www.pudn.com > OpenCV-Intel.zip > cvcalibration.cpp


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#include "_cv.h" 
 
/* 
    This is stright forward port v2 of Matlab calibration engine by Jean-Yves Bouguet 
    that is (in a large extent) based on the paper: 
    Z. Zhang. "A flexible new technique for camera calibration". 
    IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(11):1330-1334, 2000. 
 
    The 1st initial port was done by Valery Mosyagin. 
*/ 
 
static void 
icvGaussNewton( const CvMat* J, const CvMat* err, CvMat* delta, 
                CvMat* JtJ=0, CvMat* JtErr=0, CvMat* JtJW=0, CvMat* JtJV=0 ) 
{ 
    CvMat* _temp_JtJ = 0; 
    CvMat* _temp_JtErr = 0; 
    CvMat* _temp_JtJW = 0; 
    CvMat* _temp_JtJV = 0; 
     
    CV_FUNCNAME( "icvGaussNewton" ); 
 
    __BEGIN__; 
 
    if( !CV_IS_MAT(J) || !CV_IS_MAT(err) || !CV_IS_MAT(delta) ) 
        CV_ERROR( CV_StsBadArg, "Some of required arguments is not a valid matrix" ); 
 
    if( !JtJ ) 
    { 
        CV_CALL( _temp_JtJ = cvCreateMat( J->cols, J->cols, J->type )); 
        JtJ = _temp_JtJ; 
    } 
    else if( !CV_IS_MAT(JtJ) ) 
        CV_ERROR( CV_StsBadArg, "JtJ is not a valid matrix" ); 
 
    if( !JtErr ) 
    { 
        CV_CALL( _temp_JtErr = cvCreateMat( J->cols, 1, J->type )); 
        JtErr = _temp_JtErr; 
    } 
    else if( !CV_IS_MAT(JtErr) ) 
        CV_ERROR( CV_StsBadArg, "JtErr is not a valid matrix" ); 
 
    if( !JtJW ) 
    { 
        CV_CALL( _temp_JtJW = cvCreateMat( J->cols, 1, J->type )); 
        JtJW = _temp_JtJW; 
    } 
    else if( !CV_IS_MAT(JtJW) ) 
        CV_ERROR( CV_StsBadArg, "JtJW is not a valid matrix" ); 
 
    if( !JtJV ) 
    { 
        CV_CALL( _temp_JtJV = cvCreateMat( J->cols, J->cols, J->type )); 
        JtJV = _temp_JtJV; 
    } 
    else if( !CV_IS_MAT(JtJV) ) 
        CV_ERROR( CV_StsBadArg, "JtJV is not a valid matrix" ); 
 
    cvMulTransposed( J, JtJ, 1 ); 
    cvGEMM( J, err, 1, 0, 0, JtErr, CV_GEMM_A_T ); 
    cvSVD( JtJ, JtJW, 0, JtJV, CV_SVD_MODIFY_A + CV_SVD_V_T ); 
    cvSVBkSb( JtJW, JtJV, JtJV, JtErr, delta, CV_SVD_U_T + CV_SVD_V_T ); 
 
    __END__; 
 
    if( _temp_JtJ || _temp_JtErr || _temp_JtJW || _temp_JtJV ) 
    { 
        cvReleaseMat( &_temp_JtJ ); 
        cvReleaseMat( &_temp_JtErr ); 
        cvReleaseMat( &_temp_JtJW ); 
        cvReleaseMat( &_temp_JtJV ); 
    } 
} 
 
 
/*static double calc_repr_err( const double* object_points, int o_step, 
                             const double* image_points, 
                             const double* h, int count ) 
{ 
    double err = 0; 
    for( int i = 0; i < count; i++ ) 
    { 
        double X = object_points[i*o_step], Y = object_points[i*o_step + 1]; 
        double x0 = image_points[i*2], y0 = image_points[i*2 + 1]; 
        double d = 1./(h[6]*X + h[7]*Y + h[8]); 
        double x = (h[0]*X + h[1]*Y + h[2])*d; 
        double y = (h[3]*X + h[4]*Y + h[5])*d; 
        err += fabs(x - x0) + fabs(y - y0); 
    } 
    return err; 
}*/ 
 
 
// finds perspective transformation H between the object plane and image plane, 
// so that (sxi,syi,s) ~ H*(Xi,Yi,1) 
CV_IMPL void 
cvFindHomography( const CvMat* object_points, const CvMat* image_points, CvMat* __H ) 
{ 
    CvMat *_m = 0, *_M = 0; 
    CvMat *_L = 0; 
     
    CV_FUNCNAME( "cvFindHomography" ); 
 
    __BEGIN__; 
 
    int h_type; 
    int i, k, count, count2; 
    CvPoint2D64f *m, *M; 
    CvPoint2D64f cm = {0,0}, sm = {0,0}; 
    double inv_Hnorm[9] = { 0, 0, 0, 0, 0, 0, 0, 0, 1 }; 
    double H[9]; 
    CvMat _inv_Hnorm = cvMat( 3, 3, CV_64FC1, inv_Hnorm ); 
    CvMat _H = cvMat( 3, 3, CV_64FC1, H ); 
    double LtL[9*9], LW[9], LV[9*9]; 
    CvMat* _Lp; 
    double* L; 
    CvMat _LtL = cvMat( 9, 9, CV_64FC1, LtL ); 
    CvMat _LW = cvMat( 9, 1, CV_64FC1, LW ); 
    CvMat _LV = cvMat( 9, 9, CV_64FC1, LV ); 
    CvMat _Hrem = cvMat( 3, 3, CV_64FC1, LV + 8*9 ); 
 
    if( !CV_IS_MAT(image_points) || !CV_IS_MAT(object_points) || !CV_IS_MAT(__H) ) 
        CV_ERROR( CV_StsBadArg, "one of arguments is not a valid matrix" ); 
 
    h_type = CV_MAT_TYPE(__H->type); 
    if( h_type != CV_32FC1 && h_type != CV_64FC1 ) 
        CV_ERROR( CV_StsUnsupportedFormat, "Homography matrix must have 32fC1 or 64fC1 type" ); 
    if( __H->rows != 3 || __H->cols != 3 ) 
        CV_ERROR( CV_StsBadSize, "Homography matrix must be 3x3" ); 
 
    count = MAX(image_points->cols, image_points->rows); 
    count2 = MAX(object_points->cols, object_points->rows); 
    if( count != count2 ) 
        CV_ERROR( CV_StsUnmatchedSizes, "Numbers of image and object points do not match" ); 
 
    CV_CALL( _m = cvCreateMat( 1, count, CV_64FC2 )); 
    CV_CALL( cvConvertPointsHomogenious( image_points, _m )); 
    m = (CvPoint2D64f*)_m->data.ptr; 
     
    CV_CALL( _M = cvCreateMat( 1, count, CV_64FC2 )); 
    CV_CALL( cvConvertPointsHomogenious( object_points, _M )); 
    M = (CvPoint2D64f*)_M->data.ptr; 
 
    // calculate the normalization transformation Hnorm. 
    for( i = 0; i < count; i++ ) 
        cm.x += m[i].x, cm.y += m[i].y; 
    
    cm.x /= count; cm.y /= count; 
 
    for( i = 0; i < count; i++ ) 
    { 
        double x = m[i].x - cm.x; 
        double y = m[i].y - cm.y; 
        sm.x += fabs(x); sm.y += fabs(y); 
    } 
 
    sm.x /= count; sm.y /= count; 
    inv_Hnorm[0] = sm.x; 
    inv_Hnorm[4] = sm.y; 
    inv_Hnorm[2] = cm.x; 
    inv_Hnorm[5] = cm.y; 
    sm.x = 1./sm.x; 
    sm.y = 1./sm.y; 
     
    CV_CALL( _Lp = _L = cvCreateMat( 2*count, 9, CV_64FC1 ) ); 
    L = _L->data.db; 
 
    for( i = 0; i < count; i++, L += 18 ) 
    { 
        double x = -(m[i].x - cm.x)*sm.x, y = -(m[i].y - cm.y)*sm.y; 
        L[0] = L[9 + 3] = M[i].x; 
        L[1] = L[9 + 4] = M[i].y; 
        L[2] = L[9 + 5] = 1; 
        L[9 + 0] = L[9 + 1] = L[9 + 2] = L[3] = L[4] = L[5] = 0; 
        L[6] = x*M[i].x; 
        L[7] = x*M[i].y; 
        L[8] = x; 
        L[9 + 6] = y*M[i].x; 
        L[9 + 7] = y*M[i].y; 
        L[9 + 8] = y; 
    } 
 
    if( count > 4 ) 
    { 
        cvMulTransposed( _L, &_LtL, 1 ); 
        _Lp = &_LtL; 
    } 
 
    _LW.rows = MIN(count*2, 9); 
    cvSVD( _Lp, &_LW, 0, &_LV, CV_SVD_MODIFY_A + CV_SVD_V_T ); 
    cvScale( &_Hrem, &_Hrem, 1./_Hrem.data.db[8] ); 
    cvMatMul( &_inv_Hnorm, &_Hrem, &_H ); 
 
    if( count > 4 ) 
    { 
        // reuse the available storage for jacobian and other vars 
        CvMat _J = cvMat( 2*count, 8, CV_64FC1, _L->data.db ); 
        CvMat _err = cvMat( 2*count, 1, CV_64FC1, _L->data.db + 2*count*8 ); 
        CvMat _JtJ = cvMat( 8, 8, CV_64FC1, LtL ); 
        CvMat _JtErr = cvMat( 8, 1, CV_64FC1, LtL + 8*8 ); 
        CvMat _JtJW = cvMat( 8, 1, CV_64FC1, LW ); 
        CvMat _JtJV = cvMat( 8, 8, CV_64FC1, LV ); 
        CvMat _Hinnov = cvMat( 8, 1, CV_64FC1, LV + 8*8 ); 
 
        for( k = 0; k < 10; k++ ) 
        { 
            double* J = _J.data.db, *err = _err.data.db; 
            for( i = 0; i < count; i++, J += 16, err += 2 ) 
            { 
                double di = 1./(H[6]*M[i].x + H[7]*M[i].y + 1.); 
                double _xi = (H[0]*M[i].x + H[1]*M[i].y + H[2])*di; 
                double _yi = (H[3]*M[i].x + H[4]*M[i].y + H[5])*di; 
                err[0] = m[i].x - _xi; 
                err[1] = m[i].y - _yi; 
                J[0] = M[i].x*di; 
                J[1] = M[i].y*di; 
                J[2] = di; 
                J[8+3] = M[i].x; 
                J[8+4] = M[i].y; 
                J[8+5] = di; 
                J[6] = -J[0]*_xi; 
                J[7] = -J[1]*_xi; 
                J[8+6] = -J[8+3]*_yi; 
                J[8+7] = -J[8+4]*_yi; 
                J[3] = J[4] = J[5] = J[8+0] = J[8+1] = J[8+2] = 0.; 
            } 
 
            icvGaussNewton( &_J, &_err, &_Hinnov, &_JtJ, &_JtErr, &_JtJW, &_JtJV ); 
 
            for( i = 0; i < 8; i++ ) 
                H[i] += _Hinnov.data.db[i]; 
        } 
    } 
 
    cvConvert( &_H, __H ); 
 
    __END__; 
 
    cvReleaseMat( &_m ); 
    cvReleaseMat( &_M ); 
    cvReleaseMat( &_L ); 
} 
 
 
CV_IMPL int 
cvRodrigues2( const CvMat* src, CvMat* dst, CvMat* jacobian ) 
{ 
    int result = 0; 
     
    CV_FUNCNAME( "cvRogrigues2" ); 
 
    __BEGIN__; 
 
    int depth, elem_size; 
    int i, k; 
    double J[27]; 
    CvMat _J = cvMat( 3, 9, CV_64F, J ); 
 
    if( !CV_IS_MAT(src) ) 
        CV_ERROR( !src ? CV_StsNullPtr : CV_StsBadArg, "Input argument is not a valid matrix" ); 
 
    if( !CV_IS_MAT(dst) ) 
        CV_ERROR( !dst ? CV_StsNullPtr : CV_StsBadArg, 
        "The first output argument is not a valid matrix" ); 
 
    depth = CV_MAT_DEPTH(src->type); 
    elem_size = CV_ELEM_SIZE(depth); 
 
    if( depth != CV_32F && depth != CV_64F ) 
        CV_ERROR( CV_StsUnsupportedFormat, "The matrices must have 32f or 64f data type" ); 
 
    if( !CV_ARE_DEPTHS_EQ(src, dst) ) 
        CV_ERROR( CV_StsUnmatchedFormats, "All the matrices must have the same data type" ); 
 
    if( jacobian ) 
    { 
        if( !CV_IS_MAT(jacobian) ) 
            CV_ERROR( CV_StsBadArg, "Jacobian is not a valid matrix" ); 
 
        if( !CV_ARE_DEPTHS_EQ(src, jacobian) || CV_MAT_CN(jacobian->type) != 1 ) 
            CV_ERROR( CV_StsUnmatchedFormats, "Jacobian must have 32fC1 or 64fC1 datatype" ); 
 
        if( (jacobian->rows != 9 || jacobian->cols != 3) && 
            (jacobian->rows != 3 || jacobian->cols != 9)) 
            CV_ERROR( CV_StsBadSize, "Jacobian must be 3x9 or 9x3" ); 
    } 
 
    if( src->cols == 1 || src->rows == 1 ) 
    { 
        double rx, ry, rz, theta; 
        int step = src->rows > 1 ? src->step / elem_size : 1; 
 
        if( src->rows + src->cols*CV_MAT_CN(src->type) - 1 != 3 ) 
            CV_ERROR( CV_StsBadSize, "Input matrix must be 1x3, 3x1 or 3x3" ); 
 
        if( dst->rows != 3 || dst->cols != 3 || CV_MAT_CN(dst->type) != 1 ) 
            CV_ERROR( CV_StsBadSize, "Output matrix must be 3x3, single-channel floating point matrix" ); 
 
        if( depth == CV_32F ) 
        { 
            rx = src->data.fl[0]; 
            ry = src->data.fl[step]; 
            rz = src->data.fl[step*2]; 
        } 
        else 
        { 
            rx = src->data.db[0]; 
            ry = src->data.db[step]; 
            rz = src->data.db[step*2]; 
        } 
        theta = sqrt(rx*rx + ry*ry + rz*rz); 
 
        if( theta < DBL_EPSILON ) 
        { 
            cvSetIdentity( dst ); 
 
            if( jacobian ) 
            { 
                memset( J, 0, sizeof(J) ); 
                J[5] = J[15] = J[19] = 1; 
                J[7] = J[11] = J[21] = -1; 
            } 
        } 
        else 
        { 
            const double I[] = { 1, 0, 0, 0, 1, 0, 0, 0, 1 }; 
             
            double c = cos(theta); 
            double s = sin(theta); 
            double c1 = 1. - c; 
            double itheta = theta ? 1./theta : 0.; 
 
            rx *= itheta; ry *= itheta; rz *= itheta; 
 
            double rrt[] = { rx*rx, rx*ry, rx*rz, rx*ry, ry*ry, ry*rz, rx*rz, ry*rz, rz*rz }; 
            double _r_x_[] = { 0, -rz, ry, rz, 0, -rx, -ry, rx, 0 }; 
            double R[9]; 
            CvMat _R = cvMat( 3, 3, CV_64F, R ); 
 
            // R = cos(theta)*I + (1 - cos(theta))*r*rT + sin(theta)*[r_x] 
            // where [r_x] is [0 -rz ry; rz 0 -rx; -ry rx 0] 
            for( k = 0; k < 9; k++ ) 
                R[k] = c*I[k] + c1*rrt[k] + s*_r_x_[k]; 
 
            cvConvert( &_R, dst ); 
             
            if( jacobian ) 
            { 
                double drrt[] = { rx+rx, ry, rz, ry, 0, 0, rz, 0, 0, 
                                  0, rx, 0, rx, ry+ry, rz, 0, rz, 0, 
                                  0, 0, rx, 0, 0, ry, rx, ry, rz+rz }; 
                double d_r_x_[] = { 0, 0, 0, 0, 0, -1, 0, 1, 0, 
                                    0, 0, 1, 0, 0, 0, -1, 0, 0, 
                                    0, -1, 0, 1, 0, 0, 0, 0, 0 }; 
                for( i = 0; i < 3; i++ ) 
                { 
                    double ri = i == 0 ? rx : i == 1 ? ry : rz; 
                    double a0 = -s*ri, a1 = (s - 2*c1*itheta)*ri, a2 = c1*itheta; 
                    double a3 = (c - s*itheta)*ri, a4 = s*itheta; 
                    for( k = 0; k < 9; k++ ) 
                        J[i*9+k] = a0*I[k] + a1*rrt[k] + a2*drrt[i*9+k] + 
                                   a3*_r_x_[k] + a4*d_r_x_[i*9+k]; 
                } 
            } 
        } 
    } 
    else if( src->cols == 3 && src->rows == 3 ) 
    { 
        double R[9], rx, ry, rz; 
        CvMat _R = cvMat( 3, 3, CV_64F, R ); 
        double theta, s, c; 
        int step = dst->rows > 1 ? dst->step / elem_size : 1; 
         
        if( (dst->rows != 1 || dst->cols*CV_MAT_CN(dst->type) != 3) && 
            (dst->rows != 3 || dst->cols != 1 || CV_MAT_CN(dst->type) != 1)) 
            CV_ERROR( CV_StsBadSize, "Output matrix must be 1x3 or 3x1" ); 
 
        cvConvert( src, &_R ); 
        if( !cvCheckArr( &_R, CV_CHECK_RANGE+CV_CHECK_QUIET, -100, 100 ) ) 
        { 
            cvZero(dst); 
            if( jacobian ) 
                cvZero(jacobian); 
            EXIT; 
        } 
             
        rx = R[7] - R[5]; 
        ry = R[2] - R[6]; 
        rz = R[3] - R[1]; 
 
        c = (R[0] + R[4] + R[8] - 1)*0.5; 
        c = c > 1. ? 1. : c < -1. ? -1. : c; 
        theta = acos(c); 
        s = sin(theta); 
 
        if( fabs(s) < 1e-5 ) 
        { 
            double t; 
 
            if( c > 0 ) 
                rx = ry = rz = 0; 
            else 
            { 
                t = (R[0] + 1)*0.5; 
                rx = theta*sqrt(MAX(t,0.)); 
                t = (R[4] + 1)*0.5; 
                ry = theta*sqrt(MAX(t,0.))*(R[1] < 0 ? -1. : 1.); 
                t = (R[8] + 1)*0.5; 
                rz = theta*sqrt(MAX(t,0.))*(R[2] < 0 ? -1. : 1.); 
            } 
 
            if( jacobian ) 
            { 
                memset( J, 0, sizeof(J) ); 
                if( c > 0 ) 
                { 
                    J[5] = J[15] = J[19] = -0.5; 
                    J[7] = J[11] = J[21] = 0.5; 
                } 
            } 
        } 
        else 
        { 
            double vth = 1/(2*s); 
             
            if( jacobian ) 
            { 
                double t, dtheta_dtr = -1./sqrt(1 - c*c); 
                // var1 = [vth;theta] 
                // var = [om1;var1] = [om1;vth;theta] 
                double dvth_dtheta = -vth*c/s; 
                double d1 = 0.5*dvth_dtheta*dtheta_dtr; 
                double d2 = 0.5*dtheta_dtr; 
                // dvar1/dR = dvar1/dtheta*dtheta/dR = [dvth/dtheta; 1] * dtheta/dtr * dtr/dR 
                double dvardR[5*9] = 
                { 
                    0, 0, 0, 0, 0, 1, 0, -1, 0, 
                    0, 0, -1, 0, 0, 0, 1, 0, 0, 
                    0, 1, 0, -1, 0, 0, 0, 0, 0, 
                    d1, 0, 0, 0, d1, 0, 0, 0, d1, 
                    d2, 0, 0, 0, d2, 0, 0, 0, d2 
                }; 
                // var2 = [om;theta] 
                double dvar2dvar[] = 
                { 
                    vth, 0, 0, rx, 0, 
                    0, vth, 0, ry, 0, 
                    0, 0, vth, rz, 0, 
                    0, 0, 0, 0, 1 
                }; 
                double domegadvar2[] =  
                { 
                    theta, 0, 0, rx*vth, 
                    0, theta, 0, ry*vth, 
                    0, 0, theta, rz*vth 
                }; 
         
                CvMat _dvardR = cvMat( 5, 9, CV_64FC1, dvardR ); 
                CvMat _dvar2dvar = cvMat( 4, 5, CV_64FC1, dvar2dvar ); 
                CvMat _domegadvar2 = cvMat( 3, 4, CV_64FC1, domegadvar2 ); 
                double t0[3*5]; 
                CvMat _t0 = cvMat( 3, 5, CV_64FC1, t0 ); 
         
                cvMatMul( &_domegadvar2, &_dvar2dvar, &_t0 ); 
                cvMatMul( &_t0, &_dvardR, &_J ); 
 
                // transpose every row of _J (treat the rows as 3x3 matrices) 
                CV_SWAP(J[1], J[3], t); CV_SWAP(J[2], J[6], t); CV_SWAP(J[5], J[7], t); 
                CV_SWAP(J[10], J[12], t); CV_SWAP(J[11], J[15], t); CV_SWAP(J[14], J[16], t); 
                CV_SWAP(J[19], J[21], t); CV_SWAP(J[20], J[24], t); CV_SWAP(J[23], J[25], t); 
            } 
 
            vth *= theta; 
            rx *= vth; ry *= vth; rz *= vth; 
        } 
 
        if( depth == CV_32F ) 
        { 
            dst->data.fl[0] = (float)rx; 
            dst->data.fl[step] = (float)ry; 
            dst->data.fl[step*2] = (float)rz; 
        } 
        else 
        { 
            dst->data.db[0] = rx; 
            dst->data.db[step] = ry; 
            dst->data.db[step*2] = rz; 
        } 
    } 
 
    if( jacobian ) 
    { 
        if( depth == CV_32F ) 
        { 
            if( jacobian->rows == _J.rows ) 
                cvConvert( &_J, jacobian ); 
            else 
            { 
                float Jf[3*9]; 
                CvMat _Jf = cvMat( _J.rows, _J.cols, CV_32FC1, Jf ); 
                cvConvert( &_J, &_Jf ); 
                cvTranspose( &_Jf, jacobian ); 
            } 
        } 
        else if( jacobian->rows == _J.rows ) 
            cvCopy( &_J, jacobian ); 
        else 
            cvTranspose( &_J, jacobian ); 
    } 
 
    result = 1; 
 
    __END__; 
 
    return result; 
} 
 
 
CV_IMPL void 
cvProjectPoints2( const CvMat* obj_points, 
                  const CvMat* r_vec, 
                  const CvMat* t_vec, 
                  const CvMat* A, 
                  const CvMat* dist_coeffs, 
                  CvMat* img_points, CvMat* dpdr, 
                  CvMat* dpdt, CvMat* dpdf, 
                  CvMat* dpdc, CvMat* dpdk ) 
{ 
    CvMat *_M = 0, *_m = 0; 
    CvMat *_dpdr = 0, *_dpdt = 0, *_dpdc = 0, *_dpdf = 0, *_dpdk = 0; 
     
    CV_FUNCNAME( "cvProjectPoints2" ); 
 
    __BEGIN__; 
 
    int i, j, count; 
    int calc_derivatives; 
    const CvPoint3D64f* M; 
    CvPoint2D64f* m; 
    double r[3], R[9], dRdr[27], t[3], a[9], k[4] = {0,0,0,0}, fx, fy, cx, cy; 
    CvMat _r, _t, _a = cvMat( 3, 3, CV_64F, a ), _k; 
    CvMat _R = cvMat( 3, 3, CV_64F, R ), _dRdr = cvMat( 3, 9, CV_64F, dRdr ); 
    double *dpdr_p = 0, *dpdt_p = 0, *dpdk_p = 0, *dpdf_p = 0, *dpdc_p = 0; 
    int dpdr_step = 0, dpdt_step = 0, dpdk_step = 0, dpdf_step = 0, dpdc_step = 0; 
 
    if( !CV_IS_MAT(obj_points) || !CV_IS_MAT(r_vec) || 
        !CV_IS_MAT(t_vec) || !CV_IS_MAT(A) || 
        /*!CV_IS_MAT(dist_coeffs) ||*/ !CV_IS_MAT(img_points) ) 
        CV_ERROR( CV_StsBadArg, "One of required arguments is not a valid matrix" ); 
 
    count = MAX(obj_points->rows, obj_points->cols); 
 
    if( CV_IS_CONT_MAT(obj_points->type) && CV_MAT_DEPTH(obj_points->type) == CV_64F && 
        (obj_points->rows == 1 && CV_MAT_CN(obj_points->type) == 3 || 
        obj_points->rows == count && CV_MAT_CN(obj_points->type)*obj_points->cols == 3)) 
        _M = (CvMat*)obj_points; 
    else 
    { 
        CV_CALL( _M = cvCreateMat( 1, count, CV_64FC3 )); 
        CV_CALL( cvConvertPointsHomogenious( obj_points, _M )); 
    } 
 
    if( CV_IS_CONT_MAT(img_points->type) && CV_MAT_DEPTH(img_points->type) == CV_64F && 
        (img_points->rows == 1 && CV_MAT_CN(img_points->type) == 2 || 
        img_points->rows == count && CV_MAT_CN(img_points->type)*img_points->cols == 2)) 
        _m = img_points; 
    else 
        CV_CALL( _m = cvCreateMat( 1, count, CV_64FC2 )); 
 
    M = (CvPoint3D64f*)_M->data.db; 
    m = (CvPoint2D64f*)_m->data.db; 
 
    if( CV_MAT_DEPTH(r_vec->type) != CV_64F && CV_MAT_DEPTH(r_vec->type) != CV_32F || 
        (r_vec->rows != 1 && r_vec->cols != 1 || 
        r_vec->rows*r_vec->cols*CV_MAT_CN(r_vec->type) != 3) && 
        (r_vec->rows != 3 && r_vec->cols != 3 || CV_MAT_CN(r_vec->type) != 1)) 
        CV_ERROR( CV_StsBadArg, "Rotation must be represented by 1x3 or 3x1 " 
                  "floating-point rotation vector, or 3x3 rotation matrix" ); 
 
    if( r_vec->rows == 3 && r_vec->cols == 3 ) 
    { 
        _r = cvMat( 3, 1, CV_64FC1, r ); 
        CV_CALL( cvRodrigues2( r_vec, &_r )); 
        CV_CALL( cvRodrigues2( &_r, &_R, &_dRdr )); 
        cvCopy( r_vec, &_R ); 
    } 
    else 
    { 
        _r = cvMat( r_vec->rows, r_vec->cols, CV_MAKETYPE(CV_64F,CV_MAT_CN(r_vec->type)), r ); 
        CV_CALL( cvConvert( r_vec, &_r )); 
        CV_CALL( cvRodrigues2( &_r, &_R, &_dRdr ) ); 
    } 
 
    if( CV_MAT_DEPTH(t_vec->type) != CV_64F && CV_MAT_DEPTH(t_vec->type) != CV_32F || 
        t_vec->rows != 1 && t_vec->cols != 1 || 
        t_vec->rows*t_vec->cols*CV_MAT_CN(t_vec->type) != 3 ) 
        CV_ERROR( CV_StsBadArg, 
            "Translation vector must be 1x3 or 3x1 floating-point vector" ); 
 
    _t = cvMat( t_vec->rows, t_vec->cols, CV_MAKETYPE(CV_64F,CV_MAT_CN(t_vec->type)), t ); 
    CV_CALL( cvConvert( t_vec, &_t )); 
 
    if( CV_MAT_TYPE(A->type) != CV_64FC1 && CV_MAT_TYPE(A->type) != CV_32FC1 || 
        A->rows != 3 || A->cols != 3 ) 
        CV_ERROR( CV_StsBadArg, "Instrinsic parameters must be 3x3 floating-point matrix" ); 
 
    CV_CALL( cvConvert( A, &_a )); 
    fx = a[0]; fy = a[4]; 
    cx = a[2]; cy = a[5]; 
 
    if( dist_coeffs ) 
    { 
        if( !CV_IS_MAT(dist_coeffs) || 
            CV_MAT_DEPTH(dist_coeffs->type) != CV_64F && 
            CV_MAT_DEPTH(dist_coeffs->type) != CV_32F || 
            dist_coeffs->rows != 1 && dist_coeffs->cols != 1 || 
            dist_coeffs->rows*dist_coeffs->cols*CV_MAT_CN(dist_coeffs->type) != 4 ) 
            CV_ERROR( CV_StsBadArg, 
                "Distortion coefficients must be 1x4 or 4x1 floating-point vector" ); 
 
        _k = cvMat( dist_coeffs->rows, dist_coeffs->cols, 
                    CV_MAKETYPE(CV_64F,CV_MAT_CN(dist_coeffs->type)), k ); 
        CV_CALL( cvConvert( dist_coeffs, &_k )); 
    } 
     
    if( dpdr ) 
    { 
        if( !CV_IS_MAT(dpdr) || 
            CV_MAT_TYPE(dpdr->type) != CV_32FC1 && 
            CV_MAT_TYPE(dpdr->type) != CV_64FC1 || 
            dpdr->rows != count*2 || dpdr->cols != 3 ) 
            CV_ERROR( CV_StsBadArg, "dp/drot must be 2Nx3 floating-point matrix" ); 
 
        if( CV_MAT_TYPE(dpdr->type) == CV_64FC1 ) 
            _dpdr = dpdr; 
        else 
            CV_CALL( _dpdr = cvCreateMat( 2*count, 3, CV_64FC1 )); 
        dpdr_p = _dpdr->data.db; 
        dpdr_step = _dpdr->step/sizeof(dpdr_p[0]); 
    } 
 
    if( dpdt ) 
    { 
        if( !CV_IS_MAT(dpdt) || 
            CV_MAT_TYPE(dpdt->type) != CV_32FC1 && 
            CV_MAT_TYPE(dpdt->type) != CV_64FC1 || 
            dpdt->rows != count*2 || dpdt->cols != 3 ) 
            CV_ERROR( CV_StsBadArg, "dp/dT must be 2Nx3 floating-point matrix" ); 
 
        if( CV_MAT_TYPE(dpdt->type) == CV_64FC1 ) 
            _dpdt = dpdt; 
        else 
            CV_CALL( _dpdt = cvCreateMat( 2*count, 3, CV_64FC1 )); 
        dpdt_p = _dpdt->data.db; 
        dpdt_step = _dpdt->step/sizeof(dpdt_p[0]); 
    } 
 
    if( dpdf ) 
    { 
        if( !CV_IS_MAT(dpdf) || 
            CV_MAT_TYPE(dpdf->type) != CV_32FC1 && CV_MAT_TYPE(dpdf->type) != CV_64FC1 || 
            dpdf->rows != count*2 || dpdf->cols != 2 ) 
            CV_ERROR( CV_StsBadArg, "dp/df must be 2Nx2 floating-point matrix" ); 
 
        if( CV_MAT_TYPE(dpdf->type) == CV_64FC1 ) 
            _dpdf = dpdf; 
        else 
            CV_CALL( _dpdf = cvCreateMat( 2*count, 2, CV_64FC1 )); 
        dpdf_p = _dpdf->data.db; 
        dpdf_step = _dpdf->step/sizeof(dpdf_p[0]); 
    } 
 
    if( dpdc ) 
    { 
        if( !CV_IS_MAT(dpdc) || 
            CV_MAT_TYPE(dpdc->type) != CV_32FC1 && CV_MAT_TYPE(dpdc->type) != CV_64FC1 || 
            dpdc->rows != count*2 || dpdc->cols != 2 ) 
            CV_ERROR( CV_StsBadArg, "dp/dc must be 2Nx2 floating-point matrix" ); 
 
        if( CV_MAT_TYPE(dpdc->type) == CV_64FC1 ) 
            _dpdc = dpdc; 
        else 
            CV_CALL( _dpdc = cvCreateMat( 2*count, 2, CV_64FC1 )); 
        dpdc_p = _dpdc->data.db; 
        dpdc_step = _dpdc->step/sizeof(dpdc_p[0]); 
    } 
 
    if( dpdk ) 
    { 
        if( !CV_IS_MAT(dpdk) || 
            CV_MAT_TYPE(dpdk->type) != CV_32FC1 && CV_MAT_TYPE(dpdk->type) != CV_64FC1 || 
            dpdk->rows != count*2 || (dpdk->cols != 4 && dpdk->cols != 2) ) 
            CV_ERROR( CV_StsBadArg, "dp/df must be 2Nx4 or 2Nx2 floating-point matrix" ); 
 
        if( !dist_coeffs ) 
            CV_ERROR( CV_StsNullPtr, "dist_coeffs is NULL while dpdk is not" ); 
 
        if( CV_MAT_TYPE(dpdk->type) == CV_64FC1 ) 
            _dpdk = dpdk; 
        else 
            CV_CALL( _dpdk = cvCreateMat( dpdk->rows, dpdk->cols, CV_64FC1 )); 
        dpdk_p = _dpdk->data.db; 
        dpdk_step = _dpdk->step/sizeof(dpdk_p[0]); 
    } 
 
    calc_derivatives = dpdr || dpdt || dpdf || dpdc || dpdk; 
 
    for( i = 0; i < count; i++ ) 
    { 
        double X = M[i].x, Y = M[i].y, Z = M[i].z; 
        double x = R[0]*X + R[1]*Y + R[2]*Z + t[0]; 
        double y = R[3]*X + R[4]*Y + R[5]*Z + t[1]; 
        double z = R[6]*X + R[7]*Y + R[8]*Z + t[2]; 
        double r2, r4, a1, a2, a3, cdist; 
        double xd, yd; 
 
        z = z ? 1./z : 1; 
        x *= z; y *= z; 
 
        r2 = x*x + y*y; 
        r4 = r2*r2; 
        a1 = 2*x*y; 
        a2 = r2 + 2*x*x; 
        a3 = r2 + 2*y*y; 
        cdist = 1 + k[0]*r2 + k[1]*r4; 
        xd = x*cdist + k[2]*a1 + k[3]*a2; 
        yd = y*cdist + k[2]*a3 + k[3]*a1; 
 
        m[i].x = xd*fx + cx; 
        m[i].y = yd*fy + cy; 
 
        if( calc_derivatives ) 
        { 
            if( dpdc_p ) 
            { 
                dpdc_p[0] = 1; dpdc_p[1] = 0; 
                dpdc_p[dpdc_step] = 0; 
                dpdc_p[dpdc_step+1] = 1; 
                dpdc_p += dpdc_step*2; 
            } 
 
            if( dpdf_p ) 
            { 
                dpdf_p[0] = xd; dpdf_p[1] = 0; 
                dpdf_p[dpdf_step] = 0; 
                dpdf_p[dpdf_step+1] = yd; 
                dpdf_p += dpdf_step*2; 
            } 
 
            if( dpdk_p ) 
            { 
                dpdk_p[0] = fx*x*r2; 
                dpdk_p[1] = fx*x*r4; 
                dpdk_p[dpdk_step] = fy*y*r2; 
                dpdk_p[dpdk_step+1] = fy*y*r4; 
                if( _dpdk->cols > 2 ) 
                { 
                    dpdk_p[2] = fx*a1; 
                    dpdk_p[3] = fx*a2; 
                    dpdk_p[dpdk_step+2] = fy*a3; 
                    dpdk_p[dpdk_step+3] = fy*a1; 
                } 
                dpdk_p += dpdk_step*2; 
            } 
 
            if( dpdt_p ) 
            { 
                double dxdt[] = { z, 0, -x*z }, dydt[] = { 0, z, -y*z }; 
                for( j = 0; j < 3; j++ ) 
                { 
                    double dr2dt = 2*x*dxdt[j] + 2*y*dydt[j]; 
                    double dcdist_dt = k[0]*dr2dt + 2*k[1]*r2*dr2dt; 
                    double da1dt = 2*(x*dydt[j] + y*dxdt[j]); 
                    double dmxdt = fx*(dxdt[j]*cdist + x*dcdist_dt + 
                                k[2]*da1dt + k[3]*(dr2dt + 2*x*dxdt[j])); 
                    double dmydt = fy*(dydt[j]*cdist + y*dcdist_dt + 
                                k[2]*(dr2dt + 2*y*dydt[j]) + k[3]*da1dt); 
                    dpdt_p[j] = dmxdt; 
                    dpdt_p[dpdt_step+j] = dmydt; 
                } 
                dpdt_p += dpdt_step*2; 
            } 
 
            if( dpdr_p ) 
            { 
                double dx0dr[] = 
                { 
                    X*dRdr[0] + Y*dRdr[1] + Z*dRdr[2], 
                    X*dRdr[9] + Y*dRdr[10] + Z*dRdr[11], 
                    X*dRdr[18] + Y*dRdr[19] + Z*dRdr[20] 
                }; 
                double dy0dr[] = 
                { 
                    X*dRdr[3] + Y*dRdr[4] + Z*dRdr[5], 
                    X*dRdr[12] + Y*dRdr[13] + Z*dRdr[14], 
                    X*dRdr[21] + Y*dRdr[22] + Z*dRdr[23] 
                }; 
                double dz0dr[] = 
                { 
                    X*dRdr[6] + Y*dRdr[7] + Z*dRdr[8], 
                    X*dRdr[15] + Y*dRdr[16] + Z*dRdr[17], 
                    X*dRdr[24] + Y*dRdr[25] + Z*dRdr[26] 
                }; 
                for( j = 0; j < 3; j++ ) 
                { 
                    double dxdr = z*(dx0dr[j] - x*dz0dr[j]); 
                    double dydr = z*(dy0dr[j] - y*dz0dr[j]); 
                    double dr2dr = 2*x*dxdr + 2*y*dydr; 
                    double dcdist_dr = k[0]*dr2dr + 2*k[1]*r2*dr2dr; 
                    double da1dr = 2*(x*dydr + y*dxdr); 
                    double dmxdr = fx*(dxdr*cdist + x*dcdist_dr + 
                                k[2]*da1dr + k[3]*(dr2dr + 2*x*dxdr)); 
                    double dmydr = fy*(dydr*cdist + y*dcdist_dr + 
                                k[2]*(dr2dr + 2*y*dydr) + k[3]*da1dr); 
                    dpdr_p[j] = dmxdr; 
                    dpdr_p[dpdr_step+j] = dmydr; 
                } 
                dpdr_p += dpdr_step*2; 
            } 
        } 
    } 
 
    if( _m != img_points ) 
        cvConvertPointsHomogenious( _m, img_points ); 
    if( _dpdr != dpdr ) 
        cvConvert( _dpdr, dpdr ); 
    if( _dpdt != dpdt ) 
        cvConvert( _dpdt, dpdt ); 
    if( _dpdf != dpdf ) 
        cvConvert( _dpdf, dpdf ); 
    if( _dpdc != dpdc ) 
        cvConvert( _dpdc, dpdc ); 
    if( _dpdk != dpdk ) 
        cvConvert( _dpdk, dpdk ); 
 
    __END__; 
 
    if( _M != obj_points ) 
        cvReleaseMat( &_M ); 
    if( _m != img_points ) 
        cvReleaseMat( &_m ); 
    if( _dpdr != dpdr ) 
        cvReleaseMat( &_dpdr ); 
    if( _dpdt != dpdt ) 
        cvReleaseMat( &_dpdt ); 
    if( _dpdf != dpdf ) 
        cvReleaseMat( &_dpdf ); 
    if( _dpdc != dpdc ) 
        cvReleaseMat( &_dpdc ); 
    if( _dpdk != dpdk ) 
        cvReleaseMat( &_dpdk ); 
} 
 
 
CV_IMPL void 
cvFindExtrinsicCameraParams2( const CvMat* obj_points, 
                  const CvMat* img_points, const CvMat* A, 
                  const CvMat* dist_coeffs, 
                  CvMat* r_vec, CvMat* t_vec ) 
{ 
    const int max_iter = 20; 
    CvMat *_M = 0, *_Mxy = 0, *_m = 0, *_mn = 0, *_L = 0, *_J = 0; 
     
    CV_FUNCNAME( "cvFindExtrinsicCameraParams2" ); 
 
    __BEGIN__; 
 
    int i, j, count; 
    double a[9], k[4] = { 0, 0, 0, 0 }, R[9], ifx, ify, cx, cy; 
    double Mc[3] = {0, 0, 0}, MM[9], U[9], V[9], W[3]; 
    double JtJ[6*6], JtErr[6], JtJW[6], JtJV[6*6], delta[6], param[6]; 
    CvPoint3D64f* M = 0; 
    CvPoint2D64f *m = 0, *mn = 0; 
    CvMat _a = cvMat( 3, 3, CV_64F, a ); 
    CvMat _R = cvMat( 3, 3, CV_64F, R ); 
    CvMat _r = cvMat( 3, 1, CV_64F, param ); 
    CvMat _t = cvMat( 3, 1, CV_64F, param + 3 ); 
    CvMat _Mc = cvMat( 1, 3, CV_64F, Mc ); 
    CvMat _MM = cvMat( 3, 3, CV_64F, MM ); 
    CvMat _U = cvMat( 3, 3, CV_64F, U ); 
    CvMat _V = cvMat( 3, 3, CV_64F, V ); 
    CvMat _W = cvMat( 3, 1, CV_64F, W ); 
    CvMat _JtJ = cvMat( 6, 6, CV_64F, JtJ ); 
    CvMat _JtErr = cvMat( 6, 1, CV_64F, JtErr ); 
    CvMat _JtJW = cvMat( 6, 1, CV_64F, JtJW ); 
    CvMat _JtJV = cvMat( 6, 6, CV_64F, JtJV ); 
    CvMat _delta = cvMat( 6, 1, CV_64F, delta ); 
    CvMat _param = cvMat( 6, 1, CV_64F, param ); 
    CvMat _dpdr, _dpdt; 
 
    if( !CV_IS_MAT(obj_points) || !CV_IS_MAT(img_points) || 
        !CV_IS_MAT(A) || !CV_IS_MAT(r_vec) || !CV_IS_MAT(t_vec) ) 
        CV_ERROR( CV_StsBadArg, "One of required arguments is not a valid matrix" ); 
 
    count = MAX(obj_points->cols, obj_points->rows); 
    CV_CALL( _M = cvCreateMat( 1, count, CV_64FC3 )); 
    CV_CALL( _Mxy = cvCreateMat( 1, count, CV_64FC2 )); 
    CV_CALL( _m = cvCreateMat( 1, count, CV_64FC2 )); 
    CV_CALL( _mn = cvCreateMat( 1, count, CV_64FC2 )); 
    M = (CvPoint3D64f*)_M->data.db; 
    m = (CvPoint2D64f*)_m->data.db; 
    mn = (CvPoint2D64f*)_mn->data.db; 
 
    CV_CALL( cvConvertPointsHomogenious( obj_points, _M )); 
    CV_CALL( cvConvertPointsHomogenious( img_points, _m )); 
    CV_CALL( cvConvert( A, &_a )); 
 
    if( dist_coeffs ) 
    { 
        CvMat _k; 
        if( !CV_IS_MAT(dist_coeffs) || 
            CV_MAT_DEPTH(dist_coeffs->type) != CV_64F && 
            CV_MAT_DEPTH(dist_coeffs->type) != CV_32F || 
            dist_coeffs->rows != 1 && dist_coeffs->cols != 1 || 
            dist_coeffs->rows*dist_coeffs->cols*CV_MAT_CN(dist_coeffs->type) != 4 ) 
            CV_ERROR( CV_StsBadArg, 
                "Distortion coefficients must be 1x4 or 4x1 floating-point vector" ); 
 
        _k = cvMat( dist_coeffs->rows, dist_coeffs->cols, 
                    CV_MAKETYPE(CV_64F,CV_MAT_CN(dist_coeffs->type)), k ); 
        CV_CALL( cvConvert( dist_coeffs, &_k )); 
    } 
 
    if( CV_MAT_DEPTH(r_vec->type) != CV_64F && CV_MAT_DEPTH(r_vec->type) != CV_32F || 
        r_vec->rows != 1 && r_vec->cols != 1 || 
        r_vec->rows*r_vec->cols*CV_MAT_CN(r_vec->type) != 3 ) 
        CV_ERROR( CV_StsBadArg, "Rotation vector must be 1x3 or 3x1 floating-point vector" ); 
 
    if( CV_MAT_DEPTH(t_vec->type) != CV_64F && CV_MAT_DEPTH(t_vec->type) != CV_32F || 
        t_vec->rows != 1 && t_vec->cols != 1 || 
        t_vec->rows*t_vec->cols*CV_MAT_CN(t_vec->type) != 3 ) 
        CV_ERROR( CV_StsBadArg, 
            "Translation vector must be 1x3 or 3x1 floating-point vector" ); 
 
    ifx = 1./a[0]; ify = 1./a[4]; 
    cx = a[2]; cy = a[5]; 
 
    // normalize image points 
    // (unapply the intrinsic matrix transformation and distortion) 
    for( i = 0; i < count; i++ ) 
    { 
        double x = m[i].x, y = m[i].y; 
        x = (x - cx)*ifx; y = (y - cy)*ify; 
 
        // compensate distortion iteratively 
        if( dist_coeffs ) 
            for( j = 0; j < 5; j++ ) 
            { 
                double r2 = x*x + y*y; 
                double icdist = 1./(1 + k[0]*r2 + k[1]*r2*r2); 
                double delta_x = 2*k[2]*x*y + k[3]*(r2 + 2*x*x); 
                double delta_y = k[2]*(r2 + 2*y*y) + 2*k[3]*x*y; 
                x = (x - delta_x)*icdist; 
                y = (y - delta_y)*icdist; 
            } 
        mn[i].x = x; mn[i].y = y; 
 
        // calc mean(M) 
        Mc[0] += M[i].x; 
        Mc[1] += M[i].y; 
        Mc[2] += M[i].z; 
    } 
 
    Mc[0] /= count; 
    Mc[1] /= count; 
    Mc[2] /= count; 
 
    cvReshape( _M, _M, 1, count ); 
    cvMulTransposed( _M, &_MM, 1, &_Mc ); 
    cvSVD( &_MM, &_W, 0, &_V, CV_SVD_MODIFY_A + CV_SVD_V_T ); 
 
    // initialize extrinsic parameters 
    if( W[2]/W[1] < 1e-3 || count < 4 ) 
    { 
        // a planar structure case (all M's lie in the same plane) 
        double tt[3], h[9], h1_norm, h2_norm; 
        CvMat* R_transform = &_V; 
        CvMat T_transform = cvMat( 3, 1, CV_64F, tt ); 
        CvMat _H = cvMat( 3, 3, CV_64F, h ); 
        CvMat _h1, _h2, _h3; 
 
        if( V[2]*V[2] + V[5]*V[5] < 1e-10 ) 
            cvSetIdentity( R_transform ); 
 
        if( cvDet(R_transform) < 0 ) 
            cvScale( R_transform, R_transform, -1 ); 
 
        cvGEMM( R_transform, &_Mc, -1, 0, 0, &T_transform, CV_GEMM_B_T ); 
 
        for( i = 0; i < count; i++ ) 
        { 
            const double* Rp = R_transform->data.db; 
            const double* Tp = T_transform.data.db; 
            const double* src = _M->data.db + i*3; 
            double* dst = _Mxy->data.db + i*2; 
 
            dst[0] = Rp[0]*src[0] + Rp[1]*src[1] + Rp[2]*src[2] + Tp[0]; 
            dst[1] = Rp[3]*src[0] + Rp[4]*src[1] + Rp[5]*src[2] + Tp[1]; 
        } 
 
        cvFindHomography( _Mxy, _mn, &_H ); 
 
        cvGetCol( &_H, &_h1, 0 ); 
        _h2 = _h1; _h2.data.db++; 
        _h3 = _h2; _h3.data.db++; 
        h1_norm = sqrt(h[0]*h[0] + h[3]*h[3] + h[6]*h[6]); 
        h2_norm = sqrt(h[1]*h[1] + h[4]*h[4] + h[7]*h[7]); 
 
        cvScale( &_h1, &_h1, 1./h1_norm ); 
        cvScale( &_h2, &_h2, 1./h2_norm ); 
        cvScale( &_h3, &_t, 2./(h1_norm + h2_norm)); 
        cvCrossProduct( &_h1, &_h2, &_h3 ); 
 
        cvRodrigues2( &_H, &_r ); 
        cvRodrigues2( &_r, &_H ); 
        cvMatMulAdd( &_H, &T_transform, &_t, &_t ); 
        cvMatMul( &_H, R_transform, &_R ); 
        cvRodrigues2( &_R, &_r ); 
    } 
    else 
    { 
        // non-planar structure. Use DLT method 
        double* L; 
        double LL[12*12], LW[12], LV[12*12], sc; 
        CvMat _LL = cvMat( 12, 12, CV_64F, LL ); 
        CvMat _LW = cvMat( 12, 1, CV_64F, LW ); 
        CvMat _LV = cvMat( 12, 12, CV_64F, LV ); 
        CvMat _RRt, _RR, _tt; 
 
        CV_CALL( _L = cvCreateMat( 2*count, 12, CV_64F )); 
        L = _L->data.db; 
 
        for( i = 0; i < count; i++, L += 24 ) 
        { 
            double x = -mn[i].x, y = -mn[i].y; 
            L[0] = L[16] = M[i].x; 
            L[1] = L[17] = M[i].y; 
            L[2] = L[18] = M[i].z; 
            L[3] = L[19] = 1.; 
            L[4] = L[5] = L[6] = L[7] = 0.; 
            L[12] = L[13] = L[14] = L[15] = 0.; 
            L[8] = x*M[i].x; 
            L[9] = x*M[i].y; 
            L[10] = x*M[i].z; 
            L[11] = x; 
            L[20] = y*M[i].x; 
            L[21] = y*M[i].y; 
            L[22] = y*M[i].z; 
            L[23] = y; 
        } 
 
        cvMulTransposed( &_L, &_LL, 1 ); 
        cvSVD( &_LL, &_LW, 0, &_LV, CV_SVD_MODIFY_A + CV_SVD_V_T ); 
        _RRt = cvMat( 3, 4, CV_64F, LV + 11*12 ); 
        cvGetCols( &_RRt, &_RR, 0, 3 ); 
        cvGetCol( &_RRt, &_tt, 3 ); 
        if( cvDet(&_RR) < 0 ) 
            cvScale( &_RRt, &_RRt, -1 ); 
        sc = cvNorm(&_RR); 
        cvSVD( &_RR, &_W, &_U, &_V, CV_SVD_MODIFY_A + CV_SVD_U_T + CV_SVD_V_T ); 
        cvGEMM( &_U, &_V, 1, 0, 0, &_R, CV_GEMM_A_T ); 
        cvScale( &_tt, &_t, cvNorm(&_R)/sc ); 
        cvRodrigues2( &_R, &_r ); 
        cvReleaseMat( &_L ); 
    } 
 
    CV_CALL( _J = cvCreateMat( 2*count, 6, CV_64FC1 )); 
    cvGetCols( _J, &_dpdr, 0, 3 ); 
    cvGetCols( _J, &_dpdt, 3, 6 ); 
 
    // refine extrinsic parameters using iterative algorithm 
    for( i = 0; i < max_iter; i++ ) 
    { 
        double n1, n2; 
        cvReshape( _mn, _mn, 2, 1 ); 
        cvProjectPoints2( _M, &_r, &_t, &_a, dist_coeffs, 
                          _mn, &_dpdr, &_dpdt, 0, 0, 0 ); 
        cvSub( _m, _mn, _mn ); 
        cvReshape( _mn, _mn, 1, 2*count ); 
 
        cvMulTransposed( _J, &_JtJ, 1 ); 
        cvGEMM( _J, _mn, 1, 0, 0, &_JtErr, CV_GEMM_A_T ); 
        cvSVD( &_JtJ, &_JtJW, 0, &_JtJV, CV_SVD_MODIFY_A + CV_SVD_V_T ); 
        if( JtJW[5]/JtJW[0] < 1e-12 ) 
            break; 
        cvSVBkSb( &_JtJW, &_JtJV, &_JtJV, &_JtErr, 
                  &_delta, CV_SVD_U_T + CV_SVD_V_T ); 
        cvAdd( &_delta, &_param, &_param ); 
        n1 = cvNorm( &_delta ); 
        n2 = cvNorm( &_param ); 
        if( n1/n2 < 1e-10 ) 
            break; 
    } 
 
    _r = cvMat( r_vec->rows, r_vec->cols, 
        CV_MAKETYPE(CV_64F,CV_MAT_CN(r_vec->type)), param ); 
    _t = cvMat( t_vec->rows, t_vec->cols, 
        CV_MAKETYPE(CV_64F,CV_MAT_CN(t_vec->type)), param + 3 ); 
 
    cvConvert( &_r, r_vec ); 
    cvConvert( &_t, t_vec ); 
 
    __END__; 
 
    cvReleaseMat( &_M ); 
    cvReleaseMat( &_m ); 
    cvReleaseMat( &_mn ); 
    cvReleaseMat( &_L ); 
    cvReleaseMat( &_J ); 
} 
 
 
static void 
icvInitIntrinsicParams2D( const CvMat* obj_points, 
                          const CvMat* img_points, 
                          const CvMat* point_counts, 
                          CvSize image_size, 
                          CvMat* intrinsic_matrix, 
                          double aspect_ratio ) 
{ 
    CvMat *_A = 0, *_b = 0; 
     
    CV_FUNCNAME( "icvInitIntrinsicParams2D" ); 
 
    __BEGIN__; 
 
    int i, j, pos, img_count; 
    double a[9] = { 0, 0, 0, 0, 0, 0, 0, 0, 1 }; 
    double H[9], AtA[4], AtAW[2], AtAV[4], Atb[2], f[2]; 
    CvMat _a = cvMat( 3, 3, CV_64F, a ); 
    CvMat _H = cvMat( 3, 3, CV_64F, H ); 
    CvMat _AtA = cvMat( 2, 2, CV_64F, AtA ); 
    CvMat _AtAW = cvMat( 2, 1, CV_64F, AtAW ); 
    CvMat _AtAV = cvMat( 2, 2, CV_64F, AtAV ); 
    CvMat _Atb = cvMat( 2, 1, CV_64F, Atb ); 
    CvMat _f = cvMat( 2, 1, CV_64F, f ); 
 
    assert( CV_MAT_TYPE(point_counts->type) == CV_32SC1 && 
            CV_IS_MAT_CONT(point_counts->type) ); 
    img_count = point_counts->rows + point_counts->cols - 1; 
 
    if( CV_MAT_TYPE(obj_points->type) != CV_32FC3 && 
        CV_MAT_TYPE(obj_points->type) != CV_64FC3 || 
        CV_MAT_TYPE(img_points->type) != CV_32FC2 && 
        CV_MAT_TYPE(img_points->type) != CV_64FC2 ) 
        CV_ERROR( CV_StsUnsupportedFormat, "Both object points and image points must be 2D" ); 
 
    if( obj_points->rows != 1 || img_points->rows != 1 ) 
        CV_ERROR( CV_StsBadSize, "object points and image points must be a single-row matrices" ); 
 
    CV_CALL( _A = cvCreateMat( 2*img_count, 2, CV_64F )); 
    CV_CALL( _b = cvCreateMat( 2*img_count, 1, CV_64F )); 
    a[2] = (image_size.width - 1)*0.5; 
    a[5] = (image_size.height - 1)*0.5; 
 
    // extract vanishing points in order to obtain initial value for the focal length 
    for( i = 0, pos = 0; i < img_count; i++ ) 
    { 
        double* Ap = _A->data.db + i*4; 
        double* bp = _b->data.db + i*2; 
        int count = point_counts->data.i[i]; 
        double h[3], v[3], d1[3], d2[3]; 
        double n[4] = {0,0,0,0}; 
        CvMat _m, _M; 
        cvGetCols( obj_points, &_M, pos, pos + count ); 
        cvGetCols( img_points, &_m, pos, pos + count ); 
        pos += count; 
 
        CV_CALL( cvFindHomography( &_M, &_m, &_H )); 
         
        H[0] -= H[6]*a[2]; H[1] -= H[7]*a[2]; H[2] -= H[8]*a[2]; 
        H[3] -= H[6]*a[5]; H[4] -= H[7]*a[5]; H[5] -= H[8]*a[5]; 
 
        for( j = 0; j < 3; j++ ) 
        { 
            double t0 = H[j*3], t1 = H[j*3+1]; 
            h[j] = t0; v[j] = t1; 
            d1[j] = (t0 + t1)*0.5; 
            d2[j] = (t0 - t1)*0.5; 
            n[0] += t0*t0; n[1] += t1*t1; 
            n[2] += d1[j]*d1[j]; n[3] += d2[j]*d2[j]; 
        } 
 
        for( j = 0; j < 4; j++ ) 
            n[j] = 1./sqrt(n[j]); 
 
        for( j = 0; j < 3; j++ ) 
        { 
            h[j] *= n[0]; v[j] *= n[1]; 
            d1[j] *= n[2]; d2[j] *= n[3]; 
        } 
 
        Ap[0] = h[0]*v[0]; Ap[1] = h[1]*v[1]; 
        Ap[2] = d1[0]*d2[0]; Ap[3] = d1[1]*d2[1]; 
        bp[0] = -h[2]*v[2]; bp[1] = -d1[2]*d2[2]; 
    } 
 
    // while it is not about gradient descent search, 
    // the formula is the same: f = inv(At*A)*At*b 
    icvGaussNewton( _A, _b, &_f, &_AtA, &_Atb, &_AtAW, &_AtAV ); 
    a[0] = sqrt(fabs(1./f[0])); 
    a[4] = sqrt(fabs(1./f[1])); 
    if( aspect_ratio != 0 ) 
    { 
        double tf = (a[0] + a[4])/(aspect_ratio + 1.); 
        a[0] = aspect_ratio*tf; 
        a[4] = tf; 
    } 
 
    cvConvert( &_a, intrinsic_matrix ); 
 
    __END__; 
 
    cvReleaseMat( &_A ); 
    cvReleaseMat( &_b ); 
} 
 
 
/* finds intrinsic and extrinsic camera parameters 
   from a few views of known calibration pattern */ 
CV_IMPL void 
cvCalibrateCamera2( const CvMat* obj_points, 
                    const CvMat* img_points, 
                    const CvMat* point_counts, 
                    CvSize image_size, 
                    CvMat* A, CvMat* dist_coeffs, 
                    CvMat* r_vecs, CvMat* t_vecs, 
                    int flags ) 
{ 
    double alpha_smooth = 0.4; 
     
    CvMat *counts = 0, *_M = 0, *_m = 0; 
    CvMat *_Ji = 0, *_Je = 0, *_JtJ = 0, *_JtErr = 0, *_JtJW = 0, *_JtJV = 0; 
    CvMat *_param = 0, *_param_innov = 0, *_err = 0; 
     
    CV_FUNCNAME( "cvCalibrateCamera2" ); 
 
    __BEGIN__; 
 
    double a[9]; 
    CvMat _a = cvMat( 3, 3, CV_64F, a ), _k; 
    CvMat _Mi, _mi, _ri, _ti, _part; 
    CvMat _dpdr, _dpdt, _dpdf, _dpdc, _dpdk; 
    CvMat _sr_part = cvMat( 1, 3, CV_64F ), _st_part = cvMat( 1, 3, CV_64F ), _r_part, _t_part; 
    int i, j, pos, iter, img_count, count = 0, max_count = 0, total = 0, param_count; 
    int r_depth = 0, t_depth = 0, r_step = 0, t_step = 0, cn, dims; 
    int output_r_matrices = 0; 
    double aspect_ratio = 0.; 
 
    if( !CV_IS_MAT(obj_points) || !CV_IS_MAT(img_points) || 
        !CV_IS_MAT(point_counts) || !CV_IS_MAT(A) || !CV_IS_MAT(dist_coeffs) ) 
        CV_ERROR( CV_StsBadArg, "One of required vector arguments is not a valid matrix" ); 
 
    if( image_size.width <= 0 || image_size.height <= 0 ) 
        CV_ERROR( CV_StsOutOfRange, "image width and height must be positive" ); 
 
    if( CV_MAT_TYPE(point_counts->type) != CV_32SC1 || 
        point_counts->rows != 1 && point_counts->cols != 1 ) 
        CV_ERROR( CV_StsUnsupportedFormat, 
            "the array of point counters must be 1-dimensional integer vector" ); 
 
    CV_CALL( counts = cvCreateMat( point_counts->rows, point_counts->width, CV_32SC1 )); 
    cvCopy( point_counts, counts ); 
 
    img_count = counts->rows + counts->cols - 1; 
 
    if( r_vecs ) 
    { 
        r_depth = CV_MAT_DEPTH(r_vecs->type); 
        r_step = r_vecs->rows == 1 ? 3*CV_ELEM_SIZE(r_depth) : r_vecs->step; 
        cn = CV_MAT_CN(r_vecs->type); 
        if( !CV_IS_MAT(r_vecs) || r_depth != CV_32F && r_depth != CV_64F || 
            (r_vecs->rows != img_count || r_vecs->cols*cn != 3 && r_vecs->cols*cn != 9) && 
            (r_vecs->rows != 1 || r_vecs->cols != img_count || cn != 3) ) 
            CV_ERROR( CV_StsBadArg, "the output array of rotation vectors must be 3-channel " 
                "1xn or nx1 array or 1-channel nx3 or nx9 array, where n is the number of views" ); 
        output_r_matrices = r_vecs->rows == img_count && r_vecs->cols*cn == 9; 
    } 
 
    if( t_vecs ) 
    { 
        t_depth = CV_MAT_DEPTH(t_vecs->type); 
        t_step = t_vecs->rows == 1 ? 3*CV_ELEM_SIZE(t_depth) : t_vecs->step; 
        cn = CV_MAT_CN(t_vecs->type); 
        if( !CV_IS_MAT(t_vecs) || t_depth != CV_32F && t_depth != CV_64F || 
            (t_vecs->rows != img_count || t_vecs->cols*cn != 3) && 
            (t_vecs->rows != 1 || t_vecs->cols != img_count || cn != 3) ) 
            CV_ERROR( CV_StsBadArg, "the output array of rotation vectors must be 3-channel " 
                "1xn or nx1 array or 1-channel nx3 array, where n is the number of views" ); 
    } 
 
    if( CV_MAT_TYPE(A->type) != CV_32FC1 && CV_MAT_TYPE(A->type) != CV_64FC1 || 
        A->rows != 3 || A->cols != 3 ) 
        CV_ERROR( CV_StsBadArg, 
            "Intrinsic parameters must be 3x3 floating-point matrix" ); 
 
    if( CV_MAT_TYPE(dist_coeffs->type) != CV_32FC1 && 
        CV_MAT_TYPE(dist_coeffs->type) != CV_64FC1 || 
        (dist_coeffs->rows != 4 || dist_coeffs->cols != 1) && 
        (dist_coeffs->cols != 4 || dist_coeffs->rows != 1)) 
        CV_ERROR( CV_StsBadArg, 
            "Distortion coefficients must be 4x1 or 1x4 floating-point matrix" ); 
 
    for( i = 0; i < img_count; i++ ) 
    { 
        int temp_count = counts->data.i[i]; 
        if( temp_count < 4 ) 
        { 
            char buf[100]; 
            sprintf( buf, "The number of points in the view #%d is <4", i ); 
            CV_ERROR( CV_StsOutOfRange, buf ); 
        } 
        max_count = MAX( max_count, temp_count ); 
        total += temp_count; 
    } 
 
    dims = CV_MAT_CN(obj_points->type)*(obj_points->rows == 1 ? 1 : obj_points->cols); 
 
    if( CV_MAT_DEPTH(obj_points->type) != CV_32F && 
        CV_MAT_DEPTH(obj_points->type) != CV_64F || 
        (obj_points->rows != total || dims != 3 && dims != 2) && 
        (obj_points->rows != 1 || obj_points->cols != total || (dims != 3 && dims != 2)) ) 
        CV_ERROR( CV_StsBadArg, "Object points must be 1xn or nx1, 2- or 3-channel matrix, " 
                                "or nx3 or nx2 single-channel matrix" ); 
 
    cn = CV_MAT_CN(img_points->type); 
    if( CV_MAT_DEPTH(img_points->type) != CV_32F && 
        CV_MAT_DEPTH(img_points->type) != CV_64F || 
        (img_points->rows != total || img_points->cols*cn != 2) && 
        (img_points->rows != 1 || img_points->cols != total || cn != 2) ) 
        CV_ERROR( CV_StsBadArg, "Image points must be 1xn or nx1, 2-channel matrix, " 
                                "or nx2 single-channel matrix" ); 
 
    CV_CALL( _M = cvCreateMat( 1, total, CV_64FC3 )); 
    CV_CALL( _m = cvCreateMat( 1, total, CV_64FC2 )); 
 
    CV_CALL( cvConvertPointsHomogenious( obj_points, _M )); 
    CV_CALL( cvConvertPointsHomogenious( img_points, _m )); 
 
    param_count = 8 + img_count*6; 
    CV_CALL( _param = cvCreateMat( param_count, 1, CV_64FC1 )); 
    CV_CALL( _param_innov = cvCreateMat( param_count, 1, CV_64FC1 )); 
    CV_CALL( _JtJ = cvCreateMat( param_count, param_count, CV_64FC1 )); 
    CV_CALL( _JtErr = cvCreateMat( param_count, 1, CV_64FC1 )); 
    CV_CALL( _JtJW = cvCreateMat( param_count, 1, CV_64FC1 )); 
    CV_CALL( _JtJV = cvCreateMat( param_count, param_count, CV_64FC1 )); 
    CV_CALL( _Ji = cvCreateMat( max_count*2, 8, CV_64FC1 )); 
    CV_CALL( _Je = cvCreateMat( max_count*2, 6, CV_64FC1 )); 
    CV_CALL( _err = cvCreateMat( max_count*2, 1, CV_64FC1 )); 
     
    cvGetCols( _Je, &_dpdr, 0, 3 ); 
    cvGetCols( _Je, &_dpdt, 3, 6 ); 
    cvGetCols( _Ji, &_dpdf, 0, 2 ); 
    cvGetCols( _Ji, &_dpdc, 2, 4 ); 
    cvGetCols( _Ji, &_dpdk, 4, flags & CV_CALIB_ZERO_TANGENT_DIST ? 6 : 8 ); 
    cvZero( _Ji ); 
 
    // 1. initialize intrinsic parameters 
    if( flags & CV_CALIB_USE_INTRINSIC_GUESS ) 
    { 
        cvConvert( A, &_a ); 
        if( a[0] <= 0 || a[4] <= 0 ) 
            CV_ERROR( CV_StsOutOfRange, "Focal length (fx and fy) must be positive" ); 
        if( a[2] < 0 || a[2] >= image_size.width || 
            a[5] < 0 || a[5] >= image_size.height ) 
            CV_ERROR( CV_StsOutOfRange, "Principal point must be within the image" ); 
        if( fabs(a[1]) > 1e-5 ) 
            CV_ERROR( CV_StsOutOfRange, "Non-zero skew is not supported by the function" ); 
        if( fabs(a[3]) > 1e-5 || fabs(a[6]) > 1e-5 || 
            fabs(a[7]) > 1e-5 || fabs(a[8]-1) > 1e-5 ) 
            CV_ERROR( CV_StsOutOfRange, 
                "The intrinsic matrix must have [fx 0 cx; 0 fy cy; 0 0 1] shape" ); 
        a[1] = a[3] = a[6] = a[7] = 0.; 
        a[8] = 1.; 
 
        if( flags & CV_CALIB_FIX_ASPECT_RATIO ) 
            aspect_ratio = a[0]/a[4]; 
    } 
    else 
    { 
        if( dims == 3 ) 
        { 
            CvScalar mean, sdv; 
            cvAvgSdv( _M, &mean, &sdv ); 
            if( fabs(mean.val[2]) > 1e-5 && fabs(mean.val[2] - 1) > 1e-5 || 
                fabs(sdv.val[2]) > 1e-5 ) 
                CV_ERROR( CV_StsBadArg, 
                "For non-planar calibration rigs the initial intrinsic matrix must be specified" ); 
        } 
        for( i = 0; i < total; i++ ) 
            ((CvPoint3D64f*)(_M->data.db + i*3))->z = 0.; 
 
        if( flags & CV_CALIB_FIX_ASPECT_RATIO ) 
        { 
            aspect_ratio = cvmGet(A,0,0); 
            aspect_ratio /= cvmGet(A,1,1); 
            if( aspect_ratio < 0.01 || aspect_ratio > 100 ) 
                CV_ERROR( CV_StsOutOfRange, 
                    "The specified aspect ratio (=a(0,0)/a(1,1)) is incorrect" ); 
        } 
        icvInitIntrinsicParams2D( _M, _m, counts, image_size, &_a, aspect_ratio ); 
    } 
 
    _k = cvMat( dist_coeffs->rows, dist_coeffs->cols, CV_64FC1, _param->data.db + 4 ); 
    cvZero( &_k ); 
 
    // 2. initialize extrinsic parameters 
    for( i = 0, pos = 0; i < img_count; i++, pos += count ) 
    { 
        count = counts->data.i[i]; 
        _ri = cvMat( 1, 3, CV_64FC1, _param->data.db + 8 + i*6 ); 
        _ti = cvMat( 1, 3, CV_64FC1, _param->data.db + 8 + i*6 + 3 ); 
 
        cvGetCols( _M, &_Mi, pos, pos + count ); 
        cvGetCols( _m, &_mi, pos, pos + count ); 
        cvFindExtrinsicCameraParams2( &_Mi, &_mi, &_a, &_k, &_ri, &_ti ); 
    } 
 
    _param->data.db[0] = a[0]; 
    _param->data.db[1] = a[4]; 
    _param->data.db[2] = a[2]; 
    _param->data.db[3] = a[5]; 
 
    // 3. run the optimization 
    for( iter = 0; iter < 30; iter++ ) 
    { 
        double* jj = _JtJ->data.db; 
        double change; 
 
        for( i = 0, pos = 0; i < img_count; i++, pos += count ) 
        { 
            count = counts->data.i[i]; 
            _ri = cvMat( 1, 3, CV_64FC1, _param->data.db + 8 + i*6); 
            _ti = cvMat( 1, 3, CV_64FC1, _param->data.db + 8 + i*6 + 3); 
 
            cvGetCols( _M, &_Mi, pos, pos + count ); 
            _mi = cvMat( count*2, 1, CV_64FC1, _m->data.db + pos*2 ); 
 
            _dpdr.rows = _dpdt.rows = _dpdf.rows = _dpdc.rows = _dpdk.rows = count*2; 
 
            _err->cols = 1; 
            _err->rows = count*2; 
            cvReshape( _err, _err, 2, count ); 
            cvProjectPoints2( &_Mi, &_ri, &_ti, &_a, &_k, _err, &_dpdr, &_dpdt, &_dpdf, 
                              flags & CV_CALIB_FIX_PRINCIPAL_POINT ? 0 : &_dpdc, &_dpdk ); 
 
            // alter dpdf in case if only one of the focal 
            // parameters (fy) is independent variable 
            if( flags & CV_CALIB_FIX_ASPECT_RATIO ) 
                for( j = 0; j < count; j++ ) 
                { 
                    double* dpdf_j = (double*)(_dpdf.data.ptr + j*_dpdf.step*2); 
                    dpdf_j[1] = dpdf_j[0]*aspect_ratio; 
                    dpdf_j[0] = 0.; 
                } 
 
            cvReshape( _err, _err, 1, count*2 ); 
            cvSub( &_mi, _err, _err ); 
             
            _Je->rows = _Ji->rows = count*2; 
             
            cvGetSubRect( _JtJ, &_part, cvRect(0,0,8,8) ); 
            cvGEMM( _Ji, _Ji, 1, &_part, i > 0, &_part, CV_GEMM_A_T ); 
 
            cvGetSubRect( _JtJ, &_part, cvRect(8+i*6,8+i*6,6,6) ); 
            cvMulTransposed( _Je, &_part, 1 ); 
             
            cvGetSubRect( _JtJ, &_part, cvRect(8+i*6,0,6,8) ); 
            cvGEMM( _Ji, _Je, 1, 0, 0, &_part, CV_GEMM_A_T ); 
 
            cvGetRows( _JtErr, &_part, 0, 8 ); 
            cvGEMM( _Ji, _err, 1, &_part, i > 0, &_part, CV_GEMM_A_T ); 
 
            cvGetRows( _JtErr, &_part, 8 + i*6, 8 + (i+1)*6 ); 
            cvGEMM( _Je, _err, 1, 0, 0, &_part, CV_GEMM_A_T ); 
        } 
 
        // make the matrix JtJ exactly symmetrical and add missing zeros 
        for( i = 0; i < param_count; i++ ) 
        { 
            int mj = i < 8 ? param_count : ((i - 8)/6)*6 + 14; 
            for( j = i+1; j < mj; j++ ) 
                jj[j*param_count + i] = jj[i*param_count + j]; 
            for( ; j < param_count; j++ ) 
                jj[j*param_count + i] = jj[i*param_count + j] = 0; 
        } 
 
        cvSVD( _JtJ, _JtJW, 0, _JtJV, CV_SVD_MODIFY_A + CV_SVD_V_T ); 
        cvSVBkSb( _JtJW, _JtJV, _JtJV, _JtErr, _param_innov, CV_SVD_U_T + CV_SVD_V_T ); 
 
        cvScale( _param_innov, _param_innov, 1. - pow(1. - alpha_smooth, iter + 1.) ); 
        cvGetRows( _param_innov, &_part, 0, 4 ); 
        change = cvNorm( &_part ); 
        cvGetRows( _param, &_part, 0, 4 ); 
        change /= cvNorm( &_part ); 
 
        if( flags & CV_CALIB_FIX_PRINCIPAL_POINT ) 
            _param_innov->data.db[2] = _param_innov->data.db[3] = 0.; 
 
        if( flags & CV_CALIB_ZERO_TANGENT_DIST ) 
            _param_innov->data.db[6] = _param_innov->data.db[7] = 0.; 
 
        cvAdd( _param, _param_innov, _param ); 
 
        if( flags & CV_CALIB_FIX_ASPECT_RATIO ) 
            _param->data.db[0] = _param->data.db[1]*aspect_ratio; 
         
        a[0] = _param->data.db[0]; 
        a[4] = _param->data.db[1]; 
        a[2] = _param->data.db[2]; 
        a[5] = _param->data.db[3]; 
 
        if( change < FLT_EPSILON ) 
            break; 
    } 
 
    cvConvert( &_a, A ); 
    cvConvert( &_k, dist_coeffs ); 
 
    _r_part = cvMat( output_r_matrices ? 3 : 1, 3, r_depth ); 
    _t_part = cvMat( 1, 3, t_depth ); 
    for( i = 0; i < img_count; i++ ) 
    { 
        if( r_vecs ) 
        { 
            _sr_part.data.db = _param->data.db + 8 + i*6; 
            _r_part.data.ptr = r_vecs->data.ptr + i*r_step; 
            if( !output_r_matrices ) 
                cvConvert( &_sr_part, &_r_part ); 
            else 
            { 
                cvRodrigues2( &_sr_part, &_a ); 
                cvConvert( &_a, &_r_part ); 
            } 
        } 
        if( t_vecs ) 
        { 
            _st_part.data.db = _param->data.db + 8 + i*6 + 3; 
            _t_part.data.ptr = t_vecs->data.ptr + i*t_step; 
            cvConvert( &_st_part, &_t_part ); 
        } 
    } 
 
    __END__; 
 
    cvReleaseMat( &counts ); 
    cvReleaseMat( &_M ); 
    cvReleaseMat( &_m ); 
    cvReleaseMat( &_param ); 
    cvReleaseMat( &_param_innov ); 
    cvReleaseMat( &_JtJ ); 
    cvReleaseMat( &_JtErr ); 
    cvReleaseMat( &_JtJW ); 
    cvReleaseMat( &_JtJV ); 
    cvReleaseMat( &_Ji ); 
    cvReleaseMat( &_Je ); 
    cvReleaseMat( &_err ); 
} 
 
/* End of file. */