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#include "SMCalibrationWorker.h"
#include "SMCalibrationParameters.h"

#include "cvtools.h"

#include <QSettings>

#include <ceres/ceres.h>


struct CircleResidual {
    CircleResidual(std::vector<cv::Point3f> _pointsOnArc)
        : pointsOnArc(_pointsOnArc) {}

    template <typename T>
    bool operator()(const T* point, const T* axis, T* residual) const {

        T axisSqNorm = axis[0]*axis[0] + axis[1]*axis[1] + axis[2]*axis[2];

        unsigned int l = pointsOnArc.size();
        std::vector<T> dI(l);

        // note, this is automatically initialized to 0
        T sum(0.0);

        for(unsigned int i=0; i<l; i++){
            cv::Point3d p = pointsOnArc[i];
            //T p[3] = {pointsOnArc[i].x, pointsOnArc[i].y, pointsOnArc[i].z};

            // point to line distance
            T dotProd = (point[0]-p.x)*axis[0] + (point[1]-p.y)*axis[1] + (point[2]-p.z)*axis[2];
            T dIx = point[0] - p.x - (dotProd*axis[0]/axisSqNorm);
            T dIy = point[1] - p.y - (dotProd*axis[1]/axisSqNorm);
            T dIz = point[2] - p.z - (dotProd*axis[2]/axisSqNorm);
            dI[i] = ceres::sqrt(dIx*dIx + dIy*dIy + dIz*dIz);

            sum += dI[i];
        }

        T mean = sum / double(l);

        for(unsigned int i=0; i<l; i++){
            residual[i] = dI[i] - mean;
        }

        return true;
    }

private:

    // Observations for one checkerboard corner.
    const std::vector<cv::Point3f> pointsOnArc;
};


// Closed form solution to solve for the rotation axis from sets of 3D point coordinates of flat pattern feature points
// Algorithm according to Chen et al., Rotation axis calibration of a turntable using constrained global optimization, Optik 2014
// DTU, 2014, Jakob Wilm
static void rotationAxisCalibration(const std::vector< std::vector<cv::Point3f> > Qcam,
                                    const std::vector<cv::Point3f> Qobj,
                                    cv::Vec3f &axis, cv::Vec3f &point, float &error){
    assert(Qobj.size() == Qcam[0].size());

    // number of frames (points on each arch)
    int l = Qcam.size();

    // number of points in each frame
    size_t mn = Qobj.size();

    // construct matrix for axis determination
    cv::Mat M(6, 6, CV_32F, cv::Scalar(0));

    for(int k=0; k<l; k++){
        for(unsigned int idx=0; idx<mn; idx++){

            //            float i = Qobj[idx].x+4;
            //            float j = Qobj[idx].y+4;
            float i = Qobj[idx].x;
            float j = Qobj[idx].y;

            float x = Qcam[k][idx].x;
            float y = Qcam[k][idx].y;
            float z = Qcam[k][idx].z;

            M += (cv::Mat_<float>(6,6) << x*x, x*y, x*z, x, i*x, j*x,
                  0, y*y, y*z, y, i*y, j*y,
                  0,   0, z*z, z, i*z, j*z,
                  0,   0,   0, 1,   i,   j,
                  0,   0,   0, 0, i*i, i*j,
                  0,   0,   0, 0,   0, j*j);

        }
    }

    cv::completeSymm(M, false);

    // solve for axis
    std::vector<float> lambda;
    cv::Mat u;
    cv::eigen(M, lambda, u);

    float minLambda = std::abs(lambda[0]);
    int idx = 0;
    for(unsigned int i=1; i<lambda.size(); i++){
        if(abs(lambda[i]) < minLambda){
            minLambda = lambda[i];
            idx = i;
        }
    }

    axis = u.row(idx).colRange(0, 3);
    axis = cv::normalize(axis);

    float nx = u.at<float>(idx, 0);
    float ny = u.at<float>(idx, 1);
    float nz = u.at<float>(idx, 2);
    //float d  = u.at<float>(idx, 3);
    float dh = u.at<float>(idx, 4);
    float dv = u.at<float>(idx, 5);

    // Paper version: c is initially eliminated
    /*cv::Mat A(l*mn, mn+2, CV_32F, cv::Scalar(0.0));
        cv::Mat bb(l*mn, 1, CV_32F);

        for(int k=0; k<l; k++){
            for(unsigned int idx=0; idx<mn; idx++){

                float i = Qobj[idx].x;
                float j = Qobj[idx].y;

                float x = Qcam[k][idx].x;
                float y = Qcam[k][idx].y;
                float z = Qcam[k][idx].z;

                float f = x*x + y*y + z*z + (2*x*nx + 2*y*ny + 2*z*nz)*(i*dh + j*dv);

                int row = k*mn+idx;
                A.at<float>(row, 0) = 2*x - (2*z*nx)/nz;
                A.at<float>(row, 1) = 2*y - (2*z*ny)/nz;
                A.at<float>(row, idx+2) = 1.0;

                bb.at<float>(row, 0) = f + (2*z*d)/nz;
            }
        }

        // solve for point
        cv::Mat abe;
        cv::solve(A, bb, abe, cv::DECOMP_SVD);

        float a = abe.at<float>(0, 0);
        float b = abe.at<float>(1, 0);
        float c = -(nx*a+ny*b+d)/nz;
        */

    // Our version: solve simultanously for a,b,c
    cv::Mat A(l*mn, mn+3, CV_32F, cv::Scalar(0.0));
    cv::Mat bb(l*mn, 1, CV_32F);

    for(int k=0; k<l; k++){
        for(unsigned int idx=0; idx<mn; idx++){

            float i = Qobj[idx].x;
            float j = Qobj[idx].y;

            float x = Qcam[k][idx].x;
            float y = Qcam[k][idx].y;
            float z = Qcam[k][idx].z;

            float f = x*x + y*y + z*z + (2*x*nx + 2*y*ny + 2*z*nz)*(i*dh + j*dv);

            int row = k*mn+idx;
            A.at<float>(row, 0) = 2*x;
            A.at<float>(row, 1) = 2*y;
            A.at<float>(row, 2) = 2*z;
            A.at<float>(row, idx+3) = 1.0;

            bb.at<float>(row, 0) = f;
        }
    }

    // solve for point
    cv::Mat abe;
    cv::solve(A, bb, abe, cv::DECOMP_SVD);

    float a = abe.at<float>(0, 0);
    float b = abe.at<float>(1, 0);
    float c = abe.at<float>(2, 0);

    point[0] = a;
    point[1] = b;
    point[2] = c;

    // Non-linear optimization using Ceres
    double pointArray[] = {point[0], point[1], point[2]};
    double axisArray[] = {axis[0], axis[1], axis[2]};

    ceres::Problem problem;
    // loop through saddle points
    for(unsigned int idx=0; idx<mn; idx++){
        std::vector<cv::Point3f> pointsOnArch(l);
        for(int k=0; k<l; k++){
            pointsOnArch[k] = Qcam[k][idx];
        }
        ceres::CostFunction* cost_function =
                new ceres::AutoDiffCostFunction<CircleResidual, ceres::DYNAMIC, 3, 3>(
                    new CircleResidual(pointsOnArch), l);
        problem.AddResidualBlock(cost_function, NULL, pointArray, axisArray);
    }

    // Run the solver!
    ceres::Solver::Options options;
    options.linear_solver_type = ceres::DENSE_QR;
    options.minimizer_progress_to_stdout = true;
    ceres::Solver::Summary summary;
    ceres::Solve(options, &problem, &summary);

    std::cout << summary.BriefReport() << "\n";

    point = cv::Vec3f(pointArray[0], pointArray[1], pointArray[2]);
    axis = cv::Vec3f(axisArray[0], axisArray[1], axisArray[2]);
    axis /= cv::norm(axis);


    // Error estimate (sum of squared differences)
    error = 0;
    // loop through saddle points
    for(unsigned int idx=0; idx<mn; idx++){

        // vector of distances from rotation axis
        std::vector<float> dI(l);
        // loop through angular positions
        for(int k=0; k<l; k++){
            cv::Vec3f p = cv::Vec3f(Qcam[k][idx]);
            // point to line distance
            dI[k] = cv::norm((point-p)-(point-p).dot(axis)*axis);
        }
        float sum = std::accumulate(dI.begin(), dI.end(), 0.0);
        float mean = sum / dI.size();
        float meanDev = 0;
        for(int k=0; k<l; k++){
            meanDev += std::abs(dI[k] - mean);
        }
        meanDev /= l;
        error += meanDev;
    }
    error /= mn;
}

bool processCBCorners(const cv::Size & checkerCount,
                      const cv::Mat & SMCalibrationSetI_frameX,
                      cv::Mat & SMCalibrationSetI_frameXResult,
                      std::vector<cv::Point2f> & qciX){
    // Convert to grayscale
    cv::Mat gray;
    if(SMCalibrationSetI_frameX.channels() == 1)
        cv::cvtColor(SMCalibrationSetI_frameX, gray, CV_BayerBG2GRAY);
    else
        cv::cvtColor(SMCalibrationSetI_frameX, gray, CV_RGB2GRAY);

    // Extract checker corners
    bool success = cv::findChessboardCorners(gray, checkerCount, qciX, cv::CALIB_CB_ADAPTIVE_THRESH + cv::CALIB_CB_FAST_CHECK);
    if(success){
        cv::cornerSubPix(gray, qciX, cv::Size(6, 6), cv::Size(1, 1), cv::TermCriteria(CV_TERMCRIT_EPS + CV_TERMCRIT_ITER, 20, 0.0001));
        // Draw colored chessboard
        if(SMCalibrationSetI_frameX.channels() == 1)
            cv::cvtColor(SMCalibrationSetI_frameX, SMCalibrationSetI_frameXResult, CV_BayerBG2RGB);
        else
            SMCalibrationSetI_frameXResult = SMCalibrationSetI_frameX.clone();

        cvtools::drawChessboardCorners(SMCalibrationSetI_frameXResult, checkerCount, qciX, success, 10);
    }
    return success;
}

std::vector<cv::Point3f> SMCalibrationWorker::generateObjCoordsInWorldCS(const cv::Size checkerCount, const float checkerSize)
{
    std::vector<cv::Point3f> Qi;
    for (int h=0; h<checkerCount.height; h++)
        for (int w=0; w<checkerCount.width; w++)
            Qi.push_back(cv::Point3f(checkerSize * w, checkerSize* h, 0.0));

    return Qi;
}

void SMCalibrationWorker::perViewReprojError(const std::vector<bool> &success0,
                                             const std::vector< std::vector<cv::Point3f> > &Q0,
                                             const std::vector<cv::Mat> &cam_tvecs0,
                                             const std::vector<cv::Mat> &cam_rvecs0,
                                             const std::vector< std::vector<cv::Point2f> > &qc0,
                                             const cv::Matx33f &K0,
                                             const cv::Vec<float, 5> &k0,
                                             std::vector<float> &camX_errors_per_view)
{
    unsigned int nSets = success0.size();
    camX_errors_per_view.resize(nSets);
    int idx = 0;
    //#pragma omp parallel for
    for(unsigned int i = 0; i < nSets; ++i){
        if(success0[i]){
            int n = (int)Q0[idx].size();
            std::vector<cv::Point2f> qc_proj;
            cv::projectPoints(cv::Mat(Q0[idx]), cam_rvecs0[idx], cam_tvecs0[idx], K0,  k0, qc_proj);
            float err = 0;
            for(unsigned int j=0; j<qc_proj.size(); j++){
                cv::Point2f d = qc0[idx][j] - qc_proj[j];
                err += cv::sqrt(d.x*d.x + d.y*d.y);
            }
            camX_errors_per_view[i] = (float)err/n;
            idx++;
        } else
            camX_errors_per_view[i] = NAN;
    }
}

void SMCalibrationWorker::performCameraCalibration(std::vector<SMCalibrationSet> calibrationData){

    QSettings settings;
    cv::Size checkerCount(
                cv::Size(settings.value("calibration/patternSizeX", 22).toInt(),settings.value("calibration/patternSizeY", 13).toInt()));
    unsigned int nSets = calibrationData.size();

    // 2D Points collected for OpenCV's calibration procedures
#define OLD_WAYZ 0
#if OLD_WAYZ
    std::vector< std::vector<cv::Point2f> > qc0, qc1, qc0Stereo, qc1Stereo;
    std::vector<bool> fwdToStageEstimation;
    std::vector<float> angles;
    std::vector<unsigned int> TESTER;
#else
    std::vector< std::vector<cv::Point2f> > qc0(nSets), qc1(nSets), qc0Stereo(nSets), qc1Stereo(nSets);
    std::vector<bool> fwdToStageEstimation(nSets);
    std::vector<float> angles(nSets);
    std::vector<unsigned int> TESTER(nSets);
#endif
    std::vector<bool> success0(nSets, false), success1(nSets, false);
    // Loop through calibration sets
#if !OLD_WAYZ
#pragma omp parallel for
#endif
    for(unsigned int i=0; i<nSets; i++){

        SMCalibrationSet SMCalibrationSetI = calibrationData[i];

        // TODO this changes semantics of the checkboxes in the GUI
        /*if(!SMCalibrationSetI.checked)
            continue;*/

        // Camera 0
        std::vector<cv::Point2f> qci0;
        success0[i] = processCBCorners(checkerCount, SMCalibrationSetI.frame0, SMCalibrationSetI.frame0Result, qci0);
#pragma omp critical (CBCALCupdateUI1)
{
        emit newFrameResult(i, 0, success0[i], SMCalibrationSetI.frame0Result);
}
        // Camera 1
        std::vector<cv::Point2f> qci1;
        success1[i] = processCBCorners(checkerCount, SMCalibrationSetI.frame1, SMCalibrationSetI.frame1Result, qci1);
#pragma omp critical (CBCALCupdateUI2)
{
        emit newFrameResult(i, 1, success1[i], SMCalibrationSetI.frame1Result);
}
        // store results
#if OLD_WAYZ
        if(success0[i])
            qc0.push_back(qci0);

        if(success1[i])
            qc1.push_back(qci1);

        if(success0[i] && success1[i]){
            qc0Stereo.push_back(qci0);
            qc1Stereo.push_back(qci1);
            angles.push_back(SMCalibrationSetI.rotationAngle);
            fwdToStageEstimation.push_back(SMCalibrationSetI.checked);
            TESTER.push_back(i);
        }
#else
        qc0[i] = qci0;
        qc1[i] = qci1;

        qc0Stereo[i] = qci0;
        qc1Stereo[i] = qci1;
        angles[i] = SMCalibrationSetI.rotationAngle;
        fwdToStageEstimation[i] = SMCalibrationSetI.checked;
        TESTER[i] = (i);
#endif
        // Show progress
        #pragma omp critical (CBCALCupdateUI3)
        {
            emit newSetProcessed(i);
        }
    }
#if !OLD_WAYZ
    auto s0it = success0.cbegin();
    qc0.erase(std::remove_if( qc0.begin(), qc0.end(), [&s0it](std::vector<cv::Point2f>){return !*s0it++;}),
            qc0.end());

    auto s1it = success1.cbegin();
    qc1.erase(std::remove_if( qc1.begin(), qc1.end(), [&s1it](std::vector<cv::Point2f>){return !*s1it++;}),
            qc1.end());

    s0it = success0.cbegin(); s1it = success1.cbegin();
    qc0Stereo.erase(std::remove_if( qc0Stereo.begin(), qc0Stereo.end(), [&s0it,&s1it](std::vector<cv::Point2f>){return !((*s0it++)&(*s1it++));}),
            qc0Stereo.end());

    s0it = success0.cbegin(); s1it = success1.cbegin();
    qc1Stereo.erase(std::remove_if( qc1Stereo.begin(), qc1Stereo.end(), [&s0it,&s1it](std::vector<cv::Point2f>){return !((*s0it++)&(*s1it++));}),
            qc1Stereo.end());

    s0it = success0.cbegin(); s1it = success1.cbegin();
    angles.erase(std::remove_if( angles.begin(), angles.end(), [&s0it,&s1it](float){return !((*s0it++)&(*s1it++));}),
            angles.end());

    s0it = success0.cbegin(); s1it = success1.cbegin();
    fwdToStageEstimation.erase(std::remove_if( fwdToStageEstimation.begin(), fwdToStageEstimation.end(), [&s0it,&s1it](bool){return !((*s0it++)&(*s1it++));}),
            fwdToStageEstimation.end());

    s0it = success0.cbegin(); s1it = success1.cbegin();
    TESTER.erase(std::remove_if( TESTER.begin(), TESTER.end(), [&s0it,&s1it](bool){return !((*s0it++)&(*s1it++));}),
            TESTER.end());
    /*for(unsigned int i=0; i<nSets; i++){
        if(~success0[i])
            std::remove(qc0.begin(),qc0.end(),i);
        if(~success1[i])
            std::remove(qc1.begin(),qc1.end(),i);
        if(~success0[i] || ~success1[i]){
            std::remove(qc0Stereo.begin(),qc0Stereo.end(),i);
            std::remove(qc1Stereo.begin(),qc1Stereo.end(),i);
            std::remove(angles.begin(),angles.end(),i);
            std::remove(fwdToStageEstimation.begin(),fwdToStageEstimation.end(),i);
        }
    }*/
#endif
    std::copy(TESTER.begin(), TESTER.end(), std::ostream_iterator<unsigned int>(std::cout, " "));
    std::cout << std::endl;
    const size_t nValidStereoSets = angles.size();
    if(nValidStereoSets < 2){
        std::cerr << "Not enough valid calibration sequences!" << std::endl;
        emit done();
        return;
    }

    // Generate world object coordinates [mm]
    std::vector<cv::Point3f> Qi = generateObjCoordsInWorldCS(checkerCount,
                                                             settings.value("calibration/squareSize", 10.0).toFloat());

    std::vector< std::vector<cv::Point3f> >
            Q0(qc0.size(), Qi),
            Q1(qc1.size(), Qi),
            QStereo(nValidStereoSets, Qi);

    // calibrate the cameras
    SMCalibrationParameters cal;
    cal.frameWidth = calibrationData[0].frame0.cols;
    cal.frameHeight = calibrationData[0].frame0.rows;
    cv::Size frameSize(cal.frameWidth, cal.frameHeight);

    // determine only k1, k2 for lens distortion
    int flags = cv::CALIB_FIX_ASPECT_RATIO + cv::CALIB_FIX_K3 + cv::CALIB_ZERO_TANGENT_DIST + cv::CALIB_FIX_PRINCIPAL_POINT;
    // Note: several of the output arguments below must be cv::Mat, otherwise segfault
    std::vector<cv::Mat> cam_rvecs0, cam_tvecs0;
    cal.cam0_error = cv::calibrateCamera(Q0, qc0, frameSize, cal.K0, cal.k0, cam_rvecs0, cam_tvecs0, flags,
                                         cv::TermCriteria(cv::TermCriteria::COUNT+cv::TermCriteria::EPS, 100, DBL_EPSILON));
    //std::cout << cal.k0 << std::endl;
    //    // refine extrinsics for camera 0
    //    for(int i=0; i<Q.size(); i++)
    //        cv::solvePnPRansac(Q[i], qc0[i], cal.K0, cal.k0, cam_rvecs0[i], cam_tvecs0[i], true, 100, 0.05, 100, cv::noArray(), CV_ITERATIVE);

    std::vector<cv::Mat> cam_rvecs1, cam_tvecs1;
    cal.cam1_error = cv::calibrateCamera(Q1, qc1, frameSize, cal.K1, cal.k1, cam_rvecs1, cam_tvecs1, flags,
                                         cv::TermCriteria(cv::TermCriteria::COUNT+cv::TermCriteria::EPS, 100, DBL_EPSILON));
    //std::cout << cal.k1 << std::endl;
    // stereo calibration
    int flags_stereo = cv::CALIB_FIX_INTRINSIC;// + cv::CALIB_FIX_K2 + cv::CALIB_FIX_K3 + cv::CALIB_ZERO_TANGENT_DIST + cv::CALIB_FIX_PRINCIPAL_POINT + cv::CALIB_FIX_ASPECT_RATIO;
    cv::Mat E, F, R1, T1;

#if CV_MAJOR_VERSION < 3
        cal.stereo_error = cv::stereoCalibrate(QStereo, qc0Stereo, qc1Stereo, cal.K0, cal.k0, cal.K1, cal.k1,
                                               frameSize, R1, T1, E, F,
                                               cv::TermCriteria(cv::TermCriteria::COUNT + cv::TermCriteria::EPS, 200, DBL_EPSILON),
                                               flags_stereo);
#else
        cal.stereo_error = cv::stereoCalibrate(QStereo, qc0Stereo, qc1Stereo, cal.K0, cal.k0, cal.K1, cal.k1,
                                               frameSize, R1, T1, E, F,flags_stereo,
                                               cv::TermCriteria(cv::TermCriteria::COUNT + cv::TermCriteria::EPS, 200, DBL_EPSILON));
#endif

    cal.R1 = R1;
    cal.T1 = T1;
    cal.E = E;
    cal.F = F;

    // Determine per-view reprojection errors:
    perViewReprojError(success0, Q0, cam_tvecs0, cam_rvecs0, qc0, cal.K0, cal.k0, cal.cam0_errors_per_view);
    perViewReprojError(success1, Q1, cam_tvecs1, cam_rvecs1, qc1, cal.K1, cal.k1, cal.cam1_errors_per_view);

    // This would be so much nicer with range adaptors
    std::vector< std::vector<cv::Point2f> > qc0StereoFwd2Stage;
    std::vector< std::vector<cv::Point2f> > qc1StereoFwd2Stage;

    for(size_t i=0; i<qc0Stereo.size(); i++ )
        if(fwdToStageEstimation[i])
            qc0StereoFwd2Stage.push_back(qc0Stereo[i]);

    for(size_t i=0; i<qc1Stereo.size(); i++ )
        if(fwdToStageEstimation[i])
            qc1StereoFwd2Stage.push_back(qc1Stereo[i]);

    performStageCalibration(qc0StereoFwd2Stage,qc1StereoFwd2Stage,cal);

    // Print to std::cout
    std::cout << std::endl << "========== BEGIN Calibration info ================================================" << std::endl;
    std::cout << "Num. Images used for intrinsics of cam0: " << qc0.size() << std::endl;
    std::cout << "Num. Images used for intrinsics of cam1: " << qc1.size() << std::endl;
    std::cout << "Num. Images used for extrinsocs of cam1: " << nValidStereoSets << std::endl;
    std::cout << "Num. Images used for rotation stage axis estim.: " << qc0StereoFwd2Stage.size() << std::endl << std::endl;
    cal.print();
    std::cout << "========== END   Calibration info ================================================" << std::endl << std::endl;

    // save to (reentrant qsettings object)
    settings.setValue("calibration/parameters", QVariant::fromValue(cal));

    emit done();
}


void SMCalibrationWorker::performStageCalibration(
        const std::vector< std::vector<cv::Point2f> > &qc0Stereo,
        const std::vector< std::vector<cv::Point2f> > &qc1Stereo,
        SMCalibrationParameters& cal){
    assert(qc0Stereo.size()==qc1Stereo.size());
    if(qc0Stereo.size()>1 && qc1Stereo.size()>1){
        // save to (reentrant qsettings object)
        QSettings settings;

        // Generate world object coordinates [mm]
        std::vector<cv::Point3f> Qi = generateObjCoordsInWorldCS(
                    cv::Size(settings.value("calibration/patternSizeX", 22).toInt(),settings.value("calibration/patternSizeY", 13).toInt()),
                    settings.value("calibration/squareSize", 10.0).toFloat());

        // Direct rotation axis calibration //
        // full camera matrices
        cv::Matx34f P0 = cv::Matx34f::eye();
        cv::Mat RT1(3, 4, CV_32F);
        cv::Mat(cal.R1).copyTo(RT1(cv::Range(0, 3), cv::Range(0, 3)));
        cv::Mat(cal.T1).copyTo(RT1(cv::Range(0, 3), cv::Range(3, 4)));
        cv::Matx34f P1 = cv::Matx34f(RT1);

        // calibration points in camera 0 frame
        std::vector< std::vector<cv::Point3f> > Qcam(qc0Stereo.size());
#pragma omp parallel for
        for(unsigned int i=0; i<qc0Stereo.size(); i++){
            std::vector<cv::Point2f> qc0i, qc1i;

            cv::undistortPoints(qc0Stereo[i], qc0i, cal.K0, cal.k0);
            cv::undistortPoints(qc1Stereo[i], qc1i, cal.K1, cal.k1);

            cv::Mat Qhom, Qcami;
            cv::triangulatePoints(P0, P1, qc0i, qc1i, Qhom);
            cvtools::convertMatFromHomogeneous(Qhom, Qcami);
            std::vector<cv::Point3f> QcamiPoints;
            cvtools::matToPoints3f(Qcami, QcamiPoints);

            Qcam[i] = QcamiPoints;
        }

        cv::Vec3f axis, point;
        float rot_axis_error;
        rotationAxisCalibration(Qcam, Qi, axis, point, rot_axis_error);

        // construct transformation matrix
        cv::Vec3f ex = axis.cross(cv::Vec3f(0,0,1.0));
        ex = cv::normalize(ex);
        cv::Vec3f ez = ex.cross(axis);
        ez = cv::normalize(ez);

        cv::Mat RrMat(3, 3, CV_32F);
        cv::Mat(ex).copyTo(RrMat.col(0));
        cv::Mat(axis).copyTo(RrMat.col(1));
        cv::Mat(ez).copyTo(RrMat.col(2));

        cal.Rr = cv::Matx33f(RrMat).t();
        cal.Tr = -cv::Matx33f(RrMat).t()*point;
        cal.rot_axis_error = rot_axis_error;
    }else{
        cal.Rr = cv::Matx33f::eye();
        cal.Tr = cv::Vec3f(0,0,0);
        cal.rot_axis_error = -1;
    }
}