相机已经存在了很长一段时间。随着二十世纪末廉价针孔相机的推出，相机已经在日常生活中普及。虽然价格便宜，但是成像存在严重的畸变。不过，这些畸变是固定的形式，基于标定和重映技术可以纠正畸变。此外，基于标定，可以确定相机的自然单位（像素）和现实世界单位（例如毫米）之间的关系。

理论

对于畸变， OpenCV 中考虑径向和切向的因素. 对于径向的畸变因素使用如下公式:

xdistorted=x(1+k1r2+k2r4+k3r6)ydistorted=y(1+k1r2+k2r4+k3r6)

所以对于没有畸变的像素点 (x,y) 坐标, 在畸变图像中的坐标为 (xdistortedydistorted). 径向畸变的形式通常表现为"桶型(barrel)" 或者 "鱼眼"形式.

切向畸变的发生是因为拍摄图像的镜头是不能和图像平面完全平行造成的。可以用公式表示成:

xdistorted=x+[2p1xy+p2(r2+2x2)]ydistorted=y+[p1(r2+2y2)+2p2xy]

所以在OpenCV中有5个畸变参数，一般表示成具有5个元素的行矩阵:

distortion_coefficients=(k1k2p1p2k3)

现在，对于单位转换(unit conversion)，我们使用以下公式:

⎡⎣⎢⎢xyw⎤⎦⎥⎥=⎡⎣⎢⎢⎢fx000fy0cxcy1⎤⎦⎥⎥⎥⎡⎣⎢⎢XYZ⎤⎦⎥⎥

这里出现的w 表示使用齐次坐标系统 (并且 w=Z). 未知参数为 fx 和 fy (相机的焦距) 以及 (cx,cy) 光学像素坐标的中心. If for both axes a common focal length is used with a given a aspect ratio (通常为 1), 那么 fy=fx∗a and in the upper formula we will have a single focal length f. 矩阵包含的四个参数称为相机的内参(camera matrix). 虽然使用不同的相机分辨率的情况下畸变系数都是相同的, these should be scaled along with the current resolution from the calibrated resolution.

确定这两个矩阵的过程就是校准。这些参数的计算是通过基本的几何方程实现。使用的方程取决于所选择的标定对象. 目前OpenCV 支持三种类型的对象用于标定:

经典的黑白棋盘格
对称的圆形图案
非对称的圆形图案

首先,需要用待校正的相机拍摄这些标定图案,并让OpenCV 找到他们. 每一个识别到的图案样式都可以产生一个新的方程. 至少要拍摄预定数量的图案形成一个适定的方程组. 标定中棋盘格需要拍摄较多的数量，圆形的图案拍摄的数量较少.例如，理论上棋盘格至少需要拍摄两幅图案. 但是,实际上根据经验统计，如果想要得到较好的校正效果，至少要拍摄10张不同位置的图案。

目的：

展示如下功能:

确定畸变矩阵(Determine the distortion matrix)
确定相机内参(Determine the camera matrix)
输入为摄像头、视频和图像列表(Take input from Camera, Video and Image file list)
读取配置文件(Read configuration from XML/YAML file)
保存校正结果(Save the results into XML/YAML file)
再投影误差的计算(Calculate re-projection error)

源代码

#include <iostream>
#include <sstream>
#include <string>
#include <ctime>
#include <cstdio>#include <opencv2/core.hpp>
#include <opencv2/core/utility.hpp>
#include <opencv2/imgproc.hpp>
#include <opencv2/calib3d.hpp>
#include <opencv2/imgcodecs.hpp>
#include <opencv2/videoio.hpp>
#include <opencv2/highgui.hpp>using namespace cv;
using namespace std;static void help()
{cout <<  "This is a camera calibration sample." << endl<<  "Usage: camera_calibration [configuration_file -- default ./default.xml]"  << endl<<  "Near the sample file you'll find the configuration file, which has detailed help of ""how to edit it.  It may be any OpenCV supported file format XML/YAML." << endl;
}
class Settings
{
public:Settings() : goodInput(false) {}enum Pattern { NOT_EXISTING, CHESSBOARD, CIRCLES_GRID, ASYMMETRIC_CIRCLES_GRID };enum InputType { INVALID, CAMERA, VIDEO_FILE, IMAGE_LIST };void write(FileStorage& fs) const                        //Write serialization for this class{fs << "{"<< "BoardSize_Width"  << boardSize.width<< "BoardSize_Height" << boardSize.height<< "Square_Size"         << squareSize<< "Calibrate_Pattern" << patternToUse<< "Calibrate_NrOfFrameToUse" << nrFrames<< "Calibrate_FixAspectRatio" << aspectRatio<< "Calibrate_AssumeZeroTangentialDistortion" << calibZeroTangentDist<< "Calibrate_FixPrincipalPointAtTheCenter" << calibFixPrincipalPoint<< "Write_DetectedFeaturePoints" << writePoints<< "Write_extrinsicParameters"   << writeExtrinsics<< "Write_outputFileName"  << outputFileName<< "Show_UndistortedImage" << showUndistorsed<< "Input_FlipAroundHorizontalAxis" << flipVertical<< "Input_Delay" << delay<< "Input" << input<< "}";}void read(const FileNode& node)                          //Read serialization for this class{node["BoardSize_Width" ] >> boardSize.width;node["BoardSize_Height"] >> boardSize.height;node["Calibrate_Pattern"] >> patternToUse;node["Square_Size"]  >> squareSize;node["Calibrate_NrOfFrameToUse"] >> nrFrames;node["Calibrate_FixAspectRatio"] >> aspectRatio;node["Write_DetectedFeaturePoints"] >> writePoints;node["Write_extrinsicParameters"] >> writeExtrinsics;node["Write_outputFileName"] >> outputFileName;node["Calibrate_AssumeZeroTangentialDistortion"] >> calibZeroTangentDist;node["Calibrate_FixPrincipalPointAtTheCenter"] >> calibFixPrincipalPoint;node["Calibrate_UseFisheyeModel"] >> useFisheye;node["Input_FlipAroundHorizontalAxis"] >> flipVertical;node["Show_UndistortedImage"] >> showUndistorsed;node["Input"] >> input;node["Input_Delay"] >> delay;node["Fix_K1"] >> fixK1;node["Fix_K2"] >> fixK2;node["Fix_K3"] >> fixK3;node["Fix_K4"] >> fixK4;node["Fix_K5"] >> fixK5;validate();}void validate(){goodInput = true;if (boardSize.width <= 0 || boardSize.height <= 0){cerr << "Invalid Board size: " << boardSize.width << " " << boardSize.height << endl;goodInput = false;}if (squareSize <= 10e-6){cerr << "Invalid square size " << squareSize << endl;goodInput = false;}if (nrFrames <= 0){cerr << "Invalid number of frames " << nrFrames << endl;goodInput = false;}if (input.empty())      // Check for valid inputinputType = INVALID;else{if (input[0] >= '0' && input[0] <= '9'){stringstream ss(input);ss >> cameraID;inputType = CAMERA;}else{if (readStringList(input, imageList)){inputType = IMAGE_LIST;nrFrames = (nrFrames < (int)imageList.size()) ? nrFrames : (int)imageList.size();}elseinputType = VIDEO_FILE;}if (inputType == CAMERA)inputCapture.open(cameraID);if (inputType == VIDEO_FILE)inputCapture.open(input);if (inputType != IMAGE_LIST && !inputCapture.isOpened())inputType = INVALID;}if (inputType == INVALID){cerr << " Input does not exist: " << input;goodInput = false;}flag = 0;if(calibFixPrincipalPoint) flag |= CALIB_FIX_PRINCIPAL_POINT;if(calibZeroTangentDist)   flag |= CALIB_ZERO_TANGENT_DIST;if(aspectRatio)            flag |= CALIB_FIX_ASPECT_RATIO;if(fixK1)                  flag |= CALIB_FIX_K1;if(fixK2)                  flag |= CALIB_FIX_K2;if(fixK3)                  flag |= CALIB_FIX_K3;if(fixK4)                  flag |= CALIB_FIX_K4;if(fixK5)                  flag |= CALIB_FIX_K5;if (useFisheye) {// the fisheye model has its own enum, so overwrite the flagsflag = fisheye::CALIB_FIX_SKEW | fisheye::CALIB_RECOMPUTE_EXTRINSIC;if(fixK1)                  flag |= fisheye::CALIB_FIX_K1;if(fixK2)                  flag |= fisheye::CALIB_FIX_K2;if(fixK3)                  flag |= fisheye::CALIB_FIX_K3;if(fixK4)                  flag |= fisheye::CALIB_FIX_K4;}calibrationPattern = NOT_EXISTING;if (!patternToUse.compare("CHESSBOARD")) calibrationPattern = CHESSBOARD;if (!patternToUse.compare("CIRCLES_GRID")) calibrationPattern = CIRCLES_GRID;if (!patternToUse.compare("ASYMMETRIC_CIRCLES_GRID")) calibrationPattern = ASYMMETRIC_CIRCLES_GRID;if (calibrationPattern == NOT_EXISTING){cerr << " Camera calibration mode does not exist: " << patternToUse << endl;goodInput = false;}atImageList = 0;}Mat nextImage(){Mat result;if( inputCapture.isOpened() ){Mat view0;inputCapture >> view0;view0.copyTo(result);}else if( atImageList < imageList.size() )result = imread(imageList[atImageList++], IMREAD_COLOR);return result;}static bool readStringList( const string& filename, vector<string>& l ){l.clear();FileStorage fs(filename, FileStorage::READ);if( !fs.isOpened() )return false;FileNode n = fs.getFirstTopLevelNode();if( n.type() != FileNode::SEQ )return false;FileNodeIterator it = n.begin(), it_end = n.end();for( ; it != it_end; ++it )l.push_back((string)*it);return true;}
public:Size boardSize;              // The size of the board -> Number of items by width and heightPattern calibrationPattern;  // One of the Chessboard, circles, or asymmetric circle patternfloat squareSize;            // The size of a square in your defined unit (point, millimeter,etc).int nrFrames;                // The number of frames to use from the input for calibrationfloat aspectRatio;           // The aspect ratioint delay;                   // In case of a video inputbool writePoints;            // Write detected feature pointsbool writeExtrinsics;        // Write extrinsic parametersbool calibZeroTangentDist;   // Assume zero tangential distortionbool calibFixPrincipalPoint; // Fix the principal point at the centerbool flipVertical;           // Flip the captured images around the horizontal axisstring outputFileName;       // The name of the file where to writebool showUndistorsed;        // Show undistorted images after calibrationstring input;                // The input ->bool useFisheye;             // use fisheye camera model for calibrationbool fixK1;                  // fix K1 distortion coefficientbool fixK2;                  // fix K2 distortion coefficientbool fixK3;                  // fix K3 distortion coefficientbool fixK4;                  // fix K4 distortion coefficientbool fixK5;                  // fix K5 distortion coefficientint cameraID;vector<string> imageList;size_t atImageList;VideoCapture inputCapture;InputType inputType;bool goodInput;int flag;private:string patternToUse;};static inline void read(const FileNode& node, Settings& x, const Settings& default_value = Settings())
{if(node.empty())x = default_value;elsex.read(node);
}static inline void write(FileStorage& fs, const String&, const Settings& s )
{s.write(fs);
}enum { DETECTION = 0, CAPTURING = 1, CALIBRATED = 2 };bool runCalibrationAndSave(Settings& s, Size imageSize, Mat&  cameraMatrix, Mat& distCoeffs,vector<vector<Point2f> > imagePoints );int main(int argc, char* argv[])
{help();//! [file_read]Settings s;const string inputSettingsFile = argc > 1 ? argv[1] : "default.xml";FileStorage fs(inputSettingsFile, FileStorage::READ); // Read the settingsif (!fs.isOpened()){cout << "Could not open the configuration file: \"" << inputSettingsFile << "\"" << endl;return -1;}fs["Settings"] >> s;fs.release();                                         // close Settings file//! [file_read]//FileStorage fout("settings.yml", FileStorage::WRITE); // write config as YAML//fout << "Settings" << s;if (!s.goodInput){cout << "Invalid input detected. Application stopping. " << endl;return -1;}vector<vector<Point2f> > imagePoints;Mat cameraMatrix, distCoeffs;Size imageSize;int mode = s.inputType == Settings::IMAGE_LIST ? CAPTURING : DETECTION;clock_t prevTimestamp = 0;const Scalar RED(0,0,255), GREEN(0,255,0);const char ESC_KEY = 27;//! [get_input]for(;;){Mat view;bool blinkOutput = false;view = s.nextImage();//-----  If no more image, or got enough, then stop calibration and show result -------------if( mode == CAPTURING && imagePoints.size() >= (size_t)s.nrFrames ){if( runCalibrationAndSave(s, imageSize,  cameraMatrix, distCoeffs, imagePoints))mode = CALIBRATED;elsemode = DETECTION;}if(view.empty())          // If there are no more images stop the loop{// if calibration threshold was not reached yet, calibrate nowif( mode != CALIBRATED && !imagePoints.empty() )runCalibrationAndSave(s, imageSize,  cameraMatrix, distCoeffs, imagePoints);break;}//! [get_input]imageSize = view.size();  // Format input image.if( s.flipVertical )    flip( view, view, 0 );//! [find_pattern]vector<Point2f> pointBuf;bool found;int chessBoardFlags = CALIB_CB_ADAPTIVE_THRESH | CALIB_CB_NORMALIZE_IMAGE;if(!s.useFisheye) {// fast check erroneously fails with high distortions like fisheyechessBoardFlags |= CALIB_CB_FAST_CHECK;}switch( s.calibrationPattern ) // Find feature points on the input format{case Settings::CHESSBOARD:found = findChessboardCorners( view, s.boardSize, pointBuf, chessBoardFlags);break;case Settings::CIRCLES_GRID:found = findCirclesGrid( view, s.boardSize, pointBuf );break;case Settings::ASYMMETRIC_CIRCLES_GRID:found = findCirclesGrid( view, s.boardSize, pointBuf, CALIB_CB_ASYMMETRIC_GRID );break;default:found = false;break;}//! [find_pattern]//! [pattern_found]if ( found)                // If done with success,{// improve the found corners' coordinate accuracy for chessboardif( s.calibrationPattern == Settings::CHESSBOARD){Mat viewGray;cvtColor(view, viewGray, COLOR_BGR2GRAY);cornerSubPix( viewGray, pointBuf, Size(11,11),Size(-1,-1), TermCriteria( TermCriteria::EPS+TermCriteria::COUNT, 30, 0.1 ));}if( mode == CAPTURING &&  // For camera only take new samples after delay time(!s.inputCapture.isOpened() || clock() - prevTimestamp > s.delay*1e-3*CLOCKS_PER_SEC) ){imagePoints.push_back(pointBuf);prevTimestamp = clock();blinkOutput = s.inputCapture.isOpened();}// Draw the corners.drawChessboardCorners( view, s.boardSize, Mat(pointBuf), found );}//! [pattern_found]//----------------------------- Output Text ------------------------------------------------//! [output_text]string msg = (mode == CAPTURING) ? "100/100" :mode == CALIBRATED ? "Calibrated" : "Press 'g' to start";int baseLine = 0;Size textSize = getTextSize(msg, 1, 1, 1, &baseLine);Point textOrigin(view.cols - 2*textSize.width - 10, view.rows - 2*baseLine - 10);if( mode == CAPTURING ){if(s.showUndistorsed)msg = format( "%d/%d Undist", (int)imagePoints.size(), s.nrFrames );elsemsg = format( "%d/%d", (int)imagePoints.size(), s.nrFrames );}putText( view, msg, textOrigin, 1, 1, mode == CALIBRATED ?  GREEN : RED);if( blinkOutput )bitwise_not(view, view);//! [output_text]//------------------------- Video capture  output  undistorted ------------------------------//! [output_undistorted]if( mode == CALIBRATED && s.showUndistorsed ){Mat temp = view.clone();if (s.useFisheye)cv::fisheye::undistortImage(temp, view, cameraMatrix, distCoeffs);elseundistort(temp, view, cameraMatrix, distCoeffs);}//! [output_undistorted]//------------------------------ Show image and check for input commands -------------------//! [await_input]imshow("Image View", view);char key = (char)waitKey(s.inputCapture.isOpened() ? 50 : s.delay);if( key  == ESC_KEY )break;if( key == 'u' && mode == CALIBRATED )s.showUndistorsed = !s.showUndistorsed;if( s.inputCapture.isOpened() && key == 'g' ){mode = CAPTURING;imagePoints.clear();}//! [await_input]}// -----------------------Show the undistorted image for the image list ------------------------//! [show_results]if( s.inputType == Settings::IMAGE_LIST && s.showUndistorsed ){Mat view, rview, map1, map2;if (s.useFisheye){Mat newCamMat;fisheye::estimateNewCameraMatrixForUndistortRectify(cameraMatrix, distCoeffs, imageSize,Matx33d::eye(), newCamMat, 1);fisheye::initUndistortRectifyMap(cameraMatrix, distCoeffs, Matx33d::eye(), newCamMat, imageSize,CV_16SC2, map1, map2);}else{initUndistortRectifyMap(cameraMatrix, distCoeffs, Mat(),getOptimalNewCameraMatrix(cameraMatrix, distCoeffs, imageSize, 1, imageSize, 0), imageSize,CV_16SC2, map1, map2);}for(size_t i = 0; i < s.imageList.size(); i++ ){view = imread(s.imageList[i], IMREAD_COLOR);if(view.empty())continue;remap(view, rview, map1, map2, INTER_LINEAR);imshow("Image View", rview);char c = (char)waitKey();if( c  == ESC_KEY || c == 'q' || c == 'Q' )break;}}//! [show_results]return 0;
}//! [compute_errors]
static double computeReprojectionErrors( const vector<vector<Point3f> >& objectPoints,const vector<vector<Point2f> >& imagePoints,const vector<Mat>& rvecs, const vector<Mat>& tvecs,const Mat& cameraMatrix , const Mat& distCoeffs,vector<float>& perViewErrors, bool fisheye)
{vector<Point2f> imagePoints2;size_t totalPoints = 0;double totalErr = 0, err;perViewErrors.resize(objectPoints.size());for(size_t i = 0; i < objectPoints.size(); ++i ){if (fisheye){fisheye::projectPoints(objectPoints[i], imagePoints2, rvecs[i], tvecs[i], cameraMatrix,distCoeffs);}else{projectPoints(objectPoints[i], rvecs[i], tvecs[i], cameraMatrix, distCoeffs, imagePoints2);}err = norm(imagePoints[i], imagePoints2, NORM_L2);size_t n = objectPoints[i].size();perViewErrors[i] = (float) std::sqrt(err*err/n);totalErr        += err*err;totalPoints     += n;}return std::sqrt(totalErr/totalPoints);
}
//! [compute_errors]
//! [board_corners]
static void calcBoardCornerPositions(Size boardSize, float squareSize, vector<Point3f>& corners,Settings::Pattern patternType /*= Settings::CHESSBOARD*/)
{corners.clear();switch(patternType){case Settings::CHESSBOARD:case Settings::CIRCLES_GRID:for( int i = 0; i < boardSize.height; ++i )for( int j = 0; j < boardSize.width; ++j )corners.push_back(Point3f(j*squareSize, i*squareSize, 0));break;case Settings::ASYMMETRIC_CIRCLES_GRID:for( int i = 0; i < boardSize.height; i++ )for( int j = 0; j < boardSize.width; j++ )corners.push_back(Point3f((2*j + i % 2)*squareSize, i*squareSize, 0));break;default:break;}
}
//! [board_corners]
static bool runCalibration( Settings& s, Size& imageSize, Mat& cameraMatrix, Mat& distCoeffs,vector<vector<Point2f> > imagePoints, vector<Mat>& rvecs, vector<Mat>& tvecs,vector<float>& reprojErrs,  double& totalAvgErr)
{//! [fixed_aspect]cameraMatrix = Mat::eye(3, 3, CV_64F);if( s.flag & CALIB_FIX_ASPECT_RATIO )cameraMatrix.at<double>(0,0) = s.aspectRatio;//! [fixed_aspect]if (s.useFisheye) {distCoeffs = Mat::zeros(4, 1, CV_64F);} else {distCoeffs = Mat::zeros(8, 1, CV_64F);}vector<vector<Point3f> > objectPoints(1);calcBoardCornerPositions(s.boardSize, s.squareSize, objectPoints[0], s.calibrationPattern);objectPoints.resize(imagePoints.size(),objectPoints[0]);//Find intrinsic and extrinsic camera parametersdouble rms;if (s.useFisheye) {Mat _rvecs, _tvecs;rms = fisheye::calibrate(objectPoints, imagePoints, imageSize, cameraMatrix, distCoeffs, _rvecs,_tvecs, s.flag);rvecs.reserve(_rvecs.rows);tvecs.reserve(_tvecs.rows);for(int i = 0; i < int(objectPoints.size()); i++){rvecs.push_back(_rvecs.row(i));tvecs.push_back(_tvecs.row(i));}} else {rms = calibrateCamera(objectPoints, imagePoints, imageSize, cameraMatrix, distCoeffs, rvecs, tvecs,s.flag);}cout << "Re-projection error reported by calibrateCamera: "<< rms << endl;bool ok = checkRange(cameraMatrix) && checkRange(distCoeffs);totalAvgErr = computeReprojectionErrors(objectPoints, imagePoints, rvecs, tvecs, cameraMatrix,distCoeffs, reprojErrs, s.useFisheye);return ok;
}// Print camera parameters to the output file
static void saveCameraParams( Settings& s, Size& imageSize, Mat& cameraMatrix, Mat& distCoeffs,const vector<Mat>& rvecs, const vector<Mat>& tvecs,const vector<float>& reprojErrs, const vector<vector<Point2f> >& imagePoints,double totalAvgErr )
{FileStorage fs( s.outputFileName, FileStorage::WRITE );time_t tm;time( &tm );struct tm *t2 = localtime( &tm );char buf[1024];strftime( buf, sizeof(buf), "%c", t2 );fs << "calibration_time" << buf;if( !rvecs.empty() || !reprojErrs.empty() )fs << "nr_of_frames" << (int)std::max(rvecs.size(), reprojErrs.size());fs << "image_width" << imageSize.width;fs << "image_height" << imageSize.height;fs << "board_width" << s.boardSize.width;fs << "board_height" << s.boardSize.height;fs << "square_size" << s.squareSize;if( s.flag & CALIB_FIX_ASPECT_RATIO )fs << "fix_aspect_ratio" << s.aspectRatio;if (s.flag){std::stringstream flagsStringStream;if (s.useFisheye){flagsStringStream << "flags:"<< (s.flag & fisheye::CALIB_FIX_SKEW ? " +fix_skew" : "")<< (s.flag & fisheye::CALIB_FIX_K1 ? " +fix_k1" : "")<< (s.flag & fisheye::CALIB_FIX_K2 ? " +fix_k2" : "")<< (s.flag & fisheye::CALIB_FIX_K3 ? " +fix_k3" : "")<< (s.flag & fisheye::CALIB_FIX_K4 ? " +fix_k4" : "")<< (s.flag & fisheye::CALIB_RECOMPUTE_EXTRINSIC ? " +recompute_extrinsic" : "");}else{flagsStringStream << "flags:"<< (s.flag & CALIB_USE_INTRINSIC_GUESS ? " +use_intrinsic_guess" : "")<< (s.flag & CALIB_FIX_ASPECT_RATIO ? " +fix_aspectRatio" : "")<< (s.flag & CALIB_FIX_PRINCIPAL_POINT ? " +fix_principal_point" : "")<< (s.flag & CALIB_ZERO_TANGENT_DIST ? " +zero_tangent_dist" : "")<< (s.flag & CALIB_FIX_K1 ? " +fix_k1" : "")<< (s.flag & CALIB_FIX_K2 ? " +fix_k2" : "")<< (s.flag & CALIB_FIX_K3 ? " +fix_k3" : "")<< (s.flag & CALIB_FIX_K4 ? " +fix_k4" : "")<< (s.flag & CALIB_FIX_K5 ? " +fix_k5" : "");}fs.writeComment(flagsStringStream.str());}fs << "flags" << s.flag;fs << "fisheye_model" << s.useFisheye;fs << "camera_matrix" << cameraMatrix;fs << "distortion_coefficients" << distCoeffs;fs << "avg_reprojection_error" << totalAvgErr;if (s.writeExtrinsics && !reprojErrs.empty())fs << "per_view_reprojection_errors" << Mat(reprojErrs);if(s.writeExtrinsics && !rvecs.empty() && !tvecs.empty() ){CV_Assert(rvecs[0].type() == tvecs[0].type());Mat bigmat((int)rvecs.size(), 6, CV_MAKETYPE(rvecs[0].type(), 1));bool needReshapeR = rvecs[0].depth() != 1 ? true : false;bool needReshapeT = tvecs[0].depth() != 1 ? true : false;for( size_t i = 0; i < rvecs.size(); i++ ){Mat r = bigmat(Range(int(i), int(i+1)), Range(0,3));Mat t = bigmat(Range(int(i), int(i+1)), Range(3,6));if(needReshapeR)rvecs[i].reshape(1, 1).copyTo(r);else{//*.t() is MatExpr (not Mat) so we can use assignment operatorCV_Assert(rvecs[i].rows == 3 && rvecs[i].cols == 1);r = rvecs[i].t();}if(needReshapeT)tvecs[i].reshape(1, 1).copyTo(t);else{CV_Assert(tvecs[i].rows == 3 && tvecs[i].cols == 1);t = tvecs[i].t();}}fs.writeComment("a set of 6-tuples (rotation vector + translation vector) for each view");fs << "extrinsic_parameters" << bigmat;}if(s.writePoints && !imagePoints.empty() ){Mat imagePtMat((int)imagePoints.size(), (int)imagePoints[0].size(), CV_32FC2);for( size_t i = 0; i < imagePoints.size(); i++ ){Mat r = imagePtMat.row(int(i)).reshape(2, imagePtMat.cols);Mat imgpti(imagePoints[i]);imgpti.copyTo(r);}fs << "image_points" << imagePtMat;}
}//! [run_and_save]
bool runCalibrationAndSave(Settings& s, Size imageSize, Mat& cameraMatrix, Mat& distCoeffs,vector<vector<Point2f> > imagePoints)
{vector<Mat> rvecs, tvecs;vector<float> reprojErrs;double totalAvgErr = 0;bool ok = runCalibration(s, imageSize, cameraMatrix, distCoeffs, imagePoints, rvecs, tvecs, reprojErrs,totalAvgErr);cout << (ok ? "Calibration succeeded" : "Calibration failed")<< ". avg re projection error = " << totalAvgErr << endl;if (ok)saveCameraParams(s, imageSize, cameraMatrix, distCoeffs, rvecs, tvecs, reprojErrs, imagePoints,totalAvgErr);return ok;
}
//! [run_and_save]

程序只有一个参数：配置文件的名字. 如果没有给出将会尝试打开名字为 "default.xml"的配置文件.XML格式的配置文件的例子如下：

<?xml version="1.0"?>
<opencv_storage>
<Settings><!-- Number of inner corners per a item row and column. (square, circle) --><BoardSize_Width> 9</BoardSize_Width><BoardSize_Height>6</BoardSize_Height><!-- The size of a square in some user defined metric system (pixel, millimeter)--><Square_Size>50</Square_Size><!-- The type of input used for camera calibration. One of: CHESSBOARD CIRCLES_GRID ASYMMETRIC_CIRCLES_GRID --><Calibrate_Pattern>"CHESSBOARD"</Calibrate_Pattern><!-- The input to use for calibration. To use an input camera -> give the ID of the camera, like "1"To use an input video  -> give the path of the input video, like "/tmp/x.avi"To use an image list   -> give the path to the XML or YAML file containing the list of the images, like "/tmp/circles_list.xml"--><Input>"images/CameraCalibration/VID5/VID5.xml"</Input><!--  If true (non-zero) we flip the input images around the horizontal axis.--><Input_FlipAroundHorizontalAxis>0</Input_FlipAroundHorizontalAxis><!-- Time delay between frames in case of camera. --><Input_Delay>100</Input_Delay> <!-- How many frames to use, for calibration. --><Calibrate_NrOfFrameToUse>25</Calibrate_NrOfFrameToUse><!-- Consider only fy as a free parameter, the ratio fx/fy stays the same as in the input cameraMatrix. Use or not setting. 0 - False Non-Zero - True--><Calibrate_FixAspectRatio> 1 </Calibrate_FixAspectRatio><!-- If true (non-zero) tangential distortion coefficients  are set to zeros and stay zero.--><Calibrate_AssumeZeroTangentialDistortion>1</Calibrate_AssumeZeroTangentialDistortion><!-- If true (non-zero) the principal point is not changed during the global optimization.--><Calibrate_FixPrincipalPointAtTheCenter> 1 </Calibrate_FixPrincipalPointAtTheCenter><!-- The name of the output log file. --><Write_outputFileName>"out_camera_data.xml"</Write_outputFileName><!-- If true (non-zero) we write to the output file the feature points.--><Write_DetectedFeaturePoints>1</Write_DetectedFeaturePoints><!-- If true (non-zero) we write to the output file the extrinsic camera parameters.--><Write_extrinsicParameters>1</Write_extrinsicParameters><!-- If true (non-zero) we show after calibration the undistorted images.--><Show_UndistortedImage>1</Show_UndistortedImage><!-- If true (non-zero) will be used fisheye camera model.--><Calibrate_UseFisheyeModel>0</Calibrate_UseFisheyeModel><!-- If true (non-zero) distortion coefficient k1 will be equals to zero.--><Fix_K1>0</Fix_K1><!-- If true (non-zero) distortion coefficient k2 will be equals to zero.--><Fix_K2>0</Fix_K2><!-- If true (non-zero) distortion coefficient k3 will be equals to zero.--><Fix_K3>0</Fix_K3><!-- If true (non-zero) distortion coefficient k4 will be equals to zero.--><Fix_K4>1</Fix_K4><!-- If true (non-zero) distortion coefficient k5 will be equals to zero.--><Fix_K5>1</Fix_K5>
</Settings>
</opencv_storage>

配置文件中可以选择摄像头、视频或者图像列表作为输入。如果选择图像列表作为输入，你需要创建一个包含要使用的图像的配置文件，例子如下：

<?xml version="1.0"?>
<opencv_storage>
<images>
images/CameraCalibraation/VID5/xx1.jpg
images/CameraCalibraation/VID5/xx2.jpg
images/CameraCalibraation/VID5/xx3.jpg
images/CameraCalibraation/VID5/xx4.jpg
images/CameraCalibraation/VID5/xx5.jpg
images/CameraCalibraation/VID5/xx6.jpg
images/CameraCalibraation/VID5/xx7.jpg
images/CameraCalibraation/VID5/xx8.jpg
</images>
</opencv_storage>

配置文件中要指定程序执行路径下，能够访问到图像的绝对或相对路径。

程序开始先读取配置文件. 对于XML 和 YAML文件的读入和写出，请参见《OpenCV中XML文件和YAML文件的读写》。

结果

棋盘格结果

棋盘格（9 X 6）的下载地址：棋盘格

相机： AXIS IP camera

图片配置文件：VID5.XML

<?xml version="1.0"?>
<opencv_storage>
<images>
images/CameraCalibration/VID5/xx1.jpg
images/CameraCalibration/VID5/xx2.jpg
images/CameraCalibration/VID5/xx3.jpg
images/CameraCalibration/VID5/xx4.jpg
images/CameraCalibration/VID5/xx5.jpg
images/CameraCalibration/VID5/xx6.jpg
images/CameraCalibration/VID5/xx7.jpg
images/CameraCalibration/VID5/xx8.jpg
</images>
</opencv_storage>

找到的棋盘格的图案如下图所示：

畸变移除厚的效果为：

非对称圆样式图案标定

下载地址：this asymmetrical circle pattern

输入：摄像头

在设定宽度4高度11的情况下，效果如下:

校正系数输出

输出存储的XML/YAML文件如下：

<camera_matrix type_id="opencv-matrix">
<rows>3</rows>
<cols>3</cols>
<dt>d</dt>
<data>6.5746697944293521e+002 0. 3.1950000000000000e+002 0.6.5746697944293521e+002 2.3950000000000000e+002 0. 0. 1.</data></camera_matrix>
<distortion_coefficients type_id="opencv-matrix">
<rows>5</rows>
<cols>1</cols>
<dt>d</dt>
<data>-4.1802327176423804e-001 5.0715244063187526e-001 0. 0.-5.7843597214487474e-001</data></distortion_coefficients>

将这些参数以常数的形式放在你的代码中, 调用 cv::initUndistortRectifyMap 和 cv::remap 函数进行畸变的移除。

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基于OpenCV进行相机标定

理论

目的：

源代码

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