opencv-相机标定步骤、评估标定误差以及标定之后图像坐标到世界坐标的转换

前一段时间，研究了下相机标定。关于opencv相机标定，包括标定完后，世界坐标到 图像坐标的转换，以评估图像的标定误差，这些网上有很多资源和源代码。

可是，相机标定完之后，我们想要的是，知道了图像坐标，想要得到它的世界坐标，或者我们已知图像上两个点之间的像素距离，现在我们想知道两个点之间的实际距离。

楼主在网上搜了很多资源，问了很多人，都没有相关的代码，可以得到这样的结论：opencv没有提供现成的函数，满足从图像坐标到世界坐标的转换。

所以，我们最想要的这一步，是需要自己写的。（如果我理解的不对，希望看到这篇博文的人，能够批评指正）

相机标定的主要思路为：

一、获取十几张不同角度拍摄的图片，角点检测，得到每个角点的坐标；

二、分别定义十几张照片中，世界坐标系下的角点坐标，一般x、y为等间距，z为0 ；

三、开始标定，主要函数为calibrateCamera；

四、得到了相机内参和畸变系数，这是标定完后相机的属性，还会得到外参，外参代表着每张图片所在的平面；

五、opencv提供了世界坐标到图像坐标的转换函数，主要用来评估标定的误差；

六、我们最想要的，根据图像坐标到世界坐标的转换，本质上就是矩阵的运算，需要自己写；

下面贴出代码，开发环境opencv2.4.9+vs2013

#include "opencv2/core/core.hpp"#include "opencv2/imgproc/imgproc.hpp"#include "opencv2/calib3d/calib3d.hpp"#include "opencv2/highgui/highgui.hpp"#include <iostream>#include <fstream>using namespace std;using namespace cv;const int imageWidth = 1600;                             //摄像头的分辨率  const int imageHeight = 1200;const int boardWidth = 39;                               //横向的角点数目  const int boardHeight = 39;                              //纵向的角点数据  const int boardCorner = boardWidth * boardHeight;       //总的角点数据  const int frameNumber =7;                             //相机标定时需要采用的图像帧数  const int squareSize = 10;                              //标定板黑白格子的大小 单位mm  const Size boardSize = Size(boardWidth, boardHeight);   //  Mat intrinsic;                                          //相机内参数  Mat distortion_coeff;                                   //相机畸变参数  vector<Mat> rvecs;                                        //旋转向量  vector<Mat> tvecs;                                        //平移向量  vector<vector<Point2f>> corners;                        //各个图像找到的角点的集合 和objRealPoint 一一对应  vector<vector<Point3f>> objRealPoint;                   //各副图像的角点的实际物理坐标集合  vector<Point2f> corner;                                   //某一副图像找到的角点  Mat rgbImage, grayImage;/*计算标定板上模块的实际物理坐标*/void calRealPoint(vector<vector<Point3f>>& obj, int boardwidth, int boardheight, int imgNumber, int squaresize){//  Mat imgpoint(boardheight, boardwidth, CV_32FC3,Scalar(0,0,0));  vector<Point3f> imgpoint;for (int rowIndex = 0; rowIndex < boardheight; rowIndex++){for (int colIndex = 0; colIndex < boardwidth; colIndex++){//  imgpoint.at<Vec3f>(rowIndex, colIndex) = Vec3f(rowIndex * squaresize, colIndex*squaresize, 0);  imgpoint.push_back(Point3f(colIndex * squaresize, rowIndex * squaresize, 0));}}for (int imgIndex = 0; imgIndex < imgNumber; imgIndex++){obj.push_back(imgpoint);}}/*设置相机的初始参数 也可以不估计*/void CalibrationEvaluate(void)//标定结束后进行评价{double err=0;double total_err=0;//calibrateCamera(objRealPoint, corners, Size(imageWidth, imageHeight), intrinsic, distortion_coeff, rvecs, tvecs, 0);cout << "每幅图像的定标误差：" << endl;for (int i = 0; i < corners.size(); i++){vector<Point2f> image_points2;vector<Point3f> tempPointSet = objRealPoint[i];projectPoints(tempPointSet, rvecs[i], tvecs[i], intrinsic, distortion_coeff, image_points2);vector<Point2f> tempImagePoint = corners[i];Mat tempImagePointMat = Mat(1, tempImagePoint.size(), CV_32FC2);Mat image_points2Mat = Mat(1, image_points2.size(), CV_32FC2);for (int j = 0; j < tempImagePoint.size(); j++){image_points2Mat.at<Vec2f>(0, j) = Vec2f(image_points2[j].x, image_points2[j].y);tempImagePointMat.at<Vec2f>(0, j) = Vec2f(tempImagePoint[j].x, tempImagePoint[j].y);}err = norm(image_points2Mat, tempImagePointMat, NORM_L2);total_err = err + total_err;cout << "第" << i + 1 << "幅图像的平均误差：" << err << "像素" << endl;}cout << "总体平均误差：" << total_err / (corners.size() + 1) << "像素" << endl;}void guessCameraParam(void){/*分配内存*/intrinsic.create(3, 3, CV_64FC1);distortion_coeff.create(5, 1, CV_64FC1);/*fx 0 cx0 fy cy0 0  1*/intrinsic.at<double>(0, 0) = 256.8093262;   //fx         intrinsic.at<double>(0, 2) = 160.2826538;   //cx  intrinsic.at<double>(1, 1) = 254.7511139;   //fy  intrinsic.at<double>(1, 2) = 127.6264572;   //cy  intrinsic.at<double>(0, 1) = 0;intrinsic.at<double>(1, 0) = 0;intrinsic.at<double>(2, 0) = 0;intrinsic.at<double>(2, 1) = 0;intrinsic.at<double>(2, 2) = 1;/*k1 k2 p1 p2 p3*/distortion_coeff.at<double>(0, 0) = -0.193740;  //k1  distortion_coeff.at<double>(1, 0) = -0.378588;  //k2  distortion_coeff.at<double>(2, 0) = 0.028980;   //p1  distortion_coeff.at<double>(3, 0) = 0.008136;   //p2  distortion_coeff.at<double>(4, 0) = 0;          //p3  }void outputCameraParam(void){/*保存数据*///cvSave("cameraMatrix.xml", &intrinsic);  //cvSave("cameraDistoration.xml", &distortion_coeff);  //cvSave("rotatoVector.xml", &rvecs);  //cvSave("translationVector.xml", &tvecs);  /*输出数据*/cout << "fx :" << intrinsic.at<double>(0, 0) << endl << "fy :" << intrinsic.at<double>(1, 1) << endl;cout << "cx :" << intrinsic.at<double>(0, 2) << endl << "cy :" << intrinsic.at<double>(1, 2) << endl;cout << "k1 :" << distortion_coeff.at<double>(0, 0) << endl;cout << "k2 :" << distortion_coeff.at<double>(1, 0) << endl;cout << "p1 :" << distortion_coeff.at<double>(2, 0) << endl;cout << "p2 :" << distortion_coeff.at<double>(3, 0) << endl;cout << "p3 :" << distortion_coeff.at<double>(4, 0) << endl;}//int _tmain(int argc, _TCHAR* argv[])int main(){Mat img;int goodFrameCount = 0;namedWindow("chessboard");cout << "按Q退出 ..." << endl;while (goodFrameCount < frameNumber){char filename[100];sprintf_s(filename, "chao%d.bmp", goodFrameCount);//sprintf_s(filename, "chess%d.jpg", goodFrameCount);goodFrameCount++;rgbImage = imread(filename, 1);cvtColor(rgbImage, grayImage, CV_BGR2GRAY);imshow("Camera", grayImage);bool isFind = findChessboardCorners(rgbImage, boardSize, corner, 0);//bool isFind = findChessboardCorners(rgbImage, boardSize, corner, CV_CALIB_CB_NORMALIZE_IMAGE);if (isFind == true) //所有角点都被找到 说明这幅图像是可行的  {/*Size(5,5) 搜索窗口的一半大小Size(-1,-1) 死区的一半尺寸TermCriteria(CV_TERMCRIT_EPS | CV_TERMCRIT_ITER, 20, 0.1)迭代终止条件*/cornerSubPix(grayImage, corner, Size(5, 5), Size(-1, -1), TermCriteria(CV_TERMCRIT_EPS | CV_TERMCRIT_ITER, 20, 0.1));drawChessboardCorners(rgbImage, boardSize, corner, isFind);imshow("chessboard", rgbImage);corners.push_back(corner);//string filename = "res\\image\\calibration";  //filename += goodFrameCount + ".jpg";  //cvSaveImage(filename.c_str(), &IplImage(rgbImage));       //把合格的图片保存起来  cout << "The image is good" << endl;}else{cout << "The image is bad please try again" << endl;}//  cout << "Press any key to continue..." << endl;  //  waitKey(0);  if (waitKey(10) == 'q'){break;}//  imshow("chessboard", rgbImage);  }/*图像采集完毕 接下来开始摄像头的校正calibrateCamera()输入参数 objectPoints  角点的实际物理坐标imagePoints   角点的图像坐标imageSize     图像的大小输出参数cameraMatrix  相机的内参矩阵distCoeffs    相机的畸变参数rvecs         旋转矢量(外参数)tvecs         平移矢量(外参数）*//*设置实际初始参数 根据calibrateCamera来 如果flag = 0 也可以不进行设置*/guessCameraParam();cout << "guess successful" << endl;/*计算实际的校正点的三维坐标*/calRealPoint(objRealPoint, boardWidth, boardHeight, frameNumber, squareSize);cout << "cal real successful" << endl;/*标定摄像头*/calibrateCamera(objRealPoint, corners, Size(imageWidth, imageHeight), intrinsic, distortion_coeff, rvecs, tvecs, 0);cout << "calibration successful" << endl;/*保存并输出参数*/outputCameraParam();CalibrationEvaluate();cout << "out successful" << endl;/*显示畸变校正效果*/Mat cImage;undistort(rgbImage, cImage, intrinsic, distortion_coeff);imshow("Corret Image", cImage);cout << "Correct Image" << endl;cout << "Wait for Key" << endl;waitKey(0);system("pause");return 0;}

以上只贴出了部分代码，完整的C++代码，可到 Hust平凡之路相机标定工程 下载。