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1.攝像機成像原理

成像的過程實質上是4個座標系的轉換。首先空間中的一點由 世界座標系 轉換到 攝像機座標系 ，然後再將其投影到成像平面 (影象物理座標系 ) ，最後再將成像平面上的資料轉換到影象平面 (影象畫素座標系

下文對4個座標系的 變換做了詳細的解釋：

http://blog.csdn.net/humanking7/article/details/44756073

2.畸變模型

OpenCV的document中介紹如下：

http://www.opencv.org.cn/opencvdoc/2.3.2/html/doc/tutorials/calib3d/camera_calibration/camera_calibration.html#cameracalibrationopencv

所以標定的目標是就是確定這5個引數的值。

3.標定板

標定的最開始階段最需要的肯定是標定板。可以直接從opencv官網上能下載到： 

http://docs.opencv.org/2.4/_downloads/pattern.png

4.影象採集

5.標定

用OpenCV的例程來進行標定，在你的opencv目錄下  sources\samples\cpp\tutorial_code\calib3d\camera_calibration  有3個檔案 ：

camera_calibration.cpp  VID5.xml  in_VID5.xml

第一個是標定程式的原始碼。  第二個是配置檔案，你可以更改標定圖片獲取的方式以及標定板的一些引數。  第三個裡面可以修改標定圖片序列的檔名。

#include <iostream>
#include <sstream>
#include <time.h>
#include <stdio.h>
#include <opencv2/core/core.hpp>
#include <opencv2/imgproc/imgproc.hpp>
#include <opencv2/calib3d/calib3d.hpp>
#include <opencv2/highgui/highgui.hpp>
#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<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 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<string> 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<vector<Point2f> > 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<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;
    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<Point2f> 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<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)
{
    vector<Point2f> 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<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(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