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. */