Camera Calibration（opencv官方实例）

Camera Calibration

1、stereo_calib.cpp代码：

/* This is sample from the OpenCV book. The copyright notice is below */
/* *************** License:**************************
   ************************************************** */

#include "opencv2/calib3d/calib3d.hpp"
#include "opencv2/highgui/highgui.hpp"
#include "opencv2/imgproc/imgproc.hpp"

#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 

using namespace cv;
using namespace std;

static int print_help()
{
    cout <<
            " Given a list of chessboard images, the number of corners (nx, ny)\n"
            " on the chessboards, and a flag: useCalibrated for \n"
            "   calibrated (0) or\n"
            "   uncalibrated \n"
            "     (1: use cvStereoCalibrate(), 2: compute fundamental\n"
            "         matrix separately) stereo. \n"
            " Calibrate the cameras and display the\n"
            " rectified results along with the computed disparity images.   \n" << endl;
    cout << "Usage:\n ./stereo_calib -w board_width -h board_height [-nr /*dot not view results*/] \n" << endl;
    return 0;
}



static void StereoCalib(const vector& imagelist, Size boardSize, bool useCalibrated=true, bool showRectified=true)
{
    if( imagelist.size() % 2 != 0 )
    {
        cout << "Error: the image list contains odd (non-even) number of elements\n";
        return;
    }

    bool displayCorners = false;//true;
    const int maxScale = 2;
    const float squareSize = 1.f;  // Set this to your actual square size
    // ARRAY AND VECTOR STORAGE:

    vector > imagePoints[2];
    vector > objectPoints;
    Size imageSize;

    int i, j, k, nimages = (int)imagelist.size()/2;

    imagePoints[0].resize(nimages);
    imagePoints[1].resize(nimages);
    vector goodImageList;

    for( i = j = 0; i < nimages; i++ )
    {
        for( k = 0; k < 2; k++ )
        {
            const string& filename = imagelist[i*2+k];
            Mat img = imread(filename, 0);
            if(img.empty())
                break;
            if( imageSize == Size() )
                imageSize = img.size();
            else if( img.size() != imageSize )
            {
                cout << "The image " << filename << " has the size different from the first image size. Skipping the pair\n";
                break;
            }
            bool found = false;
            vector& corners = imagePoints[k][j];
            for( int scale = 1; scale <= maxScale; scale++ )
            {
                Mat timg;
                if( scale == 1 )
                    timg = img;
                else
                    resize(img, timg, Size(), scale, scale);
                found = findChessboardCorners(timg, boardSize, corners,
                    CV_CALIB_CB_ADAPTIVE_THRESH | CV_CALIB_CB_NORMALIZE_IMAGE);
                if( found )
                {
                    if( scale > 1 )
                    {
                        Mat cornersMat(corners);
                        cornersMat *= 1./scale;
                    }
                    break;
                }
            }
            if( displayCorners )
            {
                cout << filename << endl;
                Mat cimg, cimg1;
                cvtColor(img, cimg, COLOR_GRAY2BGR);
                drawChessboardCorners(cimg, boardSize, corners, found);
                double sf = 640./MAX(img.rows, img.cols);
                resize(cimg, cimg1, Size(), sf, sf);
                imshow("corners", cimg1);
                char c = (char)waitKey(500);
                if( c == 27 || c == 'q' || c == 'Q' ) //Allow ESC to quit
                    exit(-1);
            }
            else
                putchar('.');
            if( !found )
                break;
            cornerSubPix(img, corners, Size(11,11), Size(-1,-1),
                         TermCriteria(CV_TERMCRIT_ITER+CV_TERMCRIT_EPS,30, 0.01));
        }
        if( k == 2 )
        {
            goodImageList.push_back(imagelist[i*2]);
            goodImageList.push_back(imagelist[i*2+1]);
            j++;
        }
    }
    cout << j << " pairs have been successfully detected.\n";
    nimages = j;
    if( nimages < 2 )
    {
        cout << "Error: too little pairs to run the calibration\n";
        return;
    }

    imagePoints[0].resize(nimages);
    imagePoints[1].resize(nimages);
    objectPoints.resize(nimages);

    for( i = 0; i < nimages; i++ )
    {
        for( j = 0; j < boardSize.height; j++ )
            for( k = 0; k < boardSize.width; k++ )
                objectPoints[i].push_back(Point3f(j*squareSize, k*squareSize, 0));
    }

    cout << "Running stereo calibration ...\n";

    Mat cameraMatrix[2], distCoeffs[2];
    cameraMatrix[0] = Mat::eye(3, 3, CV_64F);
    cameraMatrix[1] = Mat::eye(3, 3, CV_64F);
    Mat R, T, E, F;

    double rms = stereoCalibrate(objectPoints, imagePoints[0], imagePoints[1],
                    cameraMatrix[0], distCoeffs[0],
                    cameraMatrix[1], distCoeffs[1],
                    imageSize, R, T, E, F,
                    TermCriteria(CV_TERMCRIT_ITER+CV_TERMCRIT_EPS, 100, 1e-5),
                    CV_CALIB_FIX_ASPECT_RATIO +
                    CV_CALIB_ZERO_TANGENT_DIST +
                    CV_CALIB_SAME_FOCAL_LENGTH +
                    CV_CALIB_RATIONAL_MODEL +
                    CV_CALIB_FIX_K3 + CV_CALIB_FIX_K4 + CV_CALIB_FIX_K5);
    cout << "done with RMS error=" << rms << endl;

// CALIBRATION QUALITY CHECK
// because the output fundamental matrix implicitly
// includes all the output information,
// we can check the quality of calibration using the
// epipolar geometry constraint: m2^t*F*m1=0
    double err = 0;
    int npoints = 0;
    vector lines[2];
    for( i = 0; i < nimages; i++ )
    {
        int npt = (int)imagePoints[0][i].size();
        Mat imgpt[2];
        for( k = 0; k < 2; k++ )
        {
            imgpt[k] = Mat(imagePoints[k][i]);
            undistortPoints(imgpt[k], imgpt[k], cameraMatrix[k], distCoeffs[k], Mat(), cameraMatrix[k]);
            computeCorrespondEpilines(imgpt[k], k+1, F, lines[k]);
        }
        for( j = 0; j < npt; j++ )
        {
            double errij = fabs(imagePoints[0][i][j].x*lines[1][j][0] +
                                imagePoints[0][i][j].y*lines[1][j][1] + lines[1][j][2]) +
                           fabs(imagePoints[1][i][j].x*lines[0][j][0] +
                                imagePoints[1][i][j].y*lines[0][j][1] + lines[0][j][2]);
            err += errij;
        }
        npoints += npt;
    }
    cout << "average reprojection err = " <<  err/npoints << endl;

    // save intrinsic parameters
    FileStorage fs("intrinsics.yml", CV_STORAGE_WRITE);
    if( fs.isOpened() )
    {
        fs << "M1" << cameraMatrix[0] << "D1" << distCoeffs[0] <<
            "M2" << cameraMatrix[1] << "D2" << distCoeffs[1];
        fs.release();
    }
    else
        cout << "Error: can not save the intrinsic parameters\n";

    Mat R1, R2, P1, P2, Q;
    Rect validRoi[2];

    stereoRectify(cameraMatrix[0], distCoeffs[0],
                  cameraMatrix[1], distCoeffs[1],
                  imageSize, R, T, R1, R2, P1, P2, Q,
                  CALIB_ZERO_DISPARITY, 1, imageSize, &validRoi[0], &validRoi[1]);

    fs.open("extrinsics.yml", CV_STORAGE_WRITE);
    if( fs.isOpened() )
    {
        fs << "R" << R << "T" << T << "R1" << R1 << "R2" << R2 << "P1" << P1 << "P2" << P2 << "Q" << Q;
        fs.release();
    }
    else
        cout << "Error: can not save the intrinsic parameters\n";

    // OpenCV can handle left-right
    // or up-down camera arrangements
    bool isVerticalStereo = fabs(P2.at(1, 3)) > fabs(P2.at(0, 3));

// COMPUTE AND DISPLAY RECTIFICATION
    if( !showRectified )
        return;

    Mat rmap[2][2];
// IF BY CALIBRATED (BOUGUET'S METHOD)
    if( useCalibrated )
    {
        // we already computed everything
    }
// OR ELSE HARTLEY'S METHOD
    else
 // use intrinsic parameters of each camera, but
 // compute the rectification transformation directly
 // from the fundamental matrix
    {
        vector allimgpt[2];
        for( k = 0; k < 2; k++ )
        {
            for( i = 0; i < nimages; i++ )
                std::copy(imagePoints[k][i].begin(), imagePoints[k][i].end(), back_inserter(allimgpt[k]));
        }
        F = findFundamentalMat(Mat(allimgpt[0]), Mat(allimgpt[1]), FM_8POINT, 0, 0);
        Mat H1, H2;
        stereoRectifyUncalibrated(Mat(allimgpt[0]), Mat(allimgpt[1]), F, imageSize, H1, H2, 3);

        R1 = cameraMatrix[0].inv()*H1*cameraMatrix[0];
        R2 = cameraMatrix[1].inv()*H2*cameraMatrix[1];
        P1 = cameraMatrix[0];
        P2 = cameraMatrix[1];
    }

    //Precompute maps for cv::remap()
    initUndistortRectifyMap(cameraMatrix[0], distCoeffs[0], R1, P1, imageSize, CV_16SC2, rmap[0][0], rmap[0][1]);
    initUndistortRectifyMap(cameraMatrix[1], distCoeffs[1], R2, P2, imageSize, CV_16SC2, rmap[1][0], rmap[1][1]);

    Mat canvas;
    double sf;
    int w, h;
    if( !isVerticalStereo )
    {
        sf = 600./MAX(imageSize.width, imageSize.height);
        w = cvRound(imageSize.width*sf);
        h = cvRound(imageSize.height*sf);
        canvas.create(h, w*2, CV_8UC3);
    }
    else
    {
        sf = 300./MAX(imageSize.width, imageSize.height);
        w = cvRound(imageSize.width*sf);
        h = cvRound(imageSize.height*sf);
        canvas.create(h*2, w, CV_8UC3);
    }

    for( i = 0; i < nimages; i++ )
    {
        for( k = 0; k < 2; k++ )
        {
            Mat img = imread(goodImageList[i*2+k], 0), rimg, cimg;
            remap(img, rimg, rmap[k][0], rmap[k][1], CV_INTER_LINEAR);
            cvtColor(rimg, cimg, COLOR_GRAY2BGR);
            Mat canvasPart = !isVerticalStereo ? canvas(Rect(w*k, 0, w, h)) : canvas(Rect(0, h*k, w, h));
            resize(cimg, canvasPart, canvasPart.size(), 0, 0, CV_INTER_AREA);
            if( useCalibrated )
            {
                Rect vroi(cvRound(validRoi[k].x*sf), cvRound(validRoi[k].y*sf),
                          cvRound(validRoi[k].width*sf), cvRound(validRoi[k].height*sf));
                rectangle(canvasPart, vroi, Scalar(0,0,255), 3, 8);
            }
        }

        if( !isVerticalStereo )
            for( j = 0; j < canvas.rows; j += 16 )
                line(canvas, Point(0, j), Point(canvas.cols, j), Scalar(0, 255, 0), 1, 8);
        else
            for( j = 0; j < canvas.cols; j += 16 )
                line(canvas, Point(j, 0), Point(j, canvas.rows), Scalar(0, 255, 0), 1, 8);
        imshow("rectified", canvas);
        char c = (char)waitKey();
        if( c == 27 || c == 'q' || c == 'Q' )
            break;
    }
}



static bool readStringList( const string& filename, vector& l )
{
    l.resize(0);
    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;
}

int main(int argc, char** argv)
{
    Size boardSize;
    string imagelistfn;
    bool showRectified = true;

   /* for( int i = 1; i < argc; i++ )
    {
        if( string(argv[i]) == "-w" )
        {
            if( sscanf(argv[++i], "%d", &boardSize.width) != 1 || boardSize.width <= 0 )
            {
                cout << "invalid board width" << endl;
                return print_help();
            }
        }
        else if( string(argv[i]) == "-h" )
        {
            if( sscanf(argv[++i], "%d", &boardSize.height) != 1 || boardSize.height <= 0 )
            {
                cout << "invalid board height" << endl;
                return print_help();
            }
        }
        else if( string(argv[i]) == "-nr" )
            showRectified = false;
        else if( string(argv[i]) == "--help" )
            return print_help();
        else if( argv[i][0] == '-' )
        {
            cout << "invalid option " << argv[i] << endl;
            return 0;
        }
        else
            imagelistfn = argv[i];
    }*/

    if( imagelistfn == "" )
    {
        imagelistfn = "stereo_calib.xml";	//图片列表文件
        boardSize = Size(9, 6);
    }
    else if( boardSize.width <= 0 || boardSize.height <= 0 )
    {
        cout << "if you specified XML file with chessboards, you should also specify the board width and height (-w and -h options)" << endl;
        return 0;
    }

    vector imagelist;
    bool ok = readStringList(imagelistfn, imagelist);
    if(!ok || imagelist.empty())
    {
        cout << "can not open " << imagelistfn << " or the string list is empty" << endl;
        return print_help();
    }

    StereoCalib(imagelist, boardSize, true, showRectified);
    return 0;
}

2、实验结果

（1）原图像

（2）效果图

3、函数介绍

（1）findChessboardCorners

查找棋盘格内角点位置

C++: bool findChessboardCorners(InputArray image, Size patternSize, OutputArray corners, int flags=CALIB_CB_ADAPTIVE_THRESH+CALIB_CB_NORMALIZE_IMAGE )

参数：image：输入的棋盘图，必须是8位的灰度或者彩色图像。
pattern_size：棋盘图中每行和每列角点的个数。
corners：检测到的角点
flags：各种操作标志，可以是0或者下面值的组合：

• CV_CALIB_CB_ADAPTIVE_THRESH - 使用自适应阈值（通过平均图像亮度计算得到）将图像转换为黑白图，而不是一个固定的阈值。
• CV_CALIB_CB_NORMALIZE_IMAGE - 在利用固定阈值或者自适应的阈值进行二值化之前，先使用cvNormalizeHist来均衡化图像亮度。
• CV_CALIB_CB_FILTER_QUADS - 使用其他的准则（如轮廓面积，周长，方形形状）来去除在轮廓检测阶段检测到的错误方块。

Sample usage of detecting and drawing chessboard corners:

Size patternsize(8,6); //interior number of corners
Mat gray = ....; //source image
vector corners; //this will be filled by the detected corners

//CALIB_CB_FAST_CHECK saves a lot of time on images
//that do not contain any chessboard corners
bool patternfound = findChessboardCorners(gray, patternsize, corners,
        CALIB_CB_ADAPTIVE_THRESH + CALIB_CB_NORMALIZE_IMAGE
        + CALIB_CB_FAST_CHECK);

if(patternfound)
  cornerSubPix(gray, corners, Size(11, 11), Size(-1, -1),
    TermCriteria(CV_TERMCRIT_EPS + CV_TERMCRIT_ITER, 30, 0.1));

drawChessboardCorners(img, patternsize, Mat(corners), patternfound);

（2）drawChessboardCorners

呈现发现棋盘格角点。

C++: void drawChessboardCorners(InputOutputArray image, Size patternSize, InputArray corners, bool patternWasFound)

参数：

• image：输入的单幅图像，必须为8-bit的灰度图像。

• patternSize ：棋盘格每行每列的交点个数
  
• corners：角点的坐标，findChessboardCorners（）的输出。
  
• patternWasFound：角点是否全部找到的标志，findChessboardCorners()的返回值应给传给它。
  

（3）cornerSubPix

精确角点的位置。

C++: void cornerSubPix(InputArray image, InputOutputArray corners, Size winSize, Size zeroZone, TermCriteria criteria)

参数：

• image：输入图像。

• corners：初始输入角点的坐标和精确坐标用于输出。

• winSize：搜索窗口的长度的一半。如果：winSize=Size(5,5)，那么大小为5*2+1X5*2+1=11X11的搜索窗被用。
• zeroZone：搜索禁区，有时用于避免可能的自相关矩阵的奇异性。
• criteria：终止条件，达到criteria.maxCount将停止或者corner position moves by less than criteria.epsilon on some iteration.

示例1.

代码：

#include 
#include 
using namespace std;
using namespace cv;
int main()
{
	Size patternsize(8,6); //interior number of corners
		Mat gray = imread("D:\\opencv\\sources\\samples\\cpp\\right01.jpg",0); //source image
	imshow("Source",gray);
	vector corners; //this will be filled by the detected corners


	//CALIB_CB_FAST_CHECK saves a lot of time on images
	//that do not contain any chessboard corners
	bool patternfound = findChessboardCorners(gray, patternsize, corners,CALIB_CB_ADAPTIVE_THRESH|CALIB_CB_NORMALIZE_IMAGE);


	if(patternfound)
		cornerSubPix(gray, corners, Size(11, 11), Size(-1, -1),TermCriteria(CV_TERMCRIT_EPS + CV_TERMCRIT_ITER, 30, 0.1));
	drawChessboardCorners(gray, patternsize, Mat(corners), patternfound);
	imshow("dst",gray);
	waitKey(0);
	return 0;
}

效果：

（4）stereoCalibrate

校定立体相机。

C++: double stereoCalibrate(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2, 

InputOutputArray cameraMatrix1, InputOutputArray distCoeffs1, InputOutputArray cameraMatrix2, InputOutputArray distCoeffs2, 

Size imageSize, OutputArray R, OutputArray T, OutputArray E, OutputArray F, 

TermCriteria criteria=TermCriteria(TermCriteria::COUNT+TermCriteria::EPS, 30, 1e-6), int flags=CALIB_FIX_INTRINSIC )

（5）undistortPoints

从观察到的点坐标计算理想的点坐标。

C++: void undistortPoints(InputArray src, OutputArray dst, InputArray cameraMatrix, InputArray distCoeffs, 

		InputArray R=noArray(), InputArray P=noArray())

参数：

• src：观测的点坐标, 1xN或者Nx1 2-channel (CV_32FC2 or CV_64FC2).
• dst：输出理想点坐标. 如果矩阵P 是 identity或者省略, dst将包含归一化点坐标.
• cameraMatrix：相机矩阵。

.

• distCoeffs ：输入畸变系数向量 of 4, 5, or 8 elements.如果向量是 NULL/empty, 零畸变系数b被假定。
• R ： 在对象空间的矫正转换(3x3 矩阵). R1或者R2 由stereoRectify()计算可以传递到这.如果矩阵是空的，使用的恒等变换.
• P – 新的相机矩阵(3x3)或者新的投影矩阵 (3x4). P1 或者 P2 由stereoRectify()就算 can be passed here. 如果矩阵为空, the identity new camera matrix is used.

（6）computeCorrespondEpilines

为一幅图像中的点计算其在另一幅图像中对应的对极线。

C++: void computeCorrespondEpilines(InputArray points, int whichImage, InputArray F, OutputArray lines)

参数:

• points ：输入点，是2xN 或者 3xN 数组 (N为点的个数)
• whichImage ： 包含点的图像指数(1 or 2).
• F：基本矩阵可以被评估，用 findFundamentalMat() or stereoRectify() .
• lines –输出在其他图像对应点极线向量 。每条线 ax + by + c=0 .

（7）stereoRectify

Computes rectification transforms for each head of a calibrated stereo camera.

C++: void stereoRectify(InputArray cameraMatrix1, InputArray distCoeffs1, InputArray cameraMatrix2, 

	InputArray distCoeffs2, Size imageSize, InputArray R, InputArray T, OutputArray R1, 

	OutputArray R2, OutputArray P1, OutputArray P2, OutputArray Q, int flags=CALIB_ZERO_DISPARITY, 

	double alpha=-1, Size newImageSize=Size(), Rect* validPixROI1=0, Rect* validPixROI2=0 )

（8）findFundamentalMat

由两幅图像中对应点计算出基本矩阵

C++: Mat findFundamentalMat(InputArray points1, InputArray points2, int method=FM_RANSAC, 

		double param1=3., double param2=0.99, OutputArray mask=noArray() )

（9）stereoRectifyUncalibrated

Computes a rectification transform for an uncalibrated stereo camera.

C++: bool stereoRectifyUncalibrated(InputArray points1, InputArray points2, InputArray F, Size imgSize,

	 OutputArray H1, OutputArray H2, double threshold=5 )

（10）initUndistortRectifyMap

Computes the undistortion and rectification transformation map.

C++: void initUndistortRectifyMap(InputArray cameraMatrix, InputArray distCoeffs, InputArray R, 

		InputArray newCameraMatrix, Size size, int m1type, OutputArray map1, OutputArray map2)