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• 轉載請注明作者和出處：http://blog.csdn.net/u011475210
• 代碼地址：https://github.com/WordZzzz/fisheye_calibration
• 軟件版本：VS2013+OPENCV2.4.13 OR VS2013+OPENCV3.4.0
• 編??者：WordZzzz

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• • 我的代碼
  • 可供參考資料
    • FishEye模型的畸變校正
    • 普通相機模型的畸變校正

我的代碼

??最近在整理自己以前做過的一些東西，這是基于opencv的魚眼攝像頭畸變校正程序的github地址。

其中：

• normal_calibrate：基于OPENCV2與OPENCV3通用的函數實現，可實現USB攝像頭實時畸變校正；
• fishey_calibrate：基于OPENCV3獨有的fishyey結構體實現，可實現USB攝像頭實時畸變校正；
• fishey_calibrate_img：基于OPENCV3獨有的fishyey結構體實現，可實現單張圖片畸變校正；

??opencv1.0 2.0版只有一種攝像機標定模型，就是普通的小孔成像模型，在cv：：空間下。而從opencv3.0開始，新增了一種魚眼相機標定模型，在fisheye::空間下。兩種模型的主要區別在于像與物的投影關系不同，具體的文獻資料依然是數不勝數，這里就不贅述。根據opencv官方文檔的建議，在畸變程度較大的廣角鏡頭（比如：魚眼鏡頭）上進行攝像機標定和畸變校正，最好是用fisheye模型，該模型在圖像邊緣畸變程度很大的地方比普通相機模型的效果要好。

??當然，還是要貼上官方文檔的：

• Camera calibration With OpenCV2；
• Camera calibration With OpenCV3；

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華麗的分割線

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可供參考資料

??以下是在寫這篇博客的時候偶然發現的對opencv兩個版本標定過程的講解，這里直接copy過來并稍微做了一下排版，因為自己忙于為找工作做準備，實在是沒時間自己整理了。原文鏈接。

??圖像算法中會經常用到攝像機的畸變校正，有必要總結分析OpenCV中畸變校正方法，其中包括普通針孔相機模型和魚眼相機模型fisheye兩種畸變校正方法。

??普通相機模型畸變校正函數針對OpenCV中的cv::initUndistortRectifyMap()，魚眼相機模型畸變校正函數對應OpenCV中的cv::fisheye::initUndistortRectifyMap()。兩種方法算出映射Mapx和Mapy后，統一用cv::Remap()函數進行插值得到校正后的圖像。

FishEye模型的畸變校正。

??方便起見，直接貼出OpenCV源碼，我在里面加了注釋說明。建議參考OpenCV官方文檔看畸變模型原理會更清楚。

??簡要流程就是：

• 1.求內參矩陣的逆，由于攝像機坐標系的三維點到二維圖像平面，需要乘以旋轉矩陣R和內參矩陣K。那么反向投影回去則是二維圖像坐標乘以 K*R的逆矩陣。

• 2.將目標圖像中的每一個像素點坐標(j,i)，乘以1中求出的逆矩陣iR，轉換到攝像機坐標系（_x,_y,_w）,并歸一化得到z=1平面下的三維坐標(x,y,1)。

• 3.求出平面模型下像素點對應魚眼半球模型下的極坐標(r, theta)。

• 4.利用魚眼畸變模型求出擁有畸變時像素點對應的theta_d。

• 5.利用求出的theta_d值將三維坐標點重投影到二維圖像平面得到(u,v)，(u,v)即為目標圖像對應的畸變圖像中像素點坐標。

• 6.使用cv::Remap（）函數，根據mapx,mapy取出對應坐標位置的像素值賦值給目標圖像，一般采用雙線性插值法，得到畸變校正后的目標圖像。

#include <opencv2\opencv.hpp>void cv::fisheye::initUndistortRectifyMap( InputArray K, InputArray D, InputArray R, InputArray P,const cv::Size& size, int m1type, OutputArray map1, OutputArray map2 ) {CV_Assert( m1type == CV_16SC2 || m1type == CV_32F || m1type <=0 );map1.create( size, m1type <= 0 ? CV_16SC2 : m1type );map2.create( size, map1.type() == CV_16SC2 ? CV_16UC1 : CV_32F );CV_Assert((K.depth() == CV_32F || K.depth() == CV_64F) && (D.depth() == CV_32F || D.depth() == CV_64F));CV_Assert((P.empty() || P.depth() == CV_32F || P.depth() == CV_64F) && (R.empty() || R.depth() == CV_32F || R.depth() == CV_64F));CV_Assert(K.size() == Size(3, 3) && (D.empty() || D.total() == 4));CV_Assert(R.empty() || R.size() == Size(3, 3) || R.total() * R.channels() == 3);CV_Assert(P.empty() || P.size() == Size(3, 3) || P.size() == Size(4, 3));//從內參矩陣K中取出歸一化焦距fx,fy; cx,cycv::Vec2d f, c;if (K.depth() == CV_32F){Matx33f camMat = K.getMat();f = Vec2f(camMat(0, 0), camMat(1, 1));c = Vec2f(camMat(0, 2), camMat(1, 2));}else{Matx33d camMat = K.getMat();f = Vec2d(camMat(0, 0), camMat(1, 1));c = Vec2d(camMat(0, 2), camMat(1, 2));}//從畸變系數矩陣D中取出畸變系數k1,k2,k3,k4Vec4d k = Vec4d::all(0);if (!D.empty())k = D.depth() == CV_32F ? (Vec4d)*D.getMat().ptr<Vec4f>(): *D.getMat().ptr<Vec4d>();//旋轉矩陣RR轉換數據類型為CV_64F，如果不需要旋轉，則RR為單位陣cv::Matx33d RR = cv::Matx33d::eye();if (!R.empty() && R.total() * R.channels() == 3){cv::Vec3d rvec;R.getMat().convertTo(rvec, CV_64F);RR = Affine3d(rvec).rotation();}else if (!R.empty() && R.size() == Size(3, 3))R.getMat().convertTo(RR, CV_64F);//新的內參矩陣PP轉換數據類型為CV_64Fcv::Matx33d PP = cv::Matx33d::eye();if (!P.empty())P.getMat().colRange(0, 3).convertTo(PP, CV_64F);//關鍵一步：新的內參矩陣*旋轉矩陣，然后利用SVD分解求出逆矩陣iR，后面用到cv::Matx33d iR = (PP * RR).inv(cv::DECOMP_SVD);//反向映射，遍歷目標圖像所有像素位置，找到畸變圖像中對應位置坐標(u,v)，并分別保存坐標(u,v)到mapx和mapy中for( int i = 0; i < size.height; ++i){float* m1f = map1.getMat().ptr<float>(i);float* m2f = map2.getMat().ptr<float>(i);short* m1 = (short*)m1f;ushort* m2 = (ushort*)m2f;//二維圖像平面坐標系->攝像機坐標系double _x = i*iR(0, 1) + iR(0, 2),_y = i*iR(1, 1) + iR(1, 2),_w = i*iR(2, 1) + iR(2, 2);for( int j = 0; j < size.width; ++j){//歸一化攝像機坐標系，相當于假定在Z=1平面上double x = _x/_w, y = _y/_w;//求魚眼半球體截面半徑rdouble r = sqrt(x*x + y*y);//求魚眼半球面上一點與光心的連線和光軸的夾角Thetadouble theta = atan(r);//畸變模型求出theta_d，相當于有畸變的角度值double theta2 = theta*theta, theta4 = theta2*theta2, theta6 = theta4*theta2, theta8 = theta4*theta4;double theta_d = theta * (1 + k[0]*theta2 + k[1]*theta4 + k[2]*theta6 + k[3]*theta8);//利用有畸變的Theta值，將攝像機坐標系下的歸一化三維坐標，重投影到二維圖像平面，得到(j,i)對應畸變圖像中的(u,v)double scale = (r == 0) ? 1.0 : theta_d / r;double u = f[0]*x*scale + c[0];double v = f[1]*y*scale + c[1];//保存(u,v)坐標到mapx,mapyif( m1type == CV_16SC2 ){int iu = cv::saturate_cast<int>(u*cv::INTER_TAB_SIZE);int iv = cv::saturate_cast<int>(v*cv::INTER_TAB_SIZE);m1[j*2+0] = (short)(iu >> cv::INTER_BITS);m1[j*2+1] = (short)(iv >> cv::INTER_BITS);m2[j] = (ushort)((iv & (cv::INTER_TAB_SIZE-1))*cv::INTER_TAB_SIZE + (iu & (cv::INTER_TAB_SIZE-1)));}else if( m1type == CV_32FC1 ){m1f[j] = (float)u;m2f[j] = (float)v;}//這三條語句是上面 ”//二維圖像平面坐標系->攝像機坐標系“的一部分，是矩陣iR的第一列，這樣寫能夠簡化計算_x += iR(0, 0);_y += iR(1, 0);_w += iR(2, 0);}} }

普通相機模型的畸變校正

??同樣建議參考OpenCV官方文檔閱讀代碼。

??主要流程和上面Fisheye模型差不多，只有第4部分的畸變模型不一樣，普通相機的畸變模型如下：

??同樣把源代碼貼上，并加上注解：

#include <opencv2\opencv.hpp>void cv::initUndistortRectifyMap( InputArray _cameraMatrix, InputArray _distCoeffs,InputArray _matR, InputArray _newCameraMatrix,Size size, int m1type, OutputArray _map1, OutputArray _map2 ) {Mat cameraMatrix = _cameraMatrix.getMat(), distCoeffs = _distCoeffs.getMat();Mat matR = _matR.getMat(), newCameraMatrix = _newCameraMatrix.getMat();if( m1type <= 0 )m1type = CV_16SC2;CV_Assert( m1type == CV_16SC2 || m1type == CV_32FC1 || m1type == CV_32FC2 );_map1.create( size, m1type );Mat map1 = _map1.getMat(), map2;if( m1type != CV_32FC2 ){_map2.create( size, m1type == CV_16SC2 ? CV_16UC1 : CV_32FC1 );map2 = _map2.getMat();}else_map2.release();Mat_<double> R = Mat_<double>::eye(3, 3);Mat_<double> A = Mat_<double>(cameraMatrix), Ar;if( !newCameraMatrix.empty() )Ar = Mat_<double>(newCameraMatrix);elseAr = getDefaultNewCameraMatrix( A, size, true );if( !matR.empty() )R = Mat_<double>(matR);if( !distCoeffs.empty() )distCoeffs = Mat_<double>(distCoeffs);else{distCoeffs.create(14, 1, CV_64F);distCoeffs = 0.;}CV_Assert( A.size() == Size(3,3) && A.size() == R.size() );CV_Assert( Ar.size() == Size(3,3) || Ar.size() == Size(4, 3));//LU分解求新的內參矩陣Ar與旋轉矩陣R乘積的逆矩陣iRMat_<double> iR = (Ar.colRange(0,3)*R).inv(DECOMP_LU);const double* ir = &iR(0,0);//從舊的內參矩陣中取出光心位置u0,v0,和歸一化焦距fx,fydouble u0 = A(0, 2), v0 = A(1, 2);double fx = A(0, 0), fy = A(1, 1);//尼瑪14個畸變系數，不過大多用到的只有(k1,k2,p1,p2)，最多加一個k3，用不到的置為0CV_Assert( distCoeffs.size() == Size(1, 4) || distCoeffs.size() == Size(4, 1) ||distCoeffs.size() == Size(1, 5) || distCoeffs.size() == Size(5, 1) ||distCoeffs.size() == Size(1, 8) || distCoeffs.size() == Size(8, 1) ||distCoeffs.size() == Size(1, 12) || distCoeffs.size() == Size(12, 1) ||distCoeffs.size() == Size(1, 14) || distCoeffs.size() == Size(14, 1));if( distCoeffs.rows != 1 && !distCoeffs.isContinuous() )distCoeffs = distCoeffs.t();const double* const distPtr = distCoeffs.ptr<double>();double k1 = distPtr[0];double k2 = distPtr[1];double p1 = distPtr[2];double p2 = distPtr[3];double k3 = distCoeffs.cols + distCoeffs.rows - 1 >= 5 ? distPtr[4] : 0.;double k4 = distCoeffs.cols + distCoeffs.rows - 1 >= 8 ? distPtr[5] : 0.;double k5 = distCoeffs.cols + distCoeffs.rows - 1 >= 8 ? distPtr[6] : 0.;double k6 = distCoeffs.cols + distCoeffs.rows - 1 >= 8 ? distPtr[7] : 0.;double s1 = distCoeffs.cols + distCoeffs.rows - 1 >= 12 ? distPtr[8] : 0.;double s2 = distCoeffs.cols + distCoeffs.rows - 1 >= 12 ? distPtr[9] : 0.;double s3 = distCoeffs.cols + distCoeffs.rows - 1 >= 12 ? distPtr[10] : 0.;double s4 = distCoeffs.cols + distCoeffs.rows - 1 >= 12 ? distPtr[11] : 0.;double tauX = distCoeffs.cols + distCoeffs.rows - 1 >= 14 ? distPtr[12] : 0.;double tauY = distCoeffs.cols + distCoeffs.rows - 1 >= 14 ? distPtr[13] : 0.;//tauX,tauY這個是什么梯形畸變，用不到的話matTilt為單位陣// Matrix for trapezoidal distortion of tilted image sensorcv::Matx33d matTilt = cv::Matx33d::eye();cv::detail::computeTiltProjectionMatrix(tauX, tauY, &matTilt);for( int i = 0; i < size.height; i++ ){float* m1f = map1.ptr<float>(i);float* m2f = map2.empty() ? 0 : map2.ptr<float>(i);short* m1 = (short*)m1f;ushort* m2 = (ushort*)m2f;//利用逆矩陣iR將二維圖像坐標(j,i)轉換到攝像機坐標系(_x,_y,_w)double _x = i*ir[1] + ir[2], _y = i*ir[4] + ir[5], _w = i*ir[7] + ir[8];for( int j = 0; j < size.width; j++, _x += ir[0], _y += ir[3], _w += ir[6] ){//攝像機坐標系歸一化，令Z=1平面double w = 1./_w, x = _x*w, y = _y*w;//這一部分請看OpenCV官方文檔，畸變模型部分double x2 = x*x, y2 = y*y;double r2 = x2 + y2, _2xy = 2*x*y;double kr = (1 + ((k3*r2 + k2)*r2 + k1)*r2)/(1 + ((k6*r2 + k5)*r2 + k4)*r2);double xd = (x*kr + p1*_2xy + p2*(r2 + 2*x2) + s1*r2+s2*r2*r2);double yd = (y*kr + p1*(r2 + 2*y2) + p2*_2xy + s3*r2+s4*r2*r2);//根據求取的xd,yd將三維坐標重投影到二維畸變圖像坐標(u,v)cv::Vec3d vecTilt = matTilt*cv::Vec3d(xd, yd, 1);double invProj = vecTilt(2) ? 1./vecTilt(2) : 1;double u = fx*invProj*vecTilt(0) + u0;double v = fy*invProj*vecTilt(1) + v0;//保存u,v的值到Mapx,Mapy中if( m1type == CV_16SC2 ){int iu = saturate_cast<int>(u*INTER_TAB_SIZE);int iv = saturate_cast<int>(v*INTER_TAB_SIZE);m1[j*2] = (short)(iu >> INTER_BITS);m1[j*2+1] = (short)(iv >> INTER_BITS);m2[j] = (ushort)((iv & (INTER_TAB_SIZE-1))*INTER_TAB_SIZE + (iu & (INTER_TAB_SIZE-1)));}else if( m1type == CV_32FC1 ){m1f[j] = (float)u;m2f[j] = (float)v;}else{m1f[j*2] = (float)u;m1f[j*2+1] = (float)v;}}} }

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