb(153, 153, 153);">13</li><li style="color: rgb(153, 153, 153);">14</li></ul></pre> <h5><a id="3_imagePoints__objectPoints__95"></a>3. 计算imagePoints 与 objectPoints 对应的单应性矩阵</h5> <p>之前已经写过关于单应性矩阵的求解DLP算法，具体代码中已经包含。这里直接贴出来OpenCV求解</p> <pre data-index="2" class="set-code-show prettyprint"><code class="prism language-cpp has-numbering" onclick="mdcp.signin(event)" style="position: unset;"><span class="token keyword">bool</span> <span class="token function">findHomographyByOpenCV</span><span class="token punctuation">(</span>std<span class="token operator">::</span>vector<span class="token operator"><</span>Eigen<span class="token operator">::</span>Vector2d<span class="token operator">></span><span class="token operator">&</span> srcPoints<span class="token punctuation">,</span> std<span class="token operator">::</span>vector<span class="token operator"><</span>Eigen<span class="token operator">::</span>Vector2d<span class="token operator">></span><span class="token operator">&</span> dstPoints<span class="token punctuation">,</span> Eigen<span class="token operator">::</span>Matrix3d<span class="token operator">&</span> H<span class="token punctuation">)</span> <span class="token punctuation">{</span> std<span class="token operator">::</span>vector<span class="token operator"><</span>cv<span class="token operator">::</span>Point2f<span class="token operator">></span> objectPoints<span class="token punctuation">,</span> imagePoints<span class="token punctuation">;</span> <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span> i<span class="token operator"><</span>srcPoints<span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token operator">++</span>i<span class="token punctuation">)</span> <span class="token punctuation">{</span> objectPoints<span class="token punctuation">.</span><span class="token function">push_back</span><span class="token punctuation">(</span>cv<span class="token operator">::</span><span class="token function">Point2f</span><span class="token punctuation">(</span>srcPoints<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">,</span> srcPoints<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span> imagePoints<span class="token punctuation">.</span><span class="token function">push_back</span><span class="token punctuation">(</span>cv<span class="token operator">::</span><span class="token function">Point2f</span><span class="token punctuation">(</span>dstPoints<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">,</span> dstPoints<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token punctuation">}</span> cv<span class="token operator">::</span>Mat hMat <span class="token operator">=</span> <span class="token function">findHomography</span><span class="token punctuation">(</span>objectPoints<span class="token punctuation">,</span> imagePoints<span class="token punctuation">,</span> cv<span class="token operator">::</span>RANSAC<span class="token punctuation">)</span><span class="token punctuation">;</span> cv<span class="token operator">::</span><span class="token function">cv2eigen</span><span class="token punctuation">(</span>hMat<span class="token punctuation">,</span> H<span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token punctuation">}</span> <div class="hljs-button signin active" data-title="登录复制" data-report-click="{"spm":"1001.2101.3001.4334"}"></div></code><ul class="pre-numbering" style=""><li style="color: rgb(153, 153, 153);">1</li><li style="color: rgb(153, 153, 153);">2</li><li style="color: rgb(153, 153, 153);">3</li><li style="color: rgb(153, 153, 153);">4</li><li style="color: rgb(153, 153, 153);">5</li><li style="color: rgb(153, 153, 153);">6</li><li style="color: rgb(153, 153, 153);">7</li><li style="color: rgb(153, 153, 153);">8</li><li style="color: rgb(153, 153, 153);">9</li><li style="color: rgb(153, 153, 153);">10</li><li style="color: rgb(153, 153, 153);">11</li><li style="color: rgb(153, 153, 153);">12</li><li style="color: rgb(153, 153, 153);">13</li><li style="color: rgb(153, 153, 153);">14</li></ul></pre> <h5><a id="4_HVb__0_BK_115"></a>4. 对H进行分解，构建Vb = 0, 计算B矩阵并求解K内参矩阵</h5> <pre data-index="3" class="set-code-hide prettyprint"><code class="prism language-cpp has-numbering" onclick="mdcp.signin(event)" style="position: unset;"><span class="token comment">/** * Vij=[hi1hj1 hi1hj2+hi2hj1 hi2hj2 hi3hj1+hi1hj3 hi3hj2+hi2hj3 hi3hj3] * @param H * @param i * @param j * @return */</span> VectorXd <span class="token function">getVector</span><span class="token punctuation">(</span><span class="token keyword">const</span> Matrix3d<span class="token operator">&</span> H<span class="token punctuation">,</span> <span class="token keyword">int</span> i<span class="token punctuation">,</span> <span class="token keyword">int</span> j<span class="token punctuation">)</span> <span class="token punctuation">{</span> i <span class="token operator">-</span><span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> j <span class="token operator">-</span><span class="token operator">=</span> <span class="token number">1</span><span class="token punctuation">;</span> VectorXd <span class="token function">v</span><span class="token punctuation">(</span><span class="token number">6</span><span class="token punctuation">)</span><span class="token punctuation">;</span> v <span class="token operator"><<</span> <span class="token function">H</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span> i<span class="token punctuation">)</span><span class="token operator">*</span><span class="token function">H</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span> j<span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token function">H</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span> i<span class="token punctuation">)</span><span class="token operator">*</span><span class="token function">H</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">,</span> j<span class="token punctuation">)</span> <span class="token operator">+</span> <span class="token function">H</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">,</span> i<span class="token punctuation">)</span><span class="token operator">*</span><span class="token function">H</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span> j<span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token function">H</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">,</span> i<span class="token punctuation">)</span><span class="token operator">*</span><span class="token function">H</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">,</span> j<span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token function">H</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token punctuation">,</span> i<span class="token punctuation">)</span><span class="token operator">*</span><span class="token function">H</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span> j<span class="token punctuation">)</span> <span class="token operator">+</span> <span class="token function">H</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span> i<span class="token punctuation">)</span><span class="token operator">*</span><span class="token function">H</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token punctuation">,</span> j<span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token function">H</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token punctuation">,</span> i<span class="token punctuation">)</span><span class="token operator">*</span><span class="token function">H</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">,</span> j<span class="token punctuation">)</span> <span class="token operator">+</span> <span class="token function">H</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">,</span> i<span class="token punctuation">)</span><span class="token operator">*</span><span class="token function">H</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token punctuation">,</span> j<span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token function">H</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token punctuation">,</span> i<span class="token punctuation">)</span><span class="token operator">*</span><span class="token function">H</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token punctuation">,</span> j<span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token keyword">return</span> v<span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token comment">/** * * 计算相机内参初始值, 求解Vb =0; 并计算K矩阵 * */</span> Matrix3d <span class="token function">solveInitCameraIntrinsic</span><span class="token punctuation">(</span>std<span class="token operator">::</span>vector<span class="token operator"><</span>Matrix3d<span class="token operator">></span><span class="token operator">&</span> homos<span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">int</span> n <span class="token operator">=</span> homos<span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token comment">// Vb = 0</span> MatrixXd <span class="token function">V</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token operator">*</span>n<span class="token punctuation">,</span> <span class="token number">6</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span> i<span class="token operator"><</span>n<span class="token punctuation">;</span> <span class="token operator">++</span>i<span class="token punctuation">)</span> <span class="token punctuation">{</span> VectorXd v1 <span class="token operator">=</span> <span class="token function">getVector</span><span class="token punctuation">(</span>homos<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">2</span><span class="token punctuation">)</span><span class="token punctuation">;</span> VectorXd v11 <span class="token operator">=</span> <span class="token function">getVector</span><span class="token punctuation">(</span>homos<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span> VectorXd v22 <span class="token operator">=</span> <span class="token function">getVector</span><span class="token punctuation">(</span>homos<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">,</span> <span class="token number">2</span><span class="token punctuation">,</span> <span class="token number">2</span><span class="token punctuation">)</span><span class="token punctuation">;</span> VectorXd v2 <span class="token operator">=</span> v11 <span class="token operator">-</span> v22<span class="token punctuation">;</span> <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> j<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span> j<span class="token operator"><</span><span class="token number">6</span><span class="token punctuation">;</span> <span class="token operator">++</span>j<span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token function">V</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token operator">*</span>i<span class="token punctuation">,</span> j<span class="token punctuation">)</span> <span class="token operator">=</span> <span class="token function">v1</span><span class="token punctuation">(</span>j<span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token function">V</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token operator">*</span>i<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">,</span> j<span class="token punctuation">)</span> <span class="token operator">=</span> <span class="token function">v2</span><span class="token punctuation">(</span>j<span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> <span class="token comment">//SVD 分解</span> JacobiSVD<span class="token operator"><</span>MatrixXd<span class="token operator">></span> svdSolver <span class="token punctuation">(</span>V<span class="token punctuation">,</span> ComputeThinV<span class="token punctuation">)</span><span class="token punctuation">;</span> MatrixXd v <span class="token operator">=</span> svdSolver<span class="token punctuation">.</span><span class="token function">matrixV</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span> MatrixXd b <span class="token operator">=</span> v<span class="token punctuation">.</span><span class="token function">rightCols</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span> std<span class="token operator">::</span>cout <span class="token operator"><<</span><span class="token string">"b = "</span> <span class="token operator"><<</span> b <span class="token operator"><<</span> std<span class="token operator">::</span>endl<span class="token punctuation">;</span> <span class="token comment">// 求解内参 fx fy c uo v0</span> <span class="token keyword">double</span> B11 <span class="token operator">=</span> <span class="token function">b</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">,</span> B12 <span class="token operator">=</span> <span class="token function">b</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">,</span> B22 <span class="token operator">=</span> <span class="token function">b</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token punctuation">)</span><span class="token punctuation">,</span> B13 <span class="token operator">=</span> <span class="token function">b</span><span class="token punctuation">(</span><span class="token number">3</span><span class="token punctuation">)</span><span class="token punctuation">,</span> B23 <span class="token operator">=</span> <span class="token function">b</span><span class="token punctuation">(</span><span class="token number">4</span><span class="token punctuation">)</span><span class="token punctuation">,</span> B33 <span class="token operator">=</span> <span class="token function">b</span><span class="token punctuation">(</span><span class="token number">5</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token keyword">double</span> v0 <span class="token operator">=</span> <span class="token punctuation">(</span>B12<span class="token operator">*</span>B13<span class="token operator">-</span>B11<span class="token operator">*</span>B23<span class="token punctuation">)</span> <span class="token operator">/</span> <span class="token punctuation">(</span>B11<span class="token operator">*</span>B22<span class="token operator">-</span>B12<span class="token operator">*</span>B12<span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token keyword">double</span> s <span class="token operator">=</span> B33<span class="token operator">-</span><span class="token punctuation">(</span>B13<span class="token operator">*</span>B13<span class="token operator">+</span>v0<span class="token operator">*</span><span class="token punctuation">(</span>B12<span class="token operator">*</span>B13<span class="token operator">-</span>B11<span class="token operator">*</span>B23<span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token operator">/</span> B11<span class="token punctuation">;</span> <span class="token keyword">double</span> fx <span class="token operator">=</span> <span class="token function">sqrt</span><span class="token punctuation">(</span>s<span class="token operator">/</span>B11<span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token keyword">double</span> fy <span class="token operator">=</span> <span class="token function">sqrt</span><span class="token punctuation">(</span>s<span class="token operator">*</span>B11 <span class="token operator">/</span> <span class="token punctuation">(</span>B11<span class="token operator">*</span>B22<span class="token operator">-</span>B12<span class="token operator">*</span>B12<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token keyword">double</span> c <span class="token operator">=</span> <span class="token operator">-</span>B12<span class="token operator">*</span>fx<span class="token operator">*</span>fx<span class="token operator">*</span>fy<span class="token operator">/</span>s<span class="token punctuation">;</span> <span class="token keyword">double</span> u0 <span class="token operator">=</span> c<span class="token operator">*</span>v0<span class="token operator">/</span>fx <span class="token operator">-</span> B13<span class="token operator">*</span>fx<span class="token operator">*</span>fx<span class="token operator">/</span>s<span class="token punctuation">;</span> Matrix3d K<span class="token punctuation">;</span> K <span class="token operator"><<</span> fx<span class="token punctuation">,</span> c<span class="token punctuation">,</span> u0<span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> fy<span class="token punctuation">,</span> v0<span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">;</span> <span class="token keyword">return</span> K<span class="token punctuation">;</span> <span class="token punctuation">}</span> <div class="hljs-button signin active" data-title="登录复制" data-report-click="{"spm":"1001.2101.3001.4334"}"></div></code><div class="hide-preCode-box"><span class="hide-preCode-bt" data-report-view="{"spm":"1001.2101.3001.7365"}"><img class="look-more-preCode contentImg-no-view" src="https://csdnimg.cn/release/blogv2/dist/pc/img/newCodeMoreWhite.png" alt="" title=""></span></div><ul class="pre-numbering" style=""><li style="color: rgb(153, 153, 153);">1</li><li style="color: rgb(153, 153, 153);">2</li><li style="color: rgb(153, 153, 153);">3</li><li style="color: rgb(153, 153, 153);">4</li><li style="color: rgb(153, 153, 153);">5</li><li style="color: rgb(153, 153, 153);">6</li><li style="color: rgb(153, 153, 153);">7</li><li style="color: rgb(153, 153, 153);">8</li><li style="color: rgb(153, 153, 153);">9</li><li style="color: rgb(153, 153, 153);">10</li><li style="color: rgb(153, 153, 153);">11</li><li style="color: rgb(153, 153, 153);">12</li><li style="color: rgb(153, 153, 153);">13</li><li style="color: rgb(153, 153, 153);">14</li><li style="color: rgb(153, 153, 153);">15</li><li style="color: rgb(153, 153, 153);">16</li><li style="color: rgb(153, 153, 153);">17</li><li style="color: rgb(153, 153, 153);">18</li><li style="color: rgb(153, 153, 153);">19</li><li style="color: rgb(153, 153, 153);">20</li><li style="color: rgb(153, 153, 153);">21</li><li style="color: rgb(153, 153, 153);">22</li><li style="color: rgb(153, 153, 153);">23</li><li style="color: rgb(153, 153, 153);">24</li><li style="color: rgb(153, 153, 153);">25</li><li style="color: rgb(153, 153, 153);">26</li><li style="color: rgb(153, 153, 153);">27</li><li style="color: rgb(153, 153, 153);">28</li><li style="color: rgb(153, 153, 153);">29</li><li style="color: rgb(153, 153, 153);">30</li><li style="color: rgb(153, 153, 153);">31</li><li style="color: rgb(153, 153, 153);">32</li><li style="color: rgb(153, 153, 153);">33</li><li style="color: rgb(153, 153, 153);">34</li><li style="color: rgb(153, 153, 153);">35</li><li style="color: rgb(153, 153, 153);">36</li><li style="color: rgb(153, 153, 153);">37</li><li style="color: rgb(153, 153, 153);">38</li><li style="color: rgb(153, 153, 153);">39</li><li style="color: rgb(153, 153, 153);">40</li><li style="color: rgb(153, 153, 153);">41</li><li style="color: rgb(153, 153, 153);">42</li><li style="color: rgb(153, 153, 153);">43</li><li style="color: rgb(153, 153, 153);">44</li><li style="color: rgb(153, 153, 153);">45</li><li style="color: rgb(153, 153, 153);">46</li><li style="color: rgb(153, 153, 153);">47</li><li style="color: rgb(153, 153, 153);">48</li><li style="color: rgb(153, 153, 153);">49</li><li style="color: rgb(153, 153, 153);">50</li><li style="color: rgb(153, 153, 153);">51</li><li style="color: rgb(153, 153, 153);">52</li><li style="color: rgb(153, 153, 153);">53</li><li style="color: rgb(153, 153, 153);">54</li><li style="color: rgb(153, 153, 153);">55</li><li style="color: rgb(153, 153, 153);">56</li><li style="color: rgb(153, 153, 153);">57</li><li style="color: rgb(153, 153, 153);">58</li><li style="color: rgb(153, 153, 153);">59</li><li style="color: rgb(153, 153, 153);">60</li><li style="color: rgb(153, 153, 153);">61</li><li style="color: rgb(153, 153, 153);">62</li><li style="color: rgb(153, 153, 153);">63</li><li style="color: rgb(153, 153, 153);">64</li><li style="color: rgb(153, 153, 153);">65</li></ul></pre> <h5><a id="5_KRt_185"></a>5. 根据K计算，每张棋盘格的外参R和t</h5> <pre data-index="4" class="set-code-hide prettyprint"><code class="prism language-cpp has-numbering" onclick="mdcp.signin(event)" style="position: unset;"><span class="token comment">/** * * 计算相机外参初始值 */</span> <span class="token keyword">void</span> <span class="token function">solveInitCameraExtrinsic</span><span class="token punctuation">(</span>std<span class="token operator">::</span>vector<span class="token operator"><</span>Matrix3d<span class="token operator">></span><span class="token operator">&</span> homos<span class="token punctuation">,</span> Matrix3d<span class="token operator">&</span> K<span class="token punctuation">,</span> std<span class="token operator">::</span>vector<span class="token operator"><</span>Matrix3d<span class="token operator">></span><span class="token operator">&</span> RList<span class="token punctuation">,</span> std<span class="token operator">::</span>vector<span class="token operator"><</span>Vector3d<span class="token operator">></span><span class="token operator">&</span> tList<span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">int</span> n <span class="token operator">=</span> homos<span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span> Matrix3d kInv <span class="token operator">=</span> K<span class="token punctuation">.</span><span class="token function">inverse</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token keyword">for</span> <span class="token punctuation">(</span><span class="token keyword">int</span> i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span> i<span class="token operator"><</span>n<span class="token punctuation">;</span> <span class="token operator">++</span>i<span class="token punctuation">)</span> <span class="token punctuation">{</span> Vector3d r0<span class="token punctuation">,</span> r1<span class="token punctuation">,</span> r2<span class="token punctuation">;</span> r0 <span class="token operator">=</span> kInv<span class="token operator">*</span>homos<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">.</span><span class="token function">col</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">;</span> r1 <span class="token operator">=</span> kInv<span class="token operator">*</span>homos<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">.</span><span class="token function">col</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token keyword">double</span> s0 <span class="token operator">=</span> <span class="token function">sqrt</span><span class="token punctuation">(</span>r0<span class="token punctuation">.</span><span class="token function">dot</span><span class="token punctuation">(</span>r0<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token keyword">double</span> s1 <span class="token operator">=</span> <span class="token function">sqrt</span><span class="token punctuation">(</span>r1<span class="token punctuation">.</span><span class="token function">dot</span><span class="token punctuation">(</span>r1<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span> r0<span class="token punctuation">.</span><span class="token function">array</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">col</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span> <span class="token operator">/</span><span class="token operator">=</span> s0<span class="token punctuation">;</span> r1<span class="token punctuation">.</span><span class="token function">array</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">col</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span> <span class="token operator">/</span><span class="token operator">=</span> s1<span class="token punctuation">;</span> r2 <span class="token operator">=</span> r0<span class="token punctuation">.</span><span class="token function">cross</span><span class="token punctuation">(</span>r1<span class="token punctuation">)</span><span class="token punctuation">;</span> Vector3d t <span class="token operator">=</span> kInv<span class="token operator">*</span>homos<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">.</span><span class="token function">col</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token punctuation">)</span> <span class="token operator">/</span> s0<span class="token punctuation">;</span> Matrix3d R<span class="token punctuation">;</span> R<span class="token punctuation">.</span><span class="token function">array</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">col</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span> <span class="token operator">=</span> r0<span class="token punctuation">;</span> R<span class="token punctuation">.</span><span class="token function">array</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">col</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span> <span class="token operator">=</span> r1<span class="token punctuation">;</span> R<span class="token punctuation">.</span><span class="token function">array</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">.</span><span class="token function">col</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token punctuation">)</span> <span class="token operator">=</span> r2<span class="token punctuation">;</span> std<span class="token operator">::</span>cout <span class="token operator"><<</span><span class="token string">"R "</span> <span class="token operator"><<</span> R <span class="token operator"><<</span> std<span class="token operator">::</span>endl<span class="token punctuation">;</span> std<span class="token operator">::</span>cout <span class="token operator"><<</span><span class="token string">"t "</span> <span class="token operator"><<</span> t<span class="token punctuation">.</span><span class="token function">transpose</span><span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token operator"><<</span> std<span class="token operator">::</span>endl<span class="token punctuation">;</span> RList<span class="token punctuation">.</span><span class="token function">push_back</span><span class="token punctuation">(</span>R<span class="token punctuation">)</span><span class="token punctuation">;</span> tList<span class="token punctuation">.</span><span class="token function">push_back</span><span class="token punctuation">(</span>t<span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> <div class="hljs-button signin active" data-title="登录复制" data-report-click="{"spm":"1001.2101.3001.4334"}"></div></code><div class="hide-preCode-box"><span class="hide-preCode-bt" data-report-view="{"spm":"1001.2101.3001.7365"}"><img class="look-more-preCode contentImg-no-view" src="https://csdnimg.cn/release/blogv2/dist/pc/img/newCodeMoreWhite.png" alt="" title=""></span></div><ul class="pre-numbering" style=""><li style="color: rgb(153, 153, 153);">1</li><li style="color: rgb(153, 153, 153);">2</li><li style="color: rgb(153, 153, 153);">3</li><li style="color: rgb(153, 153, 153);">4</li><li style="color: rgb(153, 153, 153);">5</li><li style="color: rgb(153, 153, 153);">6</li><li style="color: rgb(153, 153, 153);">7</li><li style="color: rgb(153, 153, 153);">8</li><li style="color: rgb(153, 153, 153);">9</li><li style="color: rgb(153, 153, 153);">10</li><li style="color: rgb(153, 153, 153);">11</li><li style="color: rgb(153, 153, 153);">12</li><li style="color: rgb(153, 153, 153);">13</li><li style="color: rgb(153, 153, 153);">14</li><li style="color: rgb(153, 153, 153);">15</li><li style="color: rgb(153, 153, 153);">16</li><li style="color: rgb(153, 153, 153);">17</li><li style="color: rgb(153, 153, 153);">18</li><li style="color: rgb(153, 153, 153);">19</li><li style="color: rgb(153, 153, 153);">20</li><li style="color: rgb(153, 153, 153);">21</li><li style="color: rgb(153, 153, 153);">22</li><li style="color: rgb(153, 153, 153);">23</li><li style="color: rgb(153, 153, 153);">24</li><li style="color: rgb(153, 153, 153);">25</li><li style="color: rgb(153, 153, 153);">26</li><li style="color: rgb(153, 153, 153);">27</li><li style="color: rgb(153, 153, 153);">28</li><li style="color: rgb(153, 153, 153);">29</li><li style="color: rgb(153, 153, 153);">30</li><li style="color: rgb(153, 153, 153);">31</li><li style="color: rgb(153, 153, 153);">32</li><li style="color: rgb(153, 153, 153);">33</li><li style="color: rgb(153, 153, 153);">34</li><li style="color: rgb(153, 153, 153);">35</li></ul></pre> <h5><a id="6__225"></a>6. 构建最优化目标函数</h5> <p>求出最优K 和畸变系数 k1、k2、k3、p1、p2以及外参。</p> <p>上面计算出的K,和13个外参 R和t作为最优化的初始值。<br> 优化框架采用ceres优化框架，首先要编写优化结构体 PROJECT_COST:</p> <pre data-index="5" class="set-code-hide prettyprint"><code class="prism language-cpp has-numbering" onclick="mdcp.signin(event)" style="position: unset;"><span class="token keyword">struct</span> PROJECT_COST <span class="token punctuation">{</span> Eigen<span class="token operator">::</span>Vector3d objPt<span class="token punctuation">;</span> Eigen<span class="token operator">::</span>Vector2d imgPt<span class="token punctuation">;</span> <span class="token function">PROJECT_COST</span><span class="token punctuation">(</span>Eigen<span class="token operator">::</span>Vector3d<span class="token operator">&</span> objPt<span class="token punctuation">,</span> Eigen<span class="token operator">::</span>Vector2d<span class="token operator">&</span> imgPt<span class="token punctuation">)</span><span class="token operator">:</span><span class="token function">objPt</span><span class="token punctuation">(</span>objPt<span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token function">imgPt</span><span class="token punctuation">(</span>imgPt<span class="token punctuation">)</span> <span class="token punctuation">{</span><span class="token punctuation">}</span> <span class="token keyword">template</span><span class="token operator"><</span><span class="token keyword">typename</span> T<span class="token operator">></span> <span class="token keyword">bool</span> <span class="token keyword">operator</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">(</span> <span class="token keyword">const</span> T <span class="token operator">*</span><span class="token keyword">const</span> k<span class="token punctuation">,</span> <span class="token keyword">const</span> T <span class="token operator">*</span><span class="token keyword">const</span> r<span class="token punctuation">,</span> <span class="token keyword">const</span> T <span class="token operator">*</span><span class="token keyword">const</span> t<span class="token punctuation">,</span> T<span class="token operator">*</span> residuals<span class="token punctuation">)</span><span class="token keyword">const</span> <span class="token punctuation">{</span> T pos3d<span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">{</span><span class="token function">T</span><span class="token punctuation">(</span><span class="token function">objPt</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token function">T</span><span class="token punctuation">(</span><span class="token function">objPt</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token function">T</span><span class="token punctuation">(</span><span class="token function">objPt</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">}</span><span class="token punctuation">;</span> T pos3d_proj<span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">]</span><span class="token punctuation">;</span> <span class="token comment">// 旋转</span> ceres<span class="token operator">::</span><span class="token function">AngleAxisRotatePoint</span><span class="token punctuation">(</span>r<span class="token punctuation">,</span> pos3d<span class="token punctuation">,</span> pos3d_proj<span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token comment">// 平移</span> pos3d_proj<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span> <span class="token operator">+</span><span class="token operator">=</span> t<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">;</span> pos3d_proj<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">+</span><span class="token operator">=</span> t<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">;</span> pos3d_proj<span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">]</span> <span class="token operator">+</span><span class="token operator">=</span> t<span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">]</span><span class="token punctuation">;</span> T xp <span class="token operator">=</span> pos3d_proj<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span> <span class="token operator">/</span> pos3d_proj<span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">]</span><span class="token punctuation">;</span> T yp <span class="token operator">=</span> pos3d_proj<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">/</span> pos3d_proj<span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">]</span><span class="token punctuation">;</span> <span class="token keyword">const</span> T<span class="token operator">&</span> fx <span class="token operator">=</span> k<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">;</span> <span class="token keyword">const</span> T<span class="token operator">&</span> fy <span class="token operator">=</span> k<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">;</span> <span class="token keyword">const</span> T<span class="token operator">&</span> cx <span class="token operator">=</span> k<span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">]</span><span class="token punctuation">;</span> <span class="token keyword">const</span> T<span class="token operator">&</span> cy <span class="token operator">=</span> k<span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">]</span><span class="token punctuation">;</span> <span class="token keyword">const</span> T<span class="token operator">&</span> k1 <span class="token operator">=</span> k<span class="token punctuation">[</span><span class="token number">4</span><span class="token punctuation">]</span><span class="token punctuation">;</span> <span class="token keyword">const</span> T<span class="token operator">&</span> k2 <span class="token operator">=</span> k<span class="token punctuation">[</span><span class="token number">5</span><span class="token punctuation">]</span><span class="token punctuation">;</span> <span class="token keyword">const</span> T<span class="token operator">&</span> k3 <span class="token operator">=</span> k<span class="token punctuation">[</span><span class="token number">6</span><span class="token punctuation">]</span><span class="token punctuation">;</span> <span class="token keyword">const</span> T<span class="token operator">&</span> p1 <span class="token operator">=</span> k<span class="token punctuation">[</span><span class="token number">7</span><span class="token punctuation">]</span><span class="token punctuation">;</span> <span class="token keyword">const</span> T<span class="token operator">&</span> p2 <span class="token operator">=</span> k<span class="token punctuation">[</span><span class="token number">8</span><span class="token punctuation">]</span><span class="token punctuation">;</span> T r_2 <span class="token operator">=</span> xp<span class="token operator">*</span>xp <span class="token operator">+</span> yp<span class="token operator">*</span>yp<span class="token punctuation">;</span> <span class="token comment">/* // 径向畸变 T xdis = xp*(T(1.) + k1*r_2 + k2*r_2*r_2 + k3*r_2*r_2*r_2); T ydis = yp*(T(1.) + k1*r_2 + k2*r_2*r_2 + k3*r_2*r_2*r_2); // 切向畸变 xdis = xdis + T(2.)*p1*xp*yp + p2*(r_2 + T(2.)*xp*xp); ydis = ydis + p1*(r_2 + T(2.)*yp*yp) + T(2.)*p2*xp*yp; */</span> <span class="token comment">// 径向畸变和切向畸变</span> T xdis <span class="token operator">=</span> xp<span class="token operator">*</span><span class="token punctuation">(</span><span class="token function">T</span><span class="token punctuation">(</span><span class="token number">1.</span><span class="token punctuation">)</span> <span class="token operator">+</span> k1<span class="token operator">*</span>r_2 <span class="token operator">+</span> k2<span class="token operator">*</span>r_2<span class="token operator">*</span>r_2 <span class="token operator">+</span> k3<span class="token operator">*</span>r_2<span class="token operator">*</span>r_2<span class="token operator">*</span>r_2<span class="token punctuation">)</span> <span class="token operator">+</span> <span class="token function">T</span><span class="token punctuation">(</span><span class="token number">2.</span><span class="token punctuation">)</span><span class="token operator">*</span>p1<span class="token operator">*</span>xp<span class="token operator">*</span>yp <span class="token operator">+</span> p2<span class="token operator">*</span><span class="token punctuation">(</span>r_2 <span class="token operator">+</span> <span class="token function">T</span><span class="token punctuation">(</span><span class="token number">2.</span><span class="token punctuation">)</span><span class="token operator">*</span>xp<span class="token operator">*</span>xp<span class="token punctuation">)</span><span class="token punctuation">;</span> T ydis <span class="token operator">=</span> yp<span class="token operator">*</span><span class="token punctuation">(</span><span class="token function">T</span><span class="token punctuation">(</span><span class="token number">1.</span><span class="token punctuation">)</span> <span class="token operator">+</span> k1<span class="token operator">*</span>r_2 <span class="token operator">+</span> k2<span class="token operator">*</span>r_2<span class="token operator">*</span>r_2 <span class="token operator">+</span> k3<span class="token operator">*</span>r_2<span class="token operator">*</span>r_2<span class="token operator">*</span>r_2<span class="token punctuation">)</span> <span class="token operator">+</span> p1<span class="token operator">*</span><span class="token punctuation">(</span>r_2 <span class="token operator">+</span> <span class="token function">T</span><span class="token punctuation">(</span><span class="token number">2.</span><span class="token punctuation">)</span><span class="token operator">*</span>yp<span class="token operator">*</span>yp<span class="token punctuation">)</span> <span class="token operator">+</span> <span class="token function">T</span><span class="token punctuation">(</span><span class="token number">2.</span><span class="token punctuation">)</span><span class="token operator">*</span>p2<span class="token operator">*</span>xp<span class="token operator">*</span>yp<span class="token punctuation">;</span> <span class="token comment">// 像素距离</span> T u <span class="token operator">=</span> fx<span class="token operator">*</span>xdis <span class="token operator">+</span> cx<span class="token punctuation">;</span> T v <span class="token operator">=</span> fy<span class="token operator">*</span>ydis <span class="token operator">+</span> cy<span class="token punctuation">;</span> residuals<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span> <span class="token operator">=</span> u <span class="token operator">-</span> <span class="token function">T</span><span class="token punctuation">(</span>imgPt<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span> residuals<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">=</span> v <span class="token operator">-</span> <span class="token function">T</span><span class="token punctuation">(</span>imgPt<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token keyword">return</span> <span class="token boolean">true</span><span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span><span class="token punctuation">;</span> <div class="hljs-button signin active" data-title="登录复制" data-report-click="{"spm":"1001.2101.3001.4334"}"></div></code><div class="hide-preCode-box"><span class="hide-preCode-bt" data-report-view="{"spm":"1001.2101.3001.7365"}"><img class="look-more-preCode contentImg-no-view" src="https://csdnimg.cn/release/blogv2/dist/pc/img/newCodeMoreWhite.png" alt="" title=""></span></div><ul class="pre-numbering" style=""><li style="color: rgb(153, 153, 153);">1</li><li style="color: rgb(153, 153, 153);">2</li><li style="color: rgb(153, 153, 153);">3</li><li style="color: rgb(153, 153, 153);">4</li><li style="color: rgb(153, 153, 153);">5</li><li style="color: rgb(153, 153, 153);">6</li><li style="color: rgb(153, 153, 153);">7</li><li style="color: rgb(153, 153, 153);">8</li><li style="color: rgb(153, 153, 153);">9</li><li style="color: rgb(153, 153, 153);">10</li><li style="color: rgb(153, 153, 153);">11</li><li style="color: rgb(153, 153, 153);">12</li><li style="color: rgb(153, 153, 153);">13</li><li style="color: rgb(153, 153, 153);">14</li><li style="color: rgb(153, 153, 153);">15</li><li style="color: rgb(153, 153, 153);">16</li><li style="color: rgb(153, 153, 153);">17</li><li style="color: rgb(153, 153, 153);">18</li><li style="color: rgb(153, 153, 153);">19</li><li style="color: rgb(153, 153, 153);">20</li><li style="color: rgb(153, 153, 153);">21</li><li style="color: rgb(153, 153, 153);">22</li><li style="color: rgb(153, 153, 153);">23</li><li style="color: rgb(153, 153, 153);">24</li><li style="color: rgb(153, 153, 153);">25</li><li style="color: rgb(153, 153, 153);">26</li><li style="color: rgb(153, 153, 153);">27</li><li style="color: rgb(153, 153, 153);">28</li><li style="color: rgb(153, 153, 153);">29</li><li style="color: rgb(153, 153, 153);">30</li><li style="color: rgb(153, 153, 153);">31</li><li style="color: rgb(153, 153, 153);">32</li><li style="color: rgb(153, 153, 153);">33</li><li style="color: rgb(153, 153, 153);">34</li><li style="color: rgb(153, 153, 153);">35</li><li style="color: rgb(153, 153, 153);">36</li><li style="color: rgb(153, 153, 153);">37</li><li style="color: rgb(153, 153, 153);">38</li><li style="color: rgb(153, 153, 153);">39</li><li style="color: rgb(153, 153, 153);">40</li><li style="color: rgb(153, 153, 153);">41</li><li style="color: rgb(153, 153, 153);">42</li><li style="color: rgb(153, 153, 153);">43</li><li style="color: rgb(153, 153, 153);">44</li><li style="color: rgb(153, 153, 153);">45</li><li style="color: rgb(153, 153, 153);">46</li><li style="color: rgb(153, 153, 153);">47</li><li style="color: rgb(153, 153, 153);">48</li><li style="color: rgb(153, 153, 153);">49</li><li style="color: rgb(153, 153, 153);">50</li><li style="color: rgb(153, 153, 153);">51</li><li style="color: rgb(153, 153, 153);">52</li><li style="color: rgb(153, 153, 153);">53</li><li style="color: rgb(153, 153, 153);">54</li><li style="color: rgb(153, 153, 153);">55</li><li style="color: rgb(153, 153, 153);">56</li><li style="color: rgb(153, 153, 153);">57</li><li style="color: rgb(153, 153, 153);">58</li><li style="color: rgb(153, 153, 153);">59</li><li style="color: rgb(153, 153, 153);">60</li><li style="color: rgb(153, 153, 153);">61</li><li style="color: rgb(153, 153, 153);">62</li><li style="color: rgb(153, 153, 153);">63</li><li style="color: rgb(153, 153, 153);">64</li><li style="color: rgb(153, 153, 153);">65</li><li style="color: rgb(153, 153, 153);">66</li><li style="color: rgb(153, 153, 153);">67</li><li style="color: rgb(153, 153, 153);">68</li><li style="color: rgb(153, 153, 153);">69</li><li style="color: rgb(153, 153, 153);">70</li><li style="color: rgb(153, 153, 153);">71</li><li style="color: rgb(153, 153, 153);">72</li></ul></pre> <p>具体使用</p> <pre data-index="6" class="set-code-hide prettyprint"><code class="prism language-cpp has-numbering" onclick="mdcp.signin(event)" style="position: unset;"> <span class="token comment">// 优化算法</span> <span class="token punctuation">{</span> <span class="token comment">//</span> ceres<span class="token operator">::</span>Problem problem<span class="token punctuation">;</span> <span class="token keyword">double</span> k<span class="token punctuation">[</span><span class="token number">9</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">{</span><span class="token function">K</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span><span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token function">K</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token function">K</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token function">K</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token number">0.</span><span class="token punctuation">,</span> <span class="token number">0.</span><span class="token punctuation">,</span> <span class="token number">0.</span><span class="token punctuation">,</span> <span class="token number">0.</span><span class="token punctuation">,</span> <span class="token number">0.</span><span class="token punctuation">}</span><span class="token punctuation">;</span> <span class="token comment">// 设置内参初值</span> <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span> i<span class="token operator"><</span>n<span class="token punctuation">;</span> <span class="token operator">++</span>i<span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> j<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span> j<span class="token operator"><</span>imagePoints<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token operator">++</span>j<span class="token punctuation">)</span> <span class="token punctuation">{</span> <span class="token comment">// 优化参数2->输出的残差数，表示x和y</span> <span class="token comment">// 9 表示内参4个畸变系数5个</span> <span class="token comment">// 3 外参，用旋转向量表示，输入需要把旋转矩阵转为旋转向量，再输入</span> <span class="token comment">// 3 外参平移向量</span> ceres<span class="token operator">::</span>CostFunction<span class="token operator">*</span> costFunction<span class="token operator">=</span><span class="token keyword">new</span> ceres<span class="token operator">::</span>AutoDiffCostFunction<span class="token operator"><</span>PROJECT_COST<span class="token punctuation">,</span> <span class="token number">2</span><span class="token punctuation">,</span> <span class="token number">9</span><span class="token punctuation">,</span> <span class="token number">3</span><span class="token punctuation">,</span> <span class="token number">3</span><span class="token operator">></span><span class="token punctuation">(</span> <span class="token keyword">new</span> <span class="token function">PROJECT_COST</span><span class="token punctuation">(</span>objectPoints<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">,</span> imagePoints<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">[</span>j<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span> problem<span class="token punctuation">.</span><span class="token function">AddResidualBlock</span><span class="token punctuation">(</span>costFunction<span class="token punctuation">,</span> <span class="token keyword">nullptr</span><span class="token punctuation">,</span> k<span class="token punctuation">,</span> rList<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">.</span><span class="token function">data</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">,</span> tList<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">.</span><span class="token function">data</span><span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> std<span class="token operator">::</span>cout <span class="token operator"><<</span> <span class="token string">" solve Options ..."</span> <span class="token operator"><<</span> std<span class="token operator">::</span>endl<span class="token punctuation">;</span> ceres<span class="token operator">::</span>Solver<span class="token operator">::</span>Options options<span class="token punctuation">;</span> options<span class="token punctuation">.</span>minimizer_progress_to_stdout <span class="token operator">=</span> <span class="token boolean">true</span><span class="token punctuation">;</span> <span class="token comment">//options.linear_solver_type = ceres::DENSE_SCHUR;</span> <span class="token comment">//options.trust_region_strategy_type = ceres::TrustRegionStrategyType::LEVENBERG_MARQUARDT;</span> <span class="token comment">//options.preconditioner_type = ceres::JACOBI;</span> <span class="token comment">//options.sparse_linear_algebra_library_type = ceres::EIGEN_SPARSE;</span> ceres<span class="token operator">::</span>Solver<span class="token operator">::</span>Summary summary<span class="token punctuation">;</span> ceres<span class="token operator">::</span><span class="token function">Solve</span><span class="token punctuation">(</span>options<span class="token punctuation">,</span> <span class="token operator">&</span>problem<span class="token punctuation">,</span> <span class="token operator">&</span>summary<span class="token punctuation">)</span><span class="token punctuation">;</span> std<span class="token operator">::</span>cout <span class="token operator"><<</span> summary<span class="token punctuation">.</span><span class="token function">BriefReport</span><span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token operator"><<</span> std<span class="token operator">::</span>endl<span class="token punctuation">;</span> <span class="token keyword">if</span> <span class="token punctuation">(</span><span class="token operator">!</span>summary<span class="token punctuation">.</span><span class="token function">IsSolutionUsable</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token punctuation">{</span> std<span class="token operator">::</span>cout <span class="token operator"><<</span> <span class="token string">"Bundle Adjustment failed."</span> <span class="token operator"><<</span> std<span class="token operator">::</span>endl<span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token keyword">else</span> <span class="token punctuation">{</span> <span class="token comment">//summary.num_</span> <span class="token comment">// Display statistics about the minimization</span> std<span class="token operator">::</span>cout <span class="token operator"><<</span> std<span class="token operator">::</span>endl <span class="token operator"><<</span> <span class="token string">"Bundle Adjustment statistics (approximated RMSE):\n"</span> <span class="token operator"><<</span> <span class="token string">" #views: "</span> <span class="token operator"><<</span> n <span class="token operator"><<</span> <span class="token string">"\n"</span> <span class="token operator"><<</span> <span class="token string">" #residuals: "</span> <span class="token operator"><<</span> summary<span class="token punctuation">.</span>num_residuals <span class="token operator"><<</span> <span class="token string">"\n"</span> <span class="token operator"><<</span> <span class="token string">" #num_parameters: "</span> <span class="token operator"><<</span> summary<span class="token punctuation">.</span>num_parameters <span class="token operator"><<</span> <span class="token string">"\n"</span> <span class="token operator"><<</span> <span class="token string">" #num_parameter_blocks: "</span> <span class="token operator"><<</span> summary<span class="token punctuation">.</span>num_parameter_blocks <span class="token operator"><<</span> <span class="token string">"\n"</span> <span class="token operator"><<</span> <span class="token string">" Initial RMSE: "</span> <span class="token operator"><<</span> std<span class="token operator">::</span><span class="token function">sqrt</span><span class="token punctuation">(</span>summary<span class="token punctuation">.</span>initial_cost <span class="token operator">/</span> summary<span class="token punctuation">.</span>num_residuals<span class="token punctuation">)</span> <span class="token operator"><<</span> <span class="token string">"\n"</span> <span class="token operator"><<</span> <span class="token string">" Final RMSE: "</span> <span class="token operator"><<</span> std<span class="token operator">::</span><span class="token function">sqrt</span><span class="token punctuation">(</span>summary<span class="token punctuation">.</span>final_cost <span class="token operator">/</span> summary<span class="token punctuation">.</span>num_residuals<span class="token punctuation">)</span> <span class="token operator"><<</span> <span class="token string">"\n"</span> <span class="token operator"><<</span> <span class="token string">" Time (s): "</span> <span class="token operator"><<</span> summary<span class="token punctuation">.</span>total_time_in_seconds <span class="token operator"><<</span> <span class="token string">"\n"</span> <span class="token operator"><<</span> std<span class="token operator">::</span>endl<span class="token punctuation">;</span> <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">auto</span><span class="token operator">&</span> a<span class="token operator">:</span> k<span class="token punctuation">)</span> std<span class="token operator">::</span>cout <span class="token operator"><<</span> a <span class="token operator"><<</span> <span class="token string">" "</span> <span class="token punctuation">;</span> <span class="token comment">//cv::Mat cameraMatrix, distCoeffs;</span> <span class="token comment">//cameraMatrix = (cv::Mat_<double>(3, 3) << k[0], 0.0, k[2], 0, k[1], k[3], 0, 0, 1);</span> <span class="token comment">//distCoeffs = (cv::Mat_<double>(1, 5) << k[4], k[5], k[7], k[8], k[6]);</span> <span class="token comment">// 输出优化结果</span> Eigen<span class="token operator">::</span>Matrix3d cameraMatrix_<span class="token punctuation">;</span> cameraMatrix_ <span class="token operator"><<</span> k<span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">,</span> <span class="token number">0.0</span><span class="token punctuation">,</span> k<span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">]</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> k<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">,</span> k<span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">]</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">;</span> Eigen<span class="token operator">::</span>VectorXd <span class="token function">distCoeffs_</span><span class="token punctuation">(</span><span class="token number">5</span><span class="token punctuation">)</span><span class="token punctuation">;</span> distCoeffs_ <span class="token operator"><<</span> k<span class="token punctuation">[</span><span class="token number">4</span><span class="token punctuation">]</span><span class="token punctuation">,</span> k<span class="token punctuation">[</span><span class="token number">5</span><span class="token punctuation">]</span><span class="token punctuation">,</span> k<span class="token punctuation">[</span><span class="token number">7</span><span class="token punctuation">]</span><span class="token punctuation">,</span> k<span class="token punctuation">[</span><span class="token number">8</span><span class="token punctuation">]</span><span class="token punctuation">,</span> k<span class="token punctuation">[</span><span class="token number">6</span><span class="token punctuation">]</span><span class="token punctuation">;</span> <span class="token comment">// 评价投影误差</span> std<span class="token operator">::</span>vector<span class="token operator"><</span><span class="token keyword">double</span><span class="token operator">></span> reprojErrs<span class="token punctuation">;</span> <span class="token keyword">double</span> totalAvgErr <span class="token operator">=</span> <span class="token function">computeReprojectionErrors</span><span class="token punctuation">(</span>objectPoints<span class="token punctuation">,</span> imagePoints<span class="token punctuation">,</span> rList<span class="token punctuation">,</span> tList<span class="token punctuation">,</span> cameraMatrix_<span class="token punctuation">,</span> distCoeffs_<span class="token punctuation">,</span> reprojErrs<span class="token punctuation">)</span><span class="token punctuation">;</span> std<span class="token operator">::</span>cout <span class="token operator"><<</span> <span class="token string">" avg re projection error = "</span> <span class="token operator"><<</span> totalAvgErr <span class="token operator"><<</span> std<span class="token operator">::</span>endl<span class="token punctuation">;</span> <span class="token keyword">for</span> <span class="token punctuation">(</span>size_t i <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span> i <span class="token operator"><</span> reprojErrs<span class="token punctuation">.</span><span class="token function">size</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span> i<span class="token operator">++</span><span class="token punctuation">)</span> <span class="token punctuation">{</span> std<span class="token operator">::</span>cout <span class="token operator"><<</span> i <span class="token operator"><<</span> <span class="token string">" projection error = "</span> <span class="token operator"><<</span> reprojErrs<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator"><<</span> std<span class="token operator">::</span>endl<span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token comment">// Mat</span> cv<span class="token operator">::</span><span class="token function">eigen2cv</span><span class="token punctuation">(</span>cameraMatrix_<span class="token punctuation">,</span> cameraMatrix<span class="token punctuation">)</span><span class="token punctuation">;</span> cv<span class="token operator">::</span><span class="token function">eigen2cv</span><span class="token punctuation">(</span>distCoeffs_<span class="token punctuation">,</span> distCoeffs<span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token punctuation">}</span> <span class="token punctuation">}</span> <div class="hljs-button signin active" data-title="登录复制" data-report-click="{"spm":"1001.2101.3001.4334"}"></div></code><div class="hide-preCode-box"><span class="hide-preCode-bt" data-report-view="{"spm":"1001.2101.3001.7365"}"><img class="look-more-preCode contentImg-no-view" src="https://csdnimg.cn/release/blogv2/dist/pc/img/newCodeMoreWhite.png" alt="" title=""></span></div><ul class="pre-numbering" style=""><li style="color: rgb(153, 153, 153);">1</li><li style="color: rgb(153, 153, 153);">2</li><li style="color: rgb(153, 153, 153);">3</li><li style="color: rgb(153, 153, 153);">4</li><li style="color: rgb(153, 153, 153);">5</li><li style="color: rgb(153, 153, 153);">6</li><li style="color: rgb(153, 153, 153);">7</li><li style="color: rgb(153, 153, 153);">8</li><li style="color: rgb(153, 153, 153);">9</li><li style="color: rgb(153, 153, 153);">10</li><li style="color: rgb(153, 153, 153);">11</li><li style="color: rgb(153, 153, 153);">12</li><li style="color: rgb(153, 153, 153);">13</li><li style="color: rgb(153, 153, 153);">14</li><li style="color: rgb(153, 153, 153);">15</li><li style="color: rgb(153, 153, 153);">16</li><li style="color: rgb(153, 153, 153);">17</li><li style="color: rgb(153, 153, 153);">18</li><li style="color: rgb(153, 153, 153);">19</li><li style="color: rgb(153, 153, 153);">20</li><li style="color: rgb(153, 153, 153);">21</li><li style="color: rgb(153, 153, 153);">22</li><li style="color: rgb(153, 153, 153);">23</li><li style="color: rgb(153, 153, 153);">24</li><li style="color: rgb(153, 153, 153);">25</li><li style="color: rgb(153, 153, 153);">26</li><li style="color: rgb(153, 153, 153);">27</li><li style="color: rgb(153, 153, 153);">28</li><li style="color: rgb(153, 153, 153);">29</li><li style="color: rgb(153, 153, 153);">30</li><li style="color: rgb(153, 153, 153);">31</li><li style="color: rgb(153, 153, 153);">32</li><li style="color: rgb(153, 153, 153);">33</li><li style="color: rgb(153, 153, 153);">34</li><li style="color: rgb(153, 153, 153);">35</li><li style="color: rgb(153, 153, 153);">36</li><li style="color: rgb(153, 153, 153);">37</li><li style="color: rgb(153, 153, 153);">38</li><li style="color: rgb(153, 153, 153);">39</li><li style="color: rgb(153, 153, 153);">40</li><li style="color: rgb(153, 153, 153);">41</li><li style="color: rgb(153, 153, 153);">42</li><li style="color: rgb(153, 153, 153);">43</li><li style="color: rgb(153, 153, 153);">44</li><li style="color: rgb(153, 153, 153);">45</li><li style="color: rgb(153, 153, 153);">46</li><li style="color: rgb(153, 153, 153);">47</li><li style="color: rgb(153, 153, 153);">48</li><li style="color: rgb(153, 153, 153);">49</li><li style="color: rgb(153, 153, 153);">50</li><li style="color: rgb(153, 153, 153);">51</li><li style="color: rgb(153, 153, 153);">52</li><li style="color: rgb(153, 153, 153);">53</li><li style="color: rgb(153, 153, 153);">54</li><li style="color: rgb(153, 153, 153);">55</li><li style="color: rgb(153, 153, 153);">56</li><li style="color: rgb(153, 153, 153);">57</li><li style="color: rgb(153, 153, 153);">58</li><li style="color: rgb(153, 153, 153);">59</li><li style="color: rgb(153, 153, 153);">60</li><li style="color: rgb(153, 153, 153);">61</li><li style="color: rgb(153, 153, 153);">62</li><li style="color: rgb(153, 153, 153);">63</li><li style="color: rgb(153, 153, 153);">64</li><li style="color: rgb(153, 153, 153);">65</li><li style="color: rgb(153, 153, 153);">66</li><li style="color: rgb(153, 153, 153);">67</li><li style="color: rgb(153, 153, 153);">68</li><li style="color: rgb(153, 153, 153);">69</li><li style="color: rgb(153, 153, 153);">70</li><li style="color: rgb(153, 153, 153);">71</li><li style="color: rgb(153, 153, 153);">72</li><li style="color: rgb(153, 153, 153);">73</li><li style="color: rgb(153, 153, 153);">74</li><li style="color: rgb(153, 153, 153);">75</li><li style="color: rgb(153, 153, 153);">76</li><li style="color: rgb(153, 153, 153);">77</li><li style="color: rgb(153, 153, 153);">78</li><li style="color: rgb(153, 153, 153);">79</li><li style="color: rgb(153, 153, 153);">80</li><li style="color: rgb(153, 153, 153);">81</li><li style="color: rgb(153, 153, 153);">82</li><li style="color: rgb(153, 153, 153);">83</li></ul></pre> <p>最后的结果</p> <pre data-index="7" class="set-code-hide prettyprint"><code class="prism language-cpp has-numbering" onclick="mdcp.signin(event)" style="position: unset;"> <span class="token number">536.073</span> <span class="token number">536.016</span> <span class="token number">342.371</span> <span class="token number">235.536</span> <span class="token operator">-</span><span class="token number">0.265091</span> <span class="token operator">-</span><span class="token number">0.0467182</span> <span class="token number">0.252215</span> <span class="token number">0.00183296</span> <span class="token operator">-</span><span class="token number">0.000314464</span> avg re projection error <span class="token operator">=</span> <span class="token number">0.234593</span> <span class="token number">0</span> projection error <span class="token operator">=</span> <span class="token number">0.16992</span> <span class="token number">1</span> projection error <span class="token operator">=</span> <span class="token number">0.846329</span> <span class="token number">2</span> projection error <span class="token operator">=</span> <span class="token number">0.159117</span> <span class="token number">3</span> projection error <span class="token operator">=</span> <span class="token number">0.176626</span> <span class="token number">4</span> projection error <span class="token operator">=</span> <span class="token number">0.141207</span> <span class="token number">5</span> projection error <span class="token operator">=</span> <span class="token number">0.162312</span> <span class="token number">6</span> projection error <span class="token operator">=</span> <span class="token number">0.18801</span> <span class="token number">7</span> projection error <span class="token operator">=</span> <span class="token number">0.214098</span> <span class="token number">8</span> projection error <span class="token operator">=</span> <span class="token number">0.22217</span> <span class="token number">9</span> projection error <span class="token operator">=</span> <span class="token number">0.153192</span> <span class="token number">10</span> projection error <span class="token operator">=</span> <span class="token number">0.177543</span> <span class="token number">11</span> projection error <span class="token operator">=</span> <span class="token number">0.28586</span> <span class="token number">12</span> projection error <span class="token operator">=</span> <span class="token number">0.15332</span> <div class="hljs-button signin active" data-title="登录复制" data-report-click="{"spm":"1001.2101.3001.4334"}"></div></code><div class="hide-preCode-box"><span class="hide-preCode-bt" data-report-view="{"spm":"1001.2101.3001.7365"}"><img class="look-more-preCode contentImg-no-view" src="https://csdnimg.cn/release/blogv2/dist/pc/img/newCodeMoreWhite.png" alt="" title=""></span></div><ul class="pre-numbering" style=""><li style="color: rgb(153, 153, 153);">1</li><li style="color: rgb(153, 153, 153);">2</li><li style="color: rgb(153, 153, 153);">3</li><li style="color: rgb(153, 153, 153);">4</li><li style="color: rgb(153, 153, 153);">5</li><li style="color: rgb(153, 153, 153);">6</li><li style="color: rgb(153, 153, 153);">7</li><li style="color: rgb(153, 153, 153);">8</li><li style="color: rgb(153, 153, 153);">9</li><li style="color: rgb(153, 153, 153);">10</li><li style="color: rgb(153, 153, 153);">11</li><li style="color: rgb(153, 153, 153);">12</li><li style="color: rgb(153, 153, 153);">13</li><li style="color: rgb(153, 153, 153);">14</li><li style="color: rgb(153, 153, 153);">15</li><li style="color: rgb(153, 153, 153);">16</li><li style="color: rgb(153, 153, 153);">17</li></ul></pre> <p>核心的代码和流程就这多，还有根据畸变系数对图像校正都在代码里，我把github地址也贴出来。<br> 里面也包含鱼眼镜头的标定。代码结构如下：<br> <img src="https://img-blog.csdnimg.cn/20201212150435257.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3poYWl0aWFueW9uZw==,size_16,color_FFFFFF,t_70" alt="在这里插入图片描述"></p> <p>附源码地址：<br> <a href="https://github.com/zhaitianyong/CameraCalibration">CameraCalibration</a><br> https://github.com/zhaitianyong/CameraCalibration</p> </div><div data-report-view="{"mod":"1585297308_001","spm":"1001.2101.3001.6548","dest":"https://blog.csdn.net/zhaitianyong/article/details/111059716","extend1":"pc","ab":"new"}"><div></div></div> <link href="https://csdnimg.cn/release/blogv2/dist/mdeditor/css/editerView/markdown_views-f23dff6052.css" rel="stylesheet"> <link href="https://csdnimg.cn/release/blogv2/dist/mdeditor/css/style-c216769e99.css" rel="stylesheet"> <div><div><span>声明：</span>本文内容由网友自发贡献，不代表【wpsshop博客】立场，版权归原作者所有，本站不承担相应法律责任。如您发现有侵权的内容，请联系我们。转载请注明出处：<a href="https://www.wpsshop.cn/w/Cpp五条/article/detail/646230">https://www.wpsshop.cn/w/Cpp五条/article/detail/646230</a></div></div></div><div class="article_recommend"><div class="list_top">推荐阅读</div><div class="ListItems"><ul class="NewsList"><li><div class="NewTitle"><a title="article" 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