史上最简单Opencv相机畸变矫正教学

最近因为项目需要研究了一下摄像头的畸变矫正，我打算通过写这篇博客记录一下相关流程。其实关于摄像头畸变矫正的原理，网络上已经有非常多的博客可以参考了，我在博客里也就不再赘述了。利用Opencv库中的接口，可以很方便地对一款固定型号的摄像头进行矫正，一般地我们将这个过程分成两步：生成参数文件和矫正。

生成参数文件

这里使用的是OpenCV的例程（非常方便非常好用~），例程可以在你的opencv源码目录下找到，具体位置在sources\samples\cpp\tutorial_code\calib3d\camera_calibration

我们可以用例程的源码在IDE上建立专门用来做摄像头标定和矫正的工程，虽然我们这篇博客讲的只有矫正，其实整个例程是可以同时把标定过程也完成的，在运行程序之前我们需要保证在工程的构建目录中有以下几个文件：

1. default.xml（后附，保存标定及矫正程序过程中的各项参数）
2. VID5.xml（后附，保存棋盘格图片的文件路径）
3. 摄像头所拍摄的棋盘格的图片10~20张：棋盘格标定板有很多规格的（其实都是自己打印出来的），一般都是9*6或者10*7的，方格的边长一般是30mm也并没有固定的标准，其实这些参数在defalut.xml中都是可以根据实际情况进行设置的，所以不同的规格并不影响最终矫正的效果。拍摄的图片要保证整个棋盘格都在成像区内，尽量保证多张图片之间棋盘格在图像中的成像角度以及所在位置都各不相同，棋盘格图片如下所示：

尽量能达到下面的这种效果，即在各个位置（红色方框）都有棋盘格的图片：

做矫正之前的所有准备都已经说清楚了，下面附上Opencv中的例程和关键文件default.xml和VID5.xml，这两个文件一定要放在工程的构建目录下。因为default.xml和VID5.xml的配置比较重要，所以就先上default.xml和VID5.xml了：

default.xml

  
   9
  6
  
  
  30
  
  
  "CHESSBOARD"
  
  
  "H:\\Distortion\\build\\VID5.xml"
  
  0
  
  
  100	
  
  
  25
  
   1 
  
  1
  
   1 
  
  
  "out_camera_data.xml"
  
  1
  
  1
  
  1
 

这就是非常关键的default.xml文件，其中有几个参数是需要根据具体情况进行对应设置的：

• BoardSize_Width表示的是棋盘格角点矩阵的宽度，BoardSize_Height表示的是棋盘格角点矩阵的高度（其实很简单，就是看棋盘格宽和高分别有多少个黑白格，然后分别减1，从上面的图片可以看到我是用的是10*7的标定板，那么这里的参数应该就是9*6）。
• Square_Size表示的是标定板每个黑白格的边长（30mm）
• Input表示的输入文件VID5.xml所在位置，我这里是直接放在了工程的构建目录中"H:\\Distortion\\build\\VID5.xml"，前面也说到了VID5.xml存放的就是棋盘格图片的文件路径。

VID5.xml

H:/Distortion/build/pic/PICT0022.jpg
H:/Distortion/build/pic/PICT0025.jpg
H:/Distortion/build/pic/PICT0026.jpg
H:/Distortion/build/pic/PICT0027.jpg
H:/Distortion/build/pic/PICT0028.jpg
H:/Distortion/build/pic/PICT0029.jpg
H:/Distortion/build/pic/PICT0030.jpg
H:/Distortion/build/pic/PICT0031.jpg
H:/Distortion/build/pic/PICT0032.jpg
H:/Distortion/build/pic/PICT0033.jpg
H:/Distortion/build/pic/PICT0034.jpg
H:/Distortion/build/pic/PICT0037.jpg

image中的每一个条目都对应这一张用来做畸变矫正的棋盘格图片，VID5.xml文件还是非常好配置的。

最后就是Opencv中标定和矫正的例程了，我们只需要把源码放进配置好Opencv环境的工程中就可以了，因为例程的代码有些长，我们就把代码放在最后了。程序运行完成之后会在构建目录下生成一个参数文件out_camera_data.xml，这个文件十分重要，它内部包含着标定和矫正的所有结果参数，也就是说同一款摄像头我们只需要做一次标定和矫正，之后的应用都只需要参数文件就行了。

矫正

其实运用参数文件进行矫正的过程非常简单，只需要将out_camera_data.xml中的参数读入，然后调用undistort函数就行了。

关键代码如下：

        Mat src = imread("PICT0039.jpg");
        Mat distortion = src.clone();
        Mat camera_matrix = Mat(3, 3, CV_32FC1);
        Mat distortion_coefficients;

//导入相机内参和畸变系数矩阵
        FileStorage file_storage("out_camera_data.xml", FileStorage::READ);
        file_storage["Camera_Matrix"] >> camera_matrix;
        file_storage["Distortion_Coefficients"] >> distortion_coefficients;
        file_storage.release();

        //矫正
        undistort(src, distortion, camera_matrix, distortion_coefficients);

camera_matrix和distortion_coefficients都是存储在cv::Mat中的参数，src和distortion分别是原图像和矫正过后的图像。效果如下：

矫正前

矫正后

最后附上Opencv中的例程：

#include 
#include 
#include 
#include 

#include 
#include 
#include 
#include 

#ifndef _CRT_SECURE_NO_WARNINGS
# define _CRT_SECURE_NO_WARNINGS
#endif

using namespace cv;
using namespace std;

static void help()
{
    cout <<  "This is a camera calibration sample." << endl
         <<  "Usage: calibration configurationFile"  << 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" << bwritePoints
                  << "Write_extrinsicParameters"   << bwriteExtrinsics
                  << "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"] >> bwritePoints;
        node["Write_extrinsicParameters"] >> bwriteExtrinsics;
        node["Write_outputFileName"] >> outputFileName;
        node["Calibrate_AssumeZeroTangentialDistortion"] >> calibZeroTangentDist;
        node["Calibrate_FixPrincipalPointAtTheCenter"] >> calibFixPrincipalPoint;
        node["Input_FlipAroundHorizontalAxis"] >> flipVertical;
        node["Show_UndistortedImage"] >> showUndistorsed;
        node["Input"] >> input;
        node["Input_Delay"] >> delay;
        interprate();
    }
    void interprate()
    {
        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 input
                inputType = 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();
                    }
                else
                    inputType = 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 << " Inexistent input: " << input;
            goodInput = false;
        }

        flag = 0;
        if(calibFixPrincipalPoint) flag |= CV_CALIB_FIX_PRINCIPAL_POINT;
        if(calibZeroTangentDist)   flag |= CV_CALIB_ZERO_TANGENT_DIST;
        if(aspectRatio)            flag |= CV_CALIB_FIX_ASPECT_RATIO;


        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 << " Inexistent camera calibration mode: " << patternToUse << endl;
                goodInput = false;
            }
        atImageList = 0;

    }
    Mat nextImage()
    {
        Mat result;
        if( inputCapture.isOpened() )
        {
            Mat view0;
            inputCapture >> view0;
            view0.copyTo(result);
        }
        else if( atImageList < (int)imageList.size() )
            result = imread(imageList[atImageList++], CV_LOAD_IMAGE_COLOR);

        return result;
    }

    static bool readStringList( const string& filename, vector& 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 height
    Pattern calibrationPattern;// One of the Chessboard, circles, or asymmetric circle pattern
    float 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 calibration
    float aspectRatio;         // The aspect ratio
    int delay;                 // In case of a video input
    bool bwritePoints;         //  Write detected feature points
    bool bwriteExtrinsics;     // Write extrinsic parameters
    bool calibZeroTangentDist; // Assume zero tangential distortion
    bool calibFixPrincipalPoint;// Fix the principal point at the center
    bool flipVertical;          // Flip the captured images around the horizontal axis
    string outputFileName;      // The name of the file where to write
    bool showUndistorsed;       // Show undistorted images after calibration
    string input;               // The input ->



    int cameraID;
    vector imageList;
    int atImageList;
    VideoCapture inputCapture;
    InputType inputType;
    bool goodInput;
    int flag;

private:
    string patternToUse;


};

static void read(const FileNode& node, Settings& x, const Settings& default_value = Settings())
{
    if(node.empty())
        x = default_value;
    else
        x.read(node);
}

enum { DETECTION = 0, CAPTURING = 1, CALIBRATED = 2 };

bool runCalibrationAndSave(Settings& s, Size imageSize, Mat&  cameraMatrix, Mat& distCoeffs,
                           vector > imagePoints );

int main(int argc, char* argv[])
{
    help();
    Settings s;
    const string inputSettingsFile = argc > 1 ? argv[1] : "default.xml";
    FileStorage fs(inputSettingsFile, FileStorage::READ); // Read the settings
    if (!fs.isOpened())
    {
        cout << "Could not open the configuration file: \"" << inputSettingsFile << "\"" << endl;
        return -1;
    }
    fs["Settings"] >> s;
    fs.release();                                         // close Settings file

    if (!s.goodInput)
    {
        cout << "Invalid input detected. Application stopping. " << endl;
        return -1;
    }

    vector > 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;

    for(int i = 0;;++i)
    {
      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() >= (unsigned)s.nrFrames )
      {
          if( runCalibrationAndSave(s, imageSize,  cameraMatrix, distCoeffs, imagePoints))
              mode = CALIBRATED;
          else
              mode = DETECTION;
      }
      if(view.empty())          // If no more images then run calibration, save and stop loop.
      {
            if( imagePoints.size() > 0 )
                runCalibrationAndSave(s, imageSize,  cameraMatrix, distCoeffs, imagePoints);
            break;
      }


        imageSize = view.size();  // Format input image.
        if( s.flipVertical )    flip( view, view, 0 );

        vector pointBuf;

        bool found;
        switch( s.calibrationPattern ) // Find feature points on the input format
        {
        case Settings::CHESSBOARD:
            found = findChessboardCorners( view, s.boardSize, pointBuf,
                CV_CALIB_CB_ADAPTIVE_THRESH | CV_CALIB_CB_FAST_CHECK | CV_CALIB_CB_NORMALIZE_IMAGE);
            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;
        }

        if (found)                // If done with success,
        {
              // improve the found corners' coordinate accuracy for chessboard
                if( s.calibrationPattern == Settings::CHESSBOARD)
                {
                    Mat viewGray;
                    cvtColor(view, viewGray, COLOR_BGR2GRAY);
                    cornerSubPix( viewGray, pointBuf, Size(11,11),
                        Size(-1,-1), TermCriteria( CV_TERMCRIT_EPS+CV_TERMCRIT_ITER, 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 );
        }

        //----------------------------- 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 );
            else
                msg = format( "%d/%d", (int)imagePoints.size(), s.nrFrames );
        }

        putText( view, msg, textOrigin, 1, 1, mode == CALIBRATED ?  GREEN : RED);

        if( blinkOutput )
            bitwise_not(view, view);

        //------------------------- Video capture  output  undistorted ------------------------------
        if( mode == CALIBRATED && s.showUndistorsed )
        {
            Mat temp = view.clone();
            undistort(temp, view, cameraMatrix, distCoeffs);
        }

        //------------------------------ Show image and check for input commands -------------------
        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();
        }
    }

    // -----------------------Show and save the undistorted image for the image list ------------------------
    if( s.inputType == Settings::IMAGE_LIST && s.showUndistorsed )
    {
        Mat view, rview, map1, map2;
        initUndistortRectifyMap(cameraMatrix, distCoeffs, Mat(),
            getOptimalNewCameraMatrix(cameraMatrix, distCoeffs, imageSize, 1, imageSize, 0),
            imageSize, CV_16SC2, map1, map2);

        for(int i = 0; i < (int)s.imageList.size(); i++ )
        {
            view = imread(s.imageList[i], 1);
            if(view.empty())
                continue;
            remap(view, rview, map1, map2, INTER_LINEAR);
            imshow("Image View", rview);

            string imageName = format( "undistorted_%d.jpg", i);
            imwrite(imageName,rview);

            char c = (char)waitKey();
            if( c  == ESC_KEY || c == 'q' || c == 'Q' )
                break;
        }
    }


    return 0;
}

static double computeReprojectionErrors( const vector >& objectPoints,
                                         const vector >& imagePoints,
                                         const vector& rvecs, const vector& tvecs,
                                         const Mat& cameraMatrix , const Mat& distCoeffs,
                                         vector& perViewErrors)
{
    vector imagePoints2;
    int i, totalPoints = 0;
    double totalErr = 0, err;
    perViewErrors.resize(objectPoints.size());

    for( i = 0; i < (int)objectPoints.size(); ++i )
    {
        projectPoints( Mat(objectPoints[i]), rvecs[i], tvecs[i], cameraMatrix,
                       distCoeffs, imagePoints2);
        err = norm(Mat(imagePoints[i]), Mat(imagePoints2), CV_L2);

        int n = (int)objectPoints[i].size();
        perViewErrors[i] = (float) std::sqrt(err*err/n);
        totalErr        += err*err;
        totalPoints     += n;
    }

    return std::sqrt(totalErr/totalPoints);
}

static void calcBoardCornerPositions(Size boardSize, float squareSize, vector& 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(float( j*squareSize ), float( 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(float((2*j + i % 2)*squareSize), float(i*squareSize), 0));
        break;
    default:
        break;
    }
}

static bool runCalibration( Settings& s, Size& imageSize, Mat& cameraMatrix, Mat& distCoeffs,
                            vector > imagePoints, vector& rvecs, vector& tvecs,
                            vector& reprojErrs,  double& totalAvgErr)
{

    cameraMatrix = Mat::eye(3, 3, CV_64F);
    if( s.flag & CV_CALIB_FIX_ASPECT_RATIO )
        cameraMatrix.at(0,0) = 1.0;

    distCoeffs = Mat::zeros(8, 1, CV_64F);

    vector > objectPoints(1);
    calcBoardCornerPositions(s.boardSize, s.squareSize, objectPoints[0], s.calibrationPattern);

    objectPoints.resize(imagePoints.size(),objectPoints[0]);

    //Find intrinsic and extrinsic camera parameters
    double rms = calibrateCamera(objectPoints, imagePoints, imageSize, cameraMatrix,
                                 distCoeffs, rvecs, tvecs, s.flag|CV_CALIB_FIX_K4|CV_CALIB_FIX_K5);

    cout << "Re-projection error reported by calibrateCamera: "<< rms << endl;

    bool ok = checkRange(cameraMatrix) && checkRange(distCoeffs);

    totalAvgErr = computeReprojectionErrors(objectPoints, imagePoints,
                                             rvecs, tvecs, cameraMatrix, distCoeffs, reprojErrs);

    return ok;
}

// Print camera parameters to the output file
static void saveCameraParams( Settings& s, Size& imageSize, Mat& cameraMatrix, Mat& distCoeffs,
                              const vector& rvecs, const vector& tvecs,
                              const vector& reprojErrs, const vector >& 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)-1, "%c", t2 );

    fs << "calibration_Time" << buf;

    if( !rvecs.empty() || !reprojErrs.empty() )
        fs << "nrOfFrames" << (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 & CV_CALIB_FIX_ASPECT_RATIO )
        fs << "FixAspectRatio" << s.aspectRatio;

    if( s.flag )
    {
        sprintf( buf, "flags: %s%s%s%s",
            s.flag & CV_CALIB_USE_INTRINSIC_GUESS ? " +use_intrinsic_guess" : "",
            s.flag & CV_CALIB_FIX_ASPECT_RATIO ? " +fix_aspectRatio" : "",
            s.flag & CV_CALIB_FIX_PRINCIPAL_POINT ? " +fix_principal_point" : "",
            s.flag & CV_CALIB_ZERO_TANGENT_DIST ? " +zero_tangent_dist" : "" );
        cvWriteComment( *fs, buf, 0 );

    }

    fs << "flagValue" << s.flag;

    fs << "Camera_Matrix" << cameraMatrix;
    fs << "Distortion_Coefficients" << distCoeffs;

    fs << "Avg_Reprojection_Error" << totalAvgErr;
    if( !reprojErrs.empty() )
        fs << "Per_View_Reprojection_Errors" << Mat(reprojErrs);

    if( !rvecs.empty() && !tvecs.empty() )
    {
        CV_Assert(rvecs[0].type() == tvecs[0].type());
        Mat bigmat((int)rvecs.size(), 6, rvecs[0].type());
        for( int i = 0; i < (int)rvecs.size(); i++ )
        {
            Mat r = bigmat(Range(i, i+1), Range(0,3));
            Mat t = bigmat(Range(i, i+1), Range(3,6));

            CV_Assert(rvecs[i].rows == 3 && rvecs[i].cols == 1);
            CV_Assert(tvecs[i].rows == 3 && tvecs[i].cols == 1);
            //*.t() is MatExpr (not Mat) so we can use assignment operator
            r = rvecs[i].t();
            t = tvecs[i].t();
        }
        cvWriteComment( *fs, "a set of 6-tuples (rotation vector + translation vector) for each view", 0 );
        fs << "Extrinsic_Parameters" << bigmat;
    }

    if( !imagePoints.empty() )
    {
        Mat imagePtMat((int)imagePoints.size(), (int)imagePoints[0].size(), CV_32FC2);
        for( int i = 0; i < (int)imagePoints.size(); i++ )
        {
            Mat r = imagePtMat.row(i).reshape(2, imagePtMat.cols);
            Mat imgpti(imagePoints[i]);
            imgpti.copyTo(r);
        }
        fs << "Image_points" << imagePtMat;
    }
}

bool runCalibrationAndSave(Settings& s, Size imageSize, Mat&  cameraMatrix, Mat& distCoeffs,vector > imagePoints )
{
    vector rvecs, tvecs;
    vector 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 ;

    if( ok )
        saveCameraParams( s, imageSize, cameraMatrix, distCoeffs, rvecs ,tvecs, reprojErrs,
                            imagePoints, totalAvgErr);
    return ok;
}

参考博客：https://blog.csdn.net/u013498583/article/details/71404323