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Commit d6bf209b authored by edgarriba's avatar edgarriba
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Updating for N=2

parent dc76ca5f
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modules/calib3d/src/upnp.cpp
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......@@ -2,21 +2,10 @@
#include "upnp.h"
#include <limits>
void printMat(cv::Mat &mat)
{
cout << mat.rows << "x" << mat.cols << endl;
for (int i = 0; i < mat.rows; ++i) {
cout << "[";
for (int j = 0; j < mat.cols; ++j) {
cout << mat.at<double>(i,j) << ",";
}
cout << "];" << endl;
}
}
upnp::upnp(const cv::Mat& cameraMatrix, const cv::Mat& opoints, const cv::Mat& ipoints)
{
if (cameraMatrix.depth() == CV_32F)
init_camera_parameters<float>(cameraMatrix);
init_camera_parameters<float>(cameraMatrix);
else
init_camera_parameters<double>(cameraMatrix);
......@@ -47,67 +36,67 @@ upnp::upnp(const cv::Mat& cameraMatrix, const cv::Mat& opoints, const cv::Mat& i
upnp::~upnp()
{
if (A1)
delete[] A1;
if (A2)
delete[] A2;
if (A1)
delete[] A1;
if (A2)
delete[] A2;
}
double upnp::compute_pose(cv::Mat& R, cv::Mat& t)
{
choose_control_points();
compute_alphas();
choose_control_points();
compute_alphas();
CvMat * M = cvCreateMat(2 * number_of_correspondences, 12, CV_64F);
CvMat * M = cvCreateMat(2 * number_of_correspondences, 12, CV_64F);
for(int i = 0; i < number_of_correspondences; i++)
{
fill_M(M, 2 * i, &alphas[0] + 4 * i, us[2 * i], us[2 * i + 1]);
}
for(int i = 0; i < number_of_correspondences; i++)
{
fill_M(M, 2 * i, &alphas[0] + 4 * i, us[2 * i], us[2 * i + 1]);
}
double mtm[12 * 12], d[12], ut[12 * 12];
CvMat MtM = cvMat(12, 12, CV_64F, mtm);
CvMat D = cvMat(12, 1, CV_64F, d);
CvMat Ut = cvMat(12, 12, CV_64F, ut);
double mtm[12 * 12], d[12], ut[12 * 12];
CvMat MtM = cvMat(12, 12, CV_64F, mtm);
CvMat D = cvMat(12, 1, CV_64F, d);
CvMat Ut = cvMat(12, 12, CV_64F, ut);
cvMulTransposed(M, &MtM, 1);
cvSVD(&MtM, &D, &Ut, 0, CV_SVD_MODIFY_A | CV_SVD_U_T);
cvReleaseMat(&M);
cvMulTransposed(M, &MtM, 1);
cvSVD(&MtM, &D, &Ut, 0, CV_SVD_MODIFY_A | CV_SVD_U_T);
cvReleaseMat(&M);
double l_6x12[6 * 12], rho[6];
CvMat L_6x12 = cvMat(6, 12, CV_64F, l_6x12);
CvMat Rho = cvMat(6, 1, CV_64F, rho);
double l_6x12[6 * 12], rho[6];
CvMat L_6x12 = cvMat(6, 12, CV_64F, l_6x12);
CvMat Rho = cvMat(6, 1, CV_64F, rho);
compute_L_6x12(ut, l_6x12);
compute_rho(rho);
compute_L_6x12(ut, l_6x12);
compute_rho(rho);
double Betas[4][4], Efs[4][1], rep_errors[4];
double Rs[4][3][3], ts[4][3];
double Betas[3][4], Efs[3][1], rep_errors[3];
double Rs[3][3][3], ts[3][3];
find_betas_and_focal_approx_1(&Ut, &Rho, Betas[1], Efs[1]);
gauss_newton(&L_6x12, &Rho, Betas[1], Efs[1]);
rep_errors[1] = compute_R_and_t(ut, Betas[1], Efs[1], Rs[1], ts[1]);
find_betas_and_focal_approx_1(&Ut, &Rho, Betas[1], Efs[1]);
gauss_newton(&L_6x12, &Rho, Betas[1], Efs[1]);
rep_errors[1] = compute_R_and_t(ut, Betas[1], Rs[1], ts[1]);
find_betas_and_focal_approx_2(&Ut, &Rho, Betas[2], Efs[2]);
//gauss_newton(&L_6x12, &Rho, Betas[2], Efs[2]);
//rep_errors[2] = compute_R_and_t(ut, Betas[2], Efs[2], Rs[2], ts[2]);
find_betas_and_focal_approx_2(&Ut, &Rho, Betas[2], Efs[2]);
gauss_newton(&L_6x12, &Rho, Betas[2], Efs[2]);
rep_errors[2] = compute_R_and_t(ut, Betas[2], Rs[2], ts[2]);
int N = 1;
//if (rep_errors[2] < rep_errors[1]) N = 2;
//if (rep_errors[3] < rep_errors[N]) N = 3;
int N = 1;
if (rep_errors[2] < rep_errors[1]) N = 2;
cv::Mat(3, 1, CV_64F, ts[N]).copyTo(t);
cv::Mat(3, 3, CV_64F, Rs[N]).copyTo(R);
cv::Mat(3, 1, CV_64F, ts[N]).copyTo(t);
cv::Mat(3, 3, CV_64F, Rs[N]).copyTo(R);
fu = fv = Efs[N][0];
return Efs[N][0];
return fu;
}
void upnp::copy_R_and_t(const double R_src[3][3], const double t_src[3],
double R_dst[3][3], double t_dst[3])
double R_dst[3][3], double t_dst[3])
{
for(int i = 0; i < 3; i++) {
for(int j = 0; j < 3; j++)
R_dst[i][j] = R_src[i][j];
R_dst[i][j] = R_src[i][j];
t_dst[i] = t_src[i];
}
}
......@@ -177,7 +166,7 @@ void upnp::solve_for_sign(void)
if (pcs[2] < 0.0) {
for(int i = 0; i < 4; i++)
for(int j = 0; j < 3; j++)
ccs[i][j] = -ccs[i][j];
ccs[i][j] = -ccs[i][j];
for(int i = 0; i < number_of_correspondences; i++) {
pcs[3 * i ] = -pcs[3 * i];
......@@ -187,10 +176,10 @@ void upnp::solve_for_sign(void)
}
}
double upnp::compute_R_and_t(const double * ut, const double * betas, const double * efs,
double R[3][3], double t[3])
double upnp::compute_R_and_t(const double * ut, const double * betas,
double R[3][3], double t[3])
{
compute_ccs(betas, efs, ut);
compute_ccs(betas, ut);
compute_pcs();
solve_for_sign();
......@@ -221,27 +210,27 @@ double upnp::reprojection_error(const double R[3][3], const double t[3])
void upnp::choose_control_points()
{
for (int i = 0; i < 4; ++i)
cws[i][0] = cws[i][1] = cws[i][2] = 0;
for (int i = 0; i < 4; ++i)
cws[i][0] = cws[i][1] = cws[i][2] = 0;
cws[0][0] = cws[1][1] = cws[2][2] = 1.;
}
void upnp::compute_alphas()
{
cv::Mat CC = cv::Mat(4, 3, CV_64F, &cws);
cv::Mat PC = cv::Mat(number_of_correspondences, 3, CV_64F, &pws.front());
cv::Mat ALPHAS = cv::Mat(number_of_correspondences, 4, CV_64F, &alphas.front());
cv::Mat CC = cv::Mat(4, 3, CV_64F, &cws);
cv::Mat PC = cv::Mat(number_of_correspondences, 3, CV_64F, &pws[0]);
cv::Mat ALPHAS = cv::Mat(number_of_correspondences, 4, CV_64F, &alphas[0]);
cv::Mat CC_ = CC.clone().t();
cv::Mat PC_ = PC.clone().t();
cv::Mat CC_ = CC.clone().t();
cv::Mat PC_ = PC.clone().t();
cv::Mat row14 = cv::Mat::ones(1, 4, CV_64F);
cv::Mat row1n = cv::Mat::ones(1, number_of_correspondences, CV_64F);
cv::Mat row14 = cv::Mat::ones(1, 4, CV_64F);
cv::Mat row1n = cv::Mat::ones(1, number_of_correspondences, CV_64F);
CC_.push_back(row14);
PC_.push_back(row1n);
CC_.push_back(row14);
PC_.push_back(row1n);
ALPHAS = cv::Mat( CC_.inv() * PC_ ).t();
ALPHAS = cv::Mat( CC_.inv() * PC_ ).t();
}
void upnp::fill_M(CvMat * M, const int row, const double * as, const double u, const double v)
......@@ -260,20 +249,20 @@ void upnp::fill_M(CvMat * M, const int row, const double * as, const double u, c
}
}
void upnp::compute_ccs(const double * betas, const double * f, const double * ut)
void upnp::compute_ccs(const double * betas, const double * ut)
{
for(int i = 0; i < 4; ++i)
ccs[i][0] = ccs[i][1] = ccs[i][2] = 0.0f;
int N = 4;
for(int i = 0; i < N; ++i) {
const double * v = ut + 12 * (9 + i);
for(int j = 0; j < 4; ++j)
for(int k = 0; k < 3; ++k)
ccs[j][k] += betas[i] * v[3 * j + k]; // be careful with that
}
for (int i = 0; i < 4; ++i) ccs[i][2] *= f[0];
for(int i = 0; i < 4; ++i)
ccs[i][0] = ccs[i][1] = ccs[i][2] = 0.0f;
int N = 4;
for(int i = 0; i < N; ++i) {
const double * v = ut + 12 * (9 + i);
for(int j = 0; j < 4; ++j)
for(int k = 0; k < 3; ++k)
ccs[j][k] += betas[i] * v[3 * j + k];
}
for (int i = 0; i < 4; ++i) ccs[i][2] *= fu;
}
void upnp::compute_pcs(void)
......@@ -289,177 +278,245 @@ void upnp::compute_pcs(void)
void upnp::find_betas_and_focal_approx_1(const CvMat * Ut, const CvMat * Rho, double * betas, double * efs)
{
cv::Mat Kmf1 = cv::Mat(12, 1, CV_64F, Ut->data.db + 11 * 12);
cv::Mat dsq = cv::Mat(6, 1, CV_64F, Rho->data.db);
cv::Mat Kmf1 = cv::Mat(12, 1, CV_64F, Ut->data.db + 11 * 12);
cv::Mat dsq = cv::Mat(6, 1, CV_64F, Rho->data.db);
cv::Mat D = compute_constraint_distance_2param_6eq_2unk_f_unk( Kmf1 );
cv::Mat Dt = D.t();
cv::Mat D = compute_constraint_distance_2param_6eq_2unk_f_unk( Kmf1 );
cv::Mat Dt = D.t();
cv::Mat A = Dt * D;
cv::Mat b = Dt * dsq;
cv::Mat A = Dt * D;
cv::Mat b = Dt * dsq;
cv::Mat x = cv::Mat(2, 1, CV_64F);
cv::solve(A, b, x);
cv::Mat x = cv::Mat(2, 1, CV_64F);
cv::solve(A, b, x);
betas[0] = std::sqrt( std::abs( x.at<double>(0) ) );
betas[1] = betas[2] = betas[3] = 0;
betas[0] = std::sqrt( std::abs( x.at<double>(0) ) );
betas[1] = betas[2] = betas[3] = 0;
efs[0] = std::sqrt( std::abs( x.at<double>(1) ) ) / betas[0];
efs[0] = std::sqrt( std::abs( x.at<double>(1) ) ) / betas[0];
}
void upnp::find_betas_and_focal_approx_2(const CvMat * Ut, const CvMat * Rho, double * betas, double * efs)
{
cv::Mat Kmf1 = cv::Mat(12, 1, CV_64F, Ut->data.db + 10 * 12);
cv::Mat Kmf2 = cv::Mat(12, 1, CV_64F, Ut->data.db + 11 * 12);
cv::Mat dsq = cv::Mat(6, 1, CV_64F, Rho->data.db);
cv::Mat Kmf1 = cv::Mat(12, 1, CV_64F, Ut->data.db + 10 * 12);
cv::Mat Kmf2 = cv::Mat(12, 1, CV_64F, Ut->data.db + 11 * 12);
cv::Mat dsq = cv::Mat(6, 1, CV_64F, Rho->data.db);
cv::Mat D = compute_constraint_distance_3param_6eq_6unk_f_unk( Kmf1, Kmf2 );
cv::Mat A = D;
cv::Mat b = dsq;
cv::Mat D = compute_constraint_distance_3param_6eq_6unk_f_unk( Kmf1, Kmf2 ); // OKAY
double x[6];
cv::Mat X = cv::Mat(6, 1, CV_64F, x);
cv::Mat A = D;
cv::Mat b = dsq;
cv::solve(A, b, X, cv::DECOMP_QR);
cv::Mat x = cv::Mat(6, 1, CV_64F);
double solutions[18][3];
generate_all_possible_solutions_for_f_unk(x, solutions);
// find solution with minimum reprojection error
double min_error = std::numeric_limits<double>::max();
int min_sol = 0;
for (int i = 0; i < 18; ++i) {
betas[3] = solutions[i][0];
betas[2] = solutions[i][1];
betas[1] = betas[0] = 0;
fu = fv = solutions[i][2];
double Rs[3][3], ts[3];
double error_i = compute_R_and_t( Ut->data.db, betas, Rs, ts);
if( error_i < min_error)
{
min_error = error_i;
min_sol = i;
}
}
cv::solve(A, b, x, cv::DECOMP_QR);
betas[0] = solutions[min_sol][0];
betas[1] = solutions[min_sol][1];
betas[2] = betas[3] = 0;
betas[0] = std::sqrt( std::abs( x.at<double>(0) ) );
betas[1] = std::sqrt( std::abs( x.at<double>(2) ) * ( x.at<double>(2) < 0 ) ? -1 : ( x.at<double>(2) > 0 ) ? 1 : 0 );
betas[2] = betas[3] = 0;
efs[0] = solutions[min_sol][2];
}
cv::Mat upnp::compute_constraint_distance_2param_6eq_2unk_f_unk(const cv::Mat& M1)
{
cv::Mat P = cv::Mat(6, 2, CV_64F);
double m[13];
for (int i = 1; i < 13; ++i) m[i] = M1.at<double>(i-1);
double t1 = std::pow( m[4], 2 );
double t4 = std::pow( m[1], 2 );
double t5 = std::pow( m[5], 2 );
double t8 = std::pow( m[2], 2 );
double t10 = std::pow( m[6], 2 );
double t13 = std::pow( m[3], 2 );
double t15 = std::pow( m[7], 2 );
double t18 = std::pow( m[8], 2 );
double t22 = std::pow( m[9], 2 );
double t26 = std::pow( m[10], 2 );
double t29 = std::pow( m[11], 2 );
double t33 = std::pow( m[12], 2 );
P.at<double>(0,0) = t1 - 2 * m[4] * m[1] + t4 + t5 - 2 * m[5] * m[2] + t8;
P.at<double>(0,1) = t10 - 2 * m[6] * m[3] + t13;
P.at<double>(1,0) = t15 - 2 * m[7] * m[1] + t4 + t18 - 2 * m[8] * m[2] + t8;
P.at<double>(1,1) = t22 - 2 * m[9] * m[3] + t13;
P.at<double>(2,0) = t26 - 2 * m[10] * m[1] + t4 + t29 - 2 * m[11] * m[2] + t8;
P.at<double>(2,1) = t33 - 2 * m[12] * m[3] + t13;
P.at<double>(3,0) = t15 - 2 * m[7] * m[4] + t1 + t18 - 2 * m[8] * m[5] + t5;
P.at<double>(3,1) = t22 - 2 * m[9] * m[6] + t10;
P.at<double>(4,0) = t26 - 2 * m[10] * m[4] + t1 + t29 - 2 * m[11] * m[5] + t5;
P.at<double>(4,1) = t33 - 2 * m[12] * m[6] + t10;
P.at<double>(5,0) = t26 - 2 * m[10] * m[7] + t15 + t29 - 2 * m[11] * m[8] + t18;
P.at<double>(5,1) = t33 - 2 * m[12] * m[9] + t22;
return P;
cv::Mat P = cv::Mat(6, 2, CV_64F);
double m[13];
for (int i = 1; i < 13; ++i) m[i] = M1.at<double>(i-1);
double t1 = std::pow( m[4], 2 );
double t4 = std::pow( m[1], 2 );
double t5 = std::pow( m[5], 2 );
double t8 = std::pow( m[2], 2 );
double t10 = std::pow( m[6], 2 );
double t13 = std::pow( m[3], 2 );
double t15 = std::pow( m[7], 2 );
double t18 = std::pow( m[8], 2 );
double t22 = std::pow( m[9], 2 );
double t26 = std::pow( m[10], 2 );
double t29 = std::pow( m[11], 2 );
double t33 = std::pow( m[12], 2 );
P.at<double>(0,0) = t1 - 2 * m[4] * m[1] + t4 + t5 - 2 * m[5] * m[2] + t8;
P.at<double>(0,1) = t10 - 2 * m[6] * m[3] + t13;
P.at<double>(1,0) = t15 - 2 * m[7] * m[1] + t4 + t18 - 2 * m[8] * m[2] + t8;
P.at<double>(1,1) = t22 - 2 * m[9] * m[3] + t13;
P.at<double>(2,0) = t26 - 2 * m[10] * m[1] + t4 + t29 - 2 * m[11] * m[2] + t8;
P.at<double>(2,1) = t33 - 2 * m[12] * m[3] + t13;
P.at<double>(3,0) = t15 - 2 * m[7] * m[4] + t1 + t18 - 2 * m[8] * m[5] + t5;
P.at<double>(3,1) = t22 - 2 * m[9] * m[6] + t10;
P.at<double>(4,0) = t26 - 2 * m[10] * m[4] + t1 + t29 - 2 * m[11] * m[5] + t5;
P.at<double>(4,1) = t33 - 2 * m[12] * m[6] + t10;
P.at<double>(5,0) = t26 - 2 * m[10] * m[7] + t15 + t29 - 2 * m[11] * m[8] + t18;
P.at<double>(5,1) = t33 - 2 * m[12] * m[9] + t22;
return P;
}
cv::Mat upnp::compute_constraint_distance_3param_6eq_6unk_f_unk(const cv::Mat& M1, const cv::Mat& M2)
{
cv::Mat P = cv::Mat(6, 6, CV_64F);
double m[3][13];
for (int i = 1; i < 13; ++i)
{
m[1][i] = M1.at<double>(i-1);
m[2][i] = M2.at<double>(i-1);
}
double t1 = std::pow( m[1][4], 2 );
double t2 = std::pow( m[1][1], 2 );
double t7 = std::pow( m[1][5], 2 );
double t8 = std::pow( m[1][2], 2 );
double t11 = m[1][1] * m[2][1];
double t12 = m[1][5] * m[2][5];
double t15 = m[1][2] * m[2][2];
double t16 = m[1][4] * m[2][4];
double t19 = std::pow( m[2][4], 2 );
double t22 = std::pow( m[2][2], 2 );
double t23 = std::pow( m[2][1], 2 );
double t24 = std::pow( m[2][5], 2 );
double t28 = std::pow( m[1][6], 2 );
double t29 = std::pow( m[1][3], 2 );
double t34 = std::pow( m[1][3], 2 );
double t36 = m[1][6] * m[2][6];
double t40 = std::pow( m[2][6], 2 );
double t41 = std::pow( m[2][3], 2 );
double t47 = std::pow( m[1][7], 2 );
double t48 = std::pow( m[1][8], 2 );
double t52 = m[1][7] * m[2][7];
double t55 = m[1][8] * m[2][8];
double t59 = std::pow( m[2][8], 2 );
double t62 = std::pow( m[2][7], 2 );
double t64 = std::pow( m[1][9], 2 );
double t68 = m[1][9] * m[2][9];
double t74 = std::pow( m[2][9], 2 );
double t78 = std::pow( m[1][10], 2 );
double t79 = std::pow( m[1][11], 2 );
double t84 = m[1][10] * m[2][10];
double t87 = m[1][11] * m[2][11];
double t90 = std::pow( m[2][10], 2 );
double t95 = std::pow( m[2][11], 2 );
double t99 = std::pow( m[1][12], 2 );
double t101 = m[1][12] * m[2][12];
double t105 = std::pow( m[2][12], 2 );
P.at<double>(0,0) = t1 + t2 - 2 * m[1][4] * m[1][1] - 2 * m[1][5] * m[1][2] + t7 + t8;
P.at<double>(0,1) = -2 * m[2][4] * m[1][1] + 2 * t11 + 2 * t12 - 2 * m[1][4] * m[2][1] - 2 * m[2][5] * m[1][2] + 2 * t15 + 2 * t16 - 2 * m[1][5] * m[2][2];
P.at<double>(0,2) = t19 - 2 * m[2][4] * m[2][1] + t22 + t23 + t24 - 2 * m[2][5] * m[2][2];
P.at<double>(0,3) = t28 + t29 - 2 * m[1][6] * m[1][3];
P.at<double>(0,4) = -2 * m[2][6] * m[1][3] + 2 * t34 - 2 * m[1][6] * m[2][3] + 2 * t36;
P.at<double>(0,5) = -2 * m[2][6] * m[2][3] + t40 + t41;
P.at<double>(1,0) = t8 - 2 * m[1][8] * m[1][2] - 2 * m[1][7] * m[1][1] + t47 + t48 + t2;
P.at<double>(1,1) = 2 * t15 - 2 * m[1][8] * m[2][2] - 2 * m[2][8] * m[1][2] + 2 * t52 - 2 * m[1][7] * m[2][1] - 2 * m[2][7] * m[1][1] + 2 * t55 + 2 * t11;
P.at<double>(1,2) = -2 * m[2][8] * m[2][2] + t22 + t23 + t59 - 2 * m[2][7] * m[2][1] + t62;
P.at<double>(1,3) = t29 + t64 - 2 * m[1][9] * m[1][3];
P.at<double>(1,4) = 2 * t34 + 2 * t68 - 2 * m[2][9] * m[1][3] - 2 * m[1][9] * m[2][3];
P.at<double>(1,5) = -2 * m[2][9] * m[2][3] + t74 + t41;
P.at<double>(2,0) = -2 * m[1][11] * m[1][2] + t2 + t8 + t78 + t79 - 2 * m[1][10] * m[1][1];
P.at<double>(2,1) = 2 * t15 - 2 * m[1][11] * m[2][2] + 2 * t84 - 2 * m[1][10] * m[2][1] - 2 * m[2][10] * m[1][1] + 2 * t87 - 2 * m[2][11] * m[1][2]+ 2 * t11;
P.at<double>(2,2) = t90 + t22 - 2 * m[2][10] * m[2][1] + t23 - 2 * m[2][11] * m[2][2] + t95;
P.at<double>(2,3) = -2 * m[1][12] * m[1][3] + t99 + t29;
P.at<double>(2,4) = 2 * t34 + 2 * t101 - 2 * m[2][12] * m[1][3] - 2 * m[1][12] * m[2][3];
P.at<double>(2,5) = t41 + t105 - 2 * m[2][12] * m[2][3];
P.at<double>(3,0) = t48 + t1 - 2 * m[1][8] * m[1][5] + t7 - 2 * m[1][7] * m[1][4] + t47;
P.at<double>(3,1) = 2 * t16 - 2 * m[1][7] * m[2][4] + 2 * t55 + 2 * t52 - 2 * m[1][8] * m[2][5] - 2 * m[2][8] * m[1][5] - 2 * m[2][7] * m[1][4] + 2 * t12;
P.at<double>(3,2) = t24 - 2 * m[2][8] * m[2][5] + t19 - 2 * m[2][7] * m[2][4] + t62 + t59;
P.at<double>(3,3) = -2 * m[1][9] * m[1][6] + t64 + t28;
P.at<double>(3,4) = 2 * t68 + 2 * t36 - 2 * m[2][9] * m[1][6] - 2 * m[1][9] * m[2][6];
P.at<double>(3,5) = t40 + t74 - 2 * m[2][9] * m[2][6];
P.at<double>(4,0) = t1 - 2 * m[1][10] * m[1][4] + t7 + t78 + t79 - 2 * m[1][11] * m[1][5];
P.at<double>(4,1) = 2 * t84 - 2 * m[1][11] * m[2][5] - 2 * m[1][10] * m[2][4] + 2 * t16 - 2 * m[2][11] * m[1][5] + 2 * t87 - 2 * m[2][10] * m[1][4] + 2 * t12;
P.at<double>(4,2) = t19 + t24 - 2 * m[2][10] * m[2][4] - 2 * m[2][11] * m[2][5] + t95 + t90;
P.at<double>(4,3) = t28 - 2 * m[1][12] * m[1][6] + t99;
P.at<double>(4,4) = 2 * t101 + 2 * t36 - 2 * m[2][12] * m[1][6] - 2 * m[1][12] * m[2][6];
P.at<double>(4,5) = t105 - 2 * m[2][12] * m[2][6] + t40;
P.at<double>(5,0) = -2 * m[1][10] * m[1][7] + t47 + t48 + t78 + t79 - 2 * m[1][11] * m[1][8];
P.at<double>(5,1) = 2 * t84 + 2 * t87 - 2 * m[2][11] * m[1][8] - 2 * m[1][10] * m[2][7] - 2 * m[2][10] * m[1][7] + 2 * t55 + 2 * t52 - 2 * m[1][11] * m[2][8];
P.at<double>(5,2) = -2 * m[2][10] * m[2][7] - 2 * m[2][11] * m[2][8] + t62 + t59 + t90 + t95;
P.at<double>(5,3) = t64 - 2 * m[1][12] * m[1][9] + t99;
P.at<double>(5,4) = 2 * t68 - 2 * m[2][12] * m[1][9] - 2 * m[1][12] * m[2][9] + 2 * t101;
P.at<double>(5,5) = t105 - 2 * m[2][12] * m[2][9] + t74;
return P;
cv::Mat P = cv::Mat(6, 6, CV_64F);
double m[3][13];
for (int i = 1; i < 13; ++i)
{
m[1][i] = M1.at<double>(i-1);
m[2][i] = M2.at<double>(i-1);
}
double t1 = std::pow( m[1][4], 2 );
double t2 = std::pow( m[1][1], 2 );
double t7 = std::pow( m[1][5], 2 );
double t8 = std::pow( m[1][2], 2 );
double t11 = m[1][1] * m[2][1];
double t12 = m[1][5] * m[2][5];
double t15 = m[1][2] * m[2][2];
double t16 = m[1][4] * m[2][4];
double t19 = std::pow( m[2][4], 2 );
double t22 = std::pow( m[2][2], 2 );
double t23 = std::pow( m[2][1], 2 );
double t24 = std::pow( m[2][5], 2 );
double t28 = std::pow( m[1][6], 2 );
double t29 = std::pow( m[1][3], 2 );
double t34 = std::pow( m[1][3], 2 );
double t36 = m[1][6] * m[2][6];
double t40 = std::pow( m[2][6], 2 );
double t41 = std::pow( m[2][3], 2 );
double t47 = std::pow( m[1][7], 2 );
double t48 = std::pow( m[1][8], 2 );
double t52 = m[1][7] * m[2][7];
double t55 = m[1][8] * m[2][8];
double t59 = std::pow( m[2][8], 2 );
double t62 = std::pow( m[2][7], 2 );
double t64 = std::pow( m[1][9], 2 );
double t68 = m[1][9] * m[2][9];
double t74 = std::pow( m[2][9], 2 );
double t78 = std::pow( m[1][10], 2 );
double t79 = std::pow( m[1][11], 2 );
double t84 = m[1][10] * m[2][10];
double t87 = m[1][11] * m[2][11];
double t90 = std::pow( m[2][10], 2 );
double t95 = std::pow( m[2][11], 2 );
double t99 = std::pow( m[1][12], 2 );
double t101 = m[1][12] * m[2][12];
double t105 = std::pow( m[2][12], 2 );
P.at<double>(0,0) = t1 + t2 - 2 * m[1][4] * m[1][1] - 2 * m[1][5] * m[1][2] + t7 + t8;
P.at<double>(0,1) = -2 * m[2][4] * m[1][1] + 2 * t11 + 2 * t12 - 2 * m[1][4] * m[2][1] - 2 * m[2][5] * m[1][2] + 2 * t15 + 2 * t16 - 2 * m[1][5] * m[2][2];
P.at<double>(0,2) = t19 - 2 * m[2][4] * m[2][1] + t22 + t23 + t24 - 2 * m[2][5] * m[2][2];
P.at<double>(0,3) = t28 + t29 - 2 * m[1][6] * m[1][3];
P.at<double>(0,4) = -2 * m[2][6] * m[1][3] + 2 * t34 - 2 * m[1][6] * m[2][3] + 2 * t36;
P.at<double>(0,5) = -2 * m[2][6] * m[2][3] + t40 + t41;
P.at<double>(1,0) = t8 - 2 * m[1][8] * m[1][2] - 2 * m[1][7] * m[1][1] + t47 + t48 + t2;
P.at<double>(1,1) = 2 * t15 - 2 * m[1][8] * m[2][2] - 2 * m[2][8] * m[1][2] + 2 * t52 - 2 * m[1][7] * m[2][1] - 2 * m[2][7] * m[1][1] + 2 * t55 + 2 * t11;
P.at<double>(1,2) = -2 * m[2][8] * m[2][2] + t22 + t23 + t59 - 2 * m[2][7] * m[2][1] + t62;
P.at<double>(1,3) = t29 + t64 - 2 * m[1][9] * m[1][3];
P.at<double>(1,4) = 2 * t34 + 2 * t68 - 2 * m[2][9] * m[1][3] - 2 * m[1][9] * m[2][3];
P.at<double>(1,5) = -2 * m[2][9] * m[2][3] + t74 + t41;
P.at<double>(2,0) = -2 * m[1][11] * m[1][2] + t2 + t8 + t78 + t79 - 2 * m[1][10] * m[1][1];
P.at<double>(2,1) = 2 * t15 - 2 * m[1][11] * m[2][2] + 2 * t84 - 2 * m[1][10] * m[2][1] - 2 * m[2][10] * m[1][1] + 2 * t87 - 2 * m[2][11] * m[1][2]+ 2 * t11;
P.at<double>(2,2) = t90 + t22 - 2 * m[2][10] * m[2][1] + t23 - 2 * m[2][11] * m[2][2] + t95;
P.at<double>(2,3) = -2 * m[1][12] * m[1][3] + t99 + t29;
P.at<double>(2,4) = 2 * t34 + 2 * t101 - 2 * m[2][12] * m[1][3] - 2 * m[1][12] * m[2][3];
P.at<double>(2,5) = t41 + t105 - 2 * m[2][12] * m[2][3];
P.at<double>(3,0) = t48 + t1 - 2 * m[1][8] * m[1][5] + t7 - 2 * m[1][7] * m[1][4] + t47;
P.at<double>(3,1) = 2 * t16 - 2 * m[1][7] * m[2][4] + 2 * t55 + 2 * t52 - 2 * m[1][8] * m[2][5] - 2 * m[2][8] * m[1][5] - 2 * m[2][7] * m[1][4] + 2 * t12;
P.at<double>(3,2) = t24 - 2 * m[2][8] * m[2][5] + t19 - 2 * m[2][7] * m[2][4] + t62 + t59;
P.at<double>(3,3) = -2 * m[1][9] * m[1][6] + t64 + t28;
P.at<double>(3,4) = 2 * t68 + 2 * t36 - 2 * m[2][9] * m[1][6] - 2 * m[1][9] * m[2][6];
P.at<double>(3,5) = t40 + t74 - 2 * m[2][9] * m[2][6];
P.at<double>(4,0) = t1 - 2 * m[1][10] * m[1][4] + t7 + t78 + t79 - 2 * m[1][11] * m[1][5];
P.at<double>(4,1) = 2 * t84 - 2 * m[1][11] * m[2][5] - 2 * m[1][10] * m[2][4] + 2 * t16 - 2 * m[2][11] * m[1][5] + 2 * t87 - 2 * m[2][10] * m[1][4] + 2 * t12;
P.at<double>(4,2) = t19 + t24 - 2 * m[2][10] * m[2][4] - 2 * m[2][11] * m[2][5] + t95 + t90;
P.at<double>(4,3) = t28 - 2 * m[1][12] * m[1][6] + t99;
P.at<double>(4,4) = 2 * t101 + 2 * t36 - 2 * m[2][12] * m[1][6] - 2 * m[1][12] * m[2][6];
P.at<double>(4,5) = t105 - 2 * m[2][12] * m[2][6] + t40;
P.at<double>(5,0) = -2 * m[1][10] * m[1][7] + t47 + t48 + t78 + t79 - 2 * m[1][11] * m[1][8];
P.at<double>(5,1) = 2 * t84 + 2 * t87 - 2 * m[2][11] * m[1][8] - 2 * m[1][10] * m[2][7] - 2 * m[2][10] * m[1][7] + 2 * t55 + 2 * t52 - 2 * m[1][11] * m[2][8];
P.at<double>(5,2) = -2 * m[2][10] * m[2][7] - 2 * m[2][11] * m[2][8] + t62 + t59 + t90 + t95;
P.at<double>(5,3) = t64 - 2 * m[1][12] * m[1][9] + t99;
P.at<double>(5,4) = 2 * t68 - 2 * m[2][12] * m[1][9] - 2 * m[1][12] * m[2][9] + 2 * t101;
P.at<double>(5,5) = t105 - 2 * m[2][12] * m[2][9] + t74;
return P;
}
void upnp::generate_all_possible_solutions_for_f_unk(const double betas[5], double solutions[18][3])
{
int matrix_to_resolve[18][9] = {
{ 2, 0, 0, 1, 1, 0, 2, 0, 2 }, { 2, 0, 0, 1, 1, 0, 1, 1, 2 },
{ 2, 0, 0, 1, 1, 0, 0, 2, 2 }, { 2, 0, 0, 0, 2, 0, 2, 0, 2 },
{ 2, 0, 0, 0, 2, 0, 1, 1, 2 }, { 2, 0, 0, 0, 2, 0, 0, 2, 2 },
{ 2, 0, 0, 2, 0, 2, 1, 1, 2 }, { 2, 0, 0, 2, 0, 2, 0, 2, 2 },
{ 2, 0, 0, 1, 1, 2, 0, 2, 2 }, { 1, 1, 0, 0, 2, 0, 2, 0, 2 },
{ 1, 1, 0, 0, 2, 0, 1, 1, 2 }, { 1, 1, 0, 2, 0, 2, 0, 2, 2 },
{ 1, 1, 0, 2, 0, 2, 1, 1, 2 }, { 1, 1, 0, 2, 0, 2, 0, 2, 2 },
{ 1, 1, 0, 1, 1, 2, 0, 2, 2 }, { 0, 2, 0, 2, 0, 2, 1, 1, 2 },
{ 0, 2, 0, 2, 0, 2, 0, 2, 2 }, { 0, 2, 0, 1, 1, 2, 0, 2, 2 }
};
int combination[18][3] = {
{ 1, 2, 4 }, { 1, 2, 5 }, { 1, 2, 6 }, { 1, 3, 4 },
{ 1, 3, 5 }, { 1, 3, 6 }, { 1, 4, 5 }, { 1, 4, 6 },
{ 1, 5, 6 }, { 2, 3, 4 }, { 2, 3, 5 }, { 2, 3, 6 },
{ 2, 4, 5 }, { 2, 4, 6 }, { 2, 5, 6 }, { 3, 4, 5 },
{ 3, 4, 6 }, { 3, 5, 6 }
};
for (int i = 0; i < 18; ++i) {
double matrix[9], independent_term[3];
cv::Mat M = cv::Mat(3, 3, CV_64F, matrix);
cv::Mat I = cv::Mat(3, 1, CV_64F, independent_term);
cv::Mat S = cv::Mat(1, 3, CV_64F);
for (int j = 0; j < 9; ++j) matrix[j] = (double)matrix_to_resolve[i][j];
independent_term[0] = std::log( std::abs( betas[ combination[i][0]-1 ] ) );
independent_term[1] = std::log( std::abs( betas[ combination[i][1]-1 ] ) );
independent_term[2] = std::log( std::abs( betas[ combination[i][2]-1 ] ) );
cv::exp( cv::Mat(M.inv() * I), S);
solutions[i][0] = S.at<double>(0);
solutions[i][1] = S.at<double>(1) * sign( betas[1] );
solutions[i][2] = std::abs( S.at<double>(2) );
}
}
void upnp::gauss_newton(const CvMat * L_6x12, const CvMat * Rho, double betas[4], double * f)
{
const int iterations_number = 100;
const int iterations_number = 50;
double a[6*4], b[6], x[4];
CvMat A = cvMat(6, 4, CV_64F, a);
......@@ -471,41 +528,43 @@ void upnp::gauss_newton(const CvMat * L_6x12, const CvMat * Rho, double betas[4]
compute_A_and_b_gauss_newton(L_6x12->data.db, Rho->data.db, betas, &A, &B, f[0]);
qr_solve(&A, &B, &X);
for(int i = 0; i < 3; i++)
betas[i] += x[i];
betas[i] += x[i];
f[0] += x[3];
}
if (f[0] < 0) f[0] = -f[0];
fu = fv = f[0];
}
void upnp::compute_A_and_b_gauss_newton(const double * l_6x12, const double * rho,
const double betas[4], CvMat * A, CvMat * b, double const f)
const double betas[4], CvMat * A, CvMat * b, double const f)
{
for(int i = 0; i < 6; i++) {
const double * rowL = l_6x12 + i * 12;
double * rowA = A->data.db + i * 4;
rowA[0] = 2 * rowL[0] * betas[0] + rowL[1] * betas[1] + rowL[2] * betas[2] + f*f * ( 2 * rowL[6]*betas[0] + rowL[7]*betas[1] + rowL[8]*betas[2] );
rowA[1] = rowL[1] * betas[0] + 2 * rowL[3] * betas[1] + rowL[4] * betas[2] + f*f * ( rowL[7]*betas[0] + 2 * rowL[9]*betas[1] + rowL[10]*betas[2] );
rowA[2] = rowL[2] * betas[0] + rowL[4] * betas[1] + 2 * rowL[5] * betas[2] + f*f * ( rowL[8]*betas[0] + rowL[10]*betas[1] + 2 * rowL[11]*betas[2] );
rowA[0] = 2 * rowL[0] * betas[0] + rowL[1] * betas[1] + rowL[2] * betas[2] + f*f * ( 2 * rowL[6]*betas[0] + rowL[7]*betas[1] + rowL[8]*betas[2] );
rowA[1] = rowL[1] * betas[0] + 2 * rowL[3] * betas[1] + rowL[4] * betas[2] + f*f * ( rowL[7]*betas[0] + 2 * rowL[9]*betas[1] + rowL[10]*betas[2] );
rowA[2] = rowL[2] * betas[0] + rowL[4] * betas[1] + 2 * rowL[5] * betas[2] + f*f * ( rowL[8]*betas[0] + rowL[10]*betas[1] + 2 * rowL[11]*betas[2] );
rowA[3] = 2*f * ( rowL[6]*betas[0]*betas[0] + rowL[7]*betas[0]*betas[1] + rowL[8]*betas[0]*betas[2] + rowL[9]*betas[1]*betas[1] + rowL[10]*betas[1]*betas[2] + rowL[11]*betas[2]*betas[2] ) ;
cvmSet(b, i, 0, rho[i] -
(
rowL[0] * betas[0] * betas[0] +
rowL[1] * betas[0] * betas[1] +
rowL[2] * betas[0] * betas[2] +
rowL[3] * betas[1] * betas[1] +
rowL[4] * betas[1] * betas[2] +
rowL[5] * betas[2] * betas[2] +
f*f * rowL[6] * betas[0] * betas[0] +
f*f * rowL[7] * betas[0] * betas[1] +
f*f * rowL[8] * betas[0] * betas[2] +
f*f * rowL[9] * betas[1] * betas[1] +
f*f * rowL[10] * betas[1] * betas[2] +
f*f * rowL[11] * betas[2] * betas[2]
));
(
rowL[0] * betas[0] * betas[0] +
rowL[1] * betas[0] * betas[1] +
rowL[2] * betas[0] * betas[2] +
rowL[3] * betas[1] * betas[1] +
rowL[4] * betas[1] * betas[2] +
rowL[5] * betas[2] * betas[2] +
f*f * rowL[6] * betas[0] * betas[0] +
f*f * rowL[7] * betas[0] * betas[1] +
f*f * rowL[8] * betas[0] * betas[2] +
f*f * rowL[9] * betas[1] * betas[1] +
f*f * rowL[10] * betas[1] * betas[2] +
f*f * rowL[11] * betas[2] * betas[2]
));
}
}
......@@ -529,8 +588,8 @@ void upnp::compute_L_6x12(const double * ut, double * l_6x12)
b++;
if (b > 3) {
a++;
b = a + 1;
a++;
b = a + 1;
}
}
}
......@@ -539,29 +598,29 @@ void upnp::compute_L_6x12(const double * ut, double * l_6x12)
double * row = l_6x12 + 12 * i;
row[0] = dotXY(dv[0][i], dv[0][i]);
row[1] = 2.0f * dotXY(dv[0][i], dv[1][i]);
row[2] = dotXY(dv[1][i], dv[1][i]);
row[3] = 2.0f * dotXY(dv[0][i], dv[2][i]);
row[4] = 2.0f * dotXY(dv[1][i], dv[2][i]);
row[5] = dotXY(dv[2][i], dv[2][i]);
row[6] = dotZ(dv[0][i], dv[0][i]);
row[7] = 2.0f * dotZ(dv[0][i], dv[1][i]);
row[8] = 2.0f * dotZ(dv[0][i], dv[2][i]);
row[9] = dotZ(dv[1][i], dv[1][i]);
row[10] = 2.0f * dotZ(dv[1][i], dv[2][i]);
row[11] = dotZ(dv[2][i], dv[2][i]);
row[1] = 2.0f * dotXY(dv[0][i], dv[1][i]);
row[2] = dotXY(dv[1][i], dv[1][i]);
row[3] = 2.0f * dotXY(dv[0][i], dv[2][i]);
row[4] = 2.0f * dotXY(dv[1][i], dv[2][i]);
row[5] = dotXY(dv[2][i], dv[2][i]);
row[6] = dotZ(dv[0][i], dv[0][i]);
row[7] = 2.0f * dotZ(dv[0][i], dv[1][i]);
row[8] = 2.0f * dotZ(dv[0][i], dv[2][i]);
row[9] = dotZ(dv[1][i], dv[1][i]);
row[10] = 2.0f * dotZ(dv[1][i], dv[2][i]);
row[11] = dotZ(dv[2][i], dv[2][i]);
}
}
void upnp::compute_rho(double * rho)
{
rho[0] = dist2(cws[0], cws[1]);
rho[1] = dist2(cws[0], cws[2]);
rho[2] = dist2(cws[0], cws[3]);
rho[3] = dist2(cws[1], cws[2]);
rho[4] = dist2(cws[1], cws[3]);
rho[5] = dist2(cws[2], cws[3]);
rho[0] = dist2(cws[0], cws[1]);
rho[1] = dist2(cws[0], cws[2]);
rho[2] = dist2(cws[0], cws[3]);
rho[3] = dist2(cws[1], cws[2]);
rho[4] = dist2(cws[1], cws[3]);
rho[5] = dist2(cws[2], cws[3]);
}
double upnp::dist2(const double * p1, const double * p2)
......@@ -587,6 +646,11 @@ double upnp::dotZ(const double * v1, const double * v2)
return v1[2] * v2[2];
}
double upnp::sign(const double v)
{
return ( v < 0 ) ? -1. : ( v > 0 ) ? 1. : 0.;
}
void upnp::qr_solve(CvMat * A, CvMat * b, CvMat * X)
{
const int nr = A->rows;
......@@ -622,35 +686,35 @@ void upnp::qr_solve(CvMat * A, CvMat * b, CvMat * X)
}
else
{
double * ppAik2 = ppAkk, sum2 = 0.0, inv_eta = 1. / eta;
for(int i = k; i < nr; i++)
{
*ppAik2 *= inv_eta;
sum2 += *ppAik2 * *ppAik2;
ppAik2 += nc;
}
double sigma = sqrt(sum2);
if (*ppAkk < 0)
sigma = -sigma;
*ppAkk += sigma;
A1[k] = sigma * *ppAkk;
A2[k] = -eta * sigma;
for(int j = k + 1; j < nc; j++)
{
double * ppAik = ppAkk, sum = 0;
for(int i = k; i < nr; i++)
{
sum += *ppAik * ppAik[j - k];
ppAik += nc;
}
double tau = sum / A1[k];
ppAik = ppAkk;
for(int i = k; i < nr; i++)
{
ppAik[j - k] -= tau * *ppAik;
ppAik += nc;
}
}
double * ppAik2 = ppAkk, sum2 = 0.0, inv_eta = 1. / eta;
for(int i = k; i < nr; i++)
{
*ppAik2 *= inv_eta;
sum2 += *ppAik2 * *ppAik2;
ppAik2 += nc;
}
double sigma = sqrt(sum2);
if (*ppAkk < 0)
sigma = -sigma;
*ppAkk += sigma;
A1[k] = sigma * *ppAkk;
A2[k] = -eta * sigma;
for(int j = k + 1; j < nc; j++)
{
double * ppAik = ppAkk, sum = 0;
for(int i = k; i < nr; i++)
{
sum += *ppAik * ppAik[j - k];
ppAik += nc;
}
double tau = sum / A1[k];
ppAik = ppAkk;
for(int i = k; i < nr; i++)
{
ppAik[j - k] -= tau * *ppAik;
ppAik += nc;
}
}
}
ppAkk += nc + 1;
}
......@@ -662,15 +726,15 @@ void upnp::qr_solve(CvMat * A, CvMat * b, CvMat * X)
double * ppAij = ppAjj, tau = 0;
for(int i = j; i < nr; i++)
{
tau += *ppAij * pb[i];
ppAij += nc;
tau += *ppAij * pb[i];
ppAij += nc;
}
tau /= A1[j];
ppAij = ppAjj;
for(int i = j; i < nr; i++)
{
pb[i] -= tau * *ppAij;
ppAij += nc;
pb[i] -= tau * *ppAij;
ppAij += nc;
}
ppAjj += nc + 1;
}
......@@ -684,8 +748,8 @@ void upnp::qr_solve(CvMat * A, CvMat * b, CvMat * X)
for(int j = i + 1; j < nc; j++)
{
sum += *ppAij * pX[j];
ppAij++;
sum += *ppAij * pX[j];
ppAij++;
}
pX[i] = (pb[i] - sum) / A2[i];
}
......
modules/calib3d/src/upnp.h
View file @ d6bf209b
......@@ -28,12 +28,12 @@ private:
{
for(int i = 0; i < number_of_correspondences; i++)
{
pws[3 * i ] = opoints.at<OpointType>(0,i).x;
pws[3 * i + 1] = opoints.at<OpointType>(0,i).y;
pws[3 * i + 2] = opoints.at<OpointType>(0,i).z;
pws[3 * i ] = opoints.at<OpointType>(0,i).x;
pws[3 * i + 1] = opoints.at<OpointType>(0,i).y;
pws[3 * i + 2] = opoints.at<OpointType>(0,i).z;
us[2 * i ] = ipoints.at<IpointType>(0,i).x;
us[2 * i + 1] = ipoints.at<IpointType>(0,i).y;
us[2 * i ] = ipoints.at<IpointType>(0,i).x;
us[2 * i + 1] = ipoints.at<IpointType>(0,i).y;
}
}
......@@ -41,7 +41,7 @@ private:
void choose_control_points();
void compute_alphas();
void fill_M(CvMat * M, const int row, const double * alphas, const double u, const double v);
void compute_ccs(const double * betas, const double * f, const double * ut);
void compute_ccs(const double * betas, const double * ut);
void compute_pcs(void);
void solve_for_sign(void);
......@@ -52,7 +52,9 @@ private:
cv::Mat compute_constraint_distance_2param_6eq_2unk_f_unk(const cv::Mat& M1);
cv::Mat compute_constraint_distance_3param_6eq_6unk_f_unk(const cv::Mat& M1, const cv::Mat& M2);
void generate_all_possible_solutions_for_f_unk(const double betas_[5], double solutions[18][3]);
double sign(const double v);
double dot(const double * v1, const double * v2);
double dotXY(const double * v1, const double * v2);
double dotZ(const double * v1, const double * v2);
......@@ -65,7 +67,7 @@ private:
void compute_A_and_b_gauss_newton(const double * l_6x12, const double * rho,
const double cb[4], CvMat * A, CvMat * b, double const f);
double compute_R_and_t(const double * ut, const double * betas, const double * efs,
double compute_R_and_t(const double * ut, const double * betas,
double R[3][3], double t[3]);
void estimate_R_and_t(double R[3][3], double t[3]);
......
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