diff --git a/modules/calib3d/include/opencv2/calib3d/calib3d.hpp b/modules/calib3d/include/opencv2/calib3d/calib3d.hpp
index fae31113d..889be59db 100644
--- a/modules/calib3d/include/opencv2/calib3d/calib3d.hpp
+++ b/modules/calib3d/include/opencv2/calib3d/calib3d.hpp
@@ -393,7 +393,6 @@ CVAPI(void) cvReprojectImageTo3D( const CvArr* disparityImage,
}
//////////////////////////////////////////////////////////////////////////////////////////
-
class CV_EXPORTS CvLevMarq
{
public:
@@ -432,6 +431,9 @@ public:
namespace cv
{
+CV_EXPORTS_W double ePnP( InputArray _opoints, InputArray _ipoints,
+ InputArray _cameraMatrix, InputArray _distCoeffs,
+ OutputArray _rvec, OutputArray _tvec);
//! converts rotation vector to rotation matrix or vice versa using Rodrigues transformation
CV_EXPORTS_W void Rodrigues(InputArray src, OutputArray dst, OutputArray jacobian=noArray());
diff --git a/modules/calib3d/src/epnp.cpp b/modules/calib3d/src/epnp.cpp
new file mode 100644
index 000000000..cbbea01a4
--- /dev/null
+++ b/modules/calib3d/src/epnp.cpp
@@ -0,0 +1,744 @@
+#include <iostream>
+using namespace std;
+#include "precomp.hpp"
+#include "epnp.h"
+
+namespace cv
+{
+double ePnP( InputArray _opoints, InputArray _ipoints,
+ InputArray _cameraMatrix, InputArray _distCoeffs,
+ OutputArray _rvec, OutputArray _tvec)
+{
+ Mat opoints = _opoints.getMat(), ipoints = _ipoints.getMat();
+ int npoints = std::max(opoints.checkVector(3, CV_32F), opoints.checkVector(3, CV_64F));
+ CV_Assert( npoints >= 0 && npoints == std::max(ipoints.checkVector(2, CV_32F), ipoints.checkVector(2, CV_64F)) );
+ Mat cameraMatrix = _cameraMatrix.getMat(), distCoeffs = _distCoeffs.getMat();
+
+ Mat undistortedPoints;
+ undistortPoints(ipoints, undistortedPoints, cameraMatrix, distCoeffs);
+
+ epnp PnP;
+ PnP.set_internal_parameters(cameraMatrix.at<double> (0, 2), cameraMatrix.at<double> (1, 2), cameraMatrix.at<double> (0, 0), cameraMatrix.at<double> (1, 1));
+ PnP.set_maximum_number_of_correspondences(npoints);
+ PnP.reset_correspondences();
+ for(int i = 0; i < npoints; i++) {
+ PnP.add_correspondence(opoints.at<Point3d>(0,i).x, opoints.at<Point3d>(0,i).y, opoints.at<Point3d>(0,i).z, undistortedPoints.at<Point2d>(0,i).x* cameraMatrix.at<double> (0, 0) + cameraMatrix.at<double> (0, 2),
+ undistortedPoints.at<Point2d>(0,i).y* cameraMatrix.at<double> (1, 1) + cameraMatrix.at<double> (1, 2));
+ }
+ double R_est[3][3], t_est[3];
+ double error = PnP.compute_pose(R_est, t_est);
+
+ _tvec.create(3,1,CV_64F);
+ _rvec.create(3,1,CV_64F);
+ Mat(3, 1, CV_64FC1, t_est).copyTo(_tvec.getMat());
+ Rodrigues(Mat(3, 3, CV_64FC1, R_est), _rvec.getMat());
+ return error;
+}
+}
+
+epnp::epnp(void)
+{
+ maximum_number_of_correspondences = 0;
+ number_of_correspondences = 0;
+
+ pws = 0;
+ us = 0;
+ alphas = 0;
+ pcs = 0;
+}
+
+epnp::~epnp()
+{
+ delete [] pws;
+ delete [] us;
+ delete [] alphas;
+ delete [] pcs;
+}
+
+void epnp::set_internal_parameters(double uc, double vc, double fu, double fv)
+{
+ this->uc = uc;
+ this->vc = vc;
+ this->fu = fu;
+ this->fv = fv;
+}
+
+void epnp::set_maximum_number_of_correspondences(int n)
+{
+ if (maximum_number_of_correspondences < n) {
+ if (pws != 0) delete [] pws;
+ if (us != 0) delete [] us;
+ if (alphas != 0) delete [] alphas;
+ if (pcs != 0) delete [] pcs;
+
+ maximum_number_of_correspondences = n;
+ pws = new double[3 * maximum_number_of_correspondences];
+ us = new double[2 * maximum_number_of_correspondences];
+ alphas = new double[4 * maximum_number_of_correspondences];
+ pcs = new double[3 * maximum_number_of_correspondences];
+ }
+}
+
+void epnp::reset_correspondences(void)
+{
+ number_of_correspondences = 0;
+}
+
+void epnp::add_correspondence(double X, double Y, double Z, double u, double v)
+{
+ pws[3 * number_of_correspondences ] = X;
+ pws[3 * number_of_correspondences + 1] = Y;
+ pws[3 * number_of_correspondences + 2] = Z;
+
+ us[2 * number_of_correspondences ] = u;
+ us[2 * number_of_correspondences + 1] = v;
+
+ number_of_correspondences++;
+}
+
+void epnp::choose_control_points(void)
+{
+ // Take C0 as the reference points centroid:
+ cws[0][0] = cws[0][1] = cws[0][2] = 0;
+ for(int i = 0; i < number_of_correspondences; i++)
+ for(int j = 0; j < 3; j++)
+ cws[0][j] += pws[3 * i + j];
+
+ for(int j = 0; j < 3; j++)
+ cws[0][j] /= number_of_correspondences;
+
+
+ // Take C1, C2, and C3 from PCA on the reference points:
+ CvMat * PW0 = cvCreateMat(number_of_correspondences, 3, CV_64F);
+
+ double pw0tpw0[3 * 3], dc[3], uct[3 * 3];
+ CvMat PW0tPW0 = cvMat(3, 3, CV_64F, pw0tpw0);
+ CvMat DC = cvMat(3, 1, CV_64F, dc);
+ CvMat UCt = cvMat(3, 3, CV_64F, uct);
+
+ for(int i = 0; i < number_of_correspondences; i++)
+ for(int j = 0; j < 3; j++)
+ PW0->data.db[3 * i + j] = pws[3 * i + j] - cws[0][j];
+
+ cvMulTransposed(PW0, &PW0tPW0, 1);
+ cvSVD(&PW0tPW0, &DC, &UCt, 0, CV_SVD_MODIFY_A | CV_SVD_U_T);
+
+ cvReleaseMat(&PW0);
+
+ for(int i = 1; i < 4; i++) {
+ double k = sqrt(dc[i - 1] / number_of_correspondences);
+ for(int j = 0; j < 3; j++)
+ cws[i][j] = cws[0][j] + k * uct[3 * (i - 1) + j];
+ }
+}
+
+void epnp::compute_barycentric_coordinates(void)
+{
+ double cc[3 * 3], cc_inv[3 * 3];
+ CvMat CC = cvMat(3, 3, CV_64F, cc);
+ CvMat CC_inv = cvMat(3, 3, CV_64F, cc_inv);
+
+ for(int i = 0; i < 3; i++)
+ for(int j = 1; j < 4; j++)
+ cc[3 * i + j - 1] = cws[j][i] - cws[0][i];
+
+ cvInvert(&CC, &CC_inv, CV_SVD);
+ double * ci = cc_inv;
+ for(int i = 0; i < number_of_correspondences; i++) {
+ double * pi = pws + 3 * i;
+ double * a = alphas + 4 * i;
+
+ for(int j = 0; j < 3; j++)
+ a[1 + j] =
+ ci[3 * j ] * (pi[0] - cws[0][0]) +
+ ci[3 * j + 1] * (pi[1] - cws[0][1]) +
+ ci[3 * j + 2] * (pi[2] - cws[0][2]);
+ a[0] = 1.0f - a[1] - a[2] - a[3];
+ }
+}
+
+void epnp::fill_M(CvMat * M,
+ const int row, const double * as, const double u, const double v)
+{
+ double * M1 = M->data.db + row * 12;
+ double * M2 = M1 + 12;
+
+ for(int i = 0; i < 4; i++) {
+ M1[3 * i ] = as[i] * fu;
+ M1[3 * i + 1] = 0.0;
+ M1[3 * i + 2] = as[i] * (uc - u);
+
+ M2[3 * i ] = 0.0;
+ M2[3 * i + 1] = as[i] * fv;
+ M2[3 * i + 2] = as[i] * (vc - v);
+ }
+}
+
+void epnp::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;
+
+ for(int i = 0; i < 4; i++) {
+ const double * v = ut + 12 * (11 - i);
+ for(int j = 0; j < 4; j++)
+ for(int k = 0; k < 3; k++)
+ ccs[j][k] += betas[i] * v[3 * j + k];
+ }
+}
+
+void epnp::compute_pcs(void)
+{
+ for(int i = 0; i < number_of_correspondences; i++) {
+ double * a = alphas + 4 * i;
+ double * pc = pcs + 3 * i;
+
+ for(int j = 0; j < 3; j++)
+ pc[j] = a[0] * ccs[0][j] + a[1] * ccs[1][j] + a[2] * ccs[2][j] + a[3] * ccs[3][j];
+ }
+}
+
+double epnp::compute_pose(double R[3][3], double t[3])
+{
+ choose_control_points();
+ compute_barycentric_coordinates();
+
+ 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 + 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);
+
+ cvMulTransposed(M, &MtM, 1);
+ cvSVD(&MtM, &D, &Ut, 0, CV_SVD_MODIFY_A | CV_SVD_U_T);
+ cvReleaseMat(&M);
+
+ double l_6x10[6 * 10], rho[6];
+ CvMat L_6x10 = cvMat(6, 10, CV_64F, l_6x10);
+ CvMat Rho = cvMat(6, 1, CV_64F, rho);
+
+ compute_L_6x10(ut, l_6x10);
+ compute_rho(rho);
+
+ double Betas[4][4], rep_errors[4];
+ double Rs[4][3][3], ts[4][3];
+
+ find_betas_approx_1(&L_6x10, &Rho, Betas[1]);
+ gauss_newton(&L_6x10, &Rho, Betas[1]);
+ rep_errors[1] = compute_R_and_t(ut, Betas[1], Rs[1], ts[1]);
+
+ find_betas_approx_2(&L_6x10, &Rho, Betas[2]);
+ gauss_newton(&L_6x10, &Rho, Betas[2]);
+ rep_errors[2] = compute_R_and_t(ut, Betas[2], Rs[2], ts[2]);
+
+ find_betas_approx_3(&L_6x10, &Rho, Betas[3]);
+ gauss_newton(&L_6x10, &Rho, Betas[3]);
+ rep_errors[3] = compute_R_and_t(ut, Betas[3], Rs[3], ts[3]);
+
+ int N = 1;
+ if (rep_errors[2] < rep_errors[1]) N = 2;
+ if (rep_errors[3] < rep_errors[N]) N = 3;
+
+ copy_R_and_t(Rs[N], ts[N], R, t);
+
+ return rep_errors[N];
+}
+
+void epnp::copy_R_and_t(const double R_src[3][3], const double t_src[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];
+ t_dst[i] = t_src[i];
+ }
+}
+
+double epnp::dist2(const double * p1, const double * p2)
+{
+ return
+ (p1[0] - p2[0]) * (p1[0] - p2[0]) +
+ (p1[1] - p2[1]) * (p1[1] - p2[1]) +
+ (p1[2] - p2[2]) * (p1[2] - p2[2]);
+}
+
+double epnp::dot(const double * v1, const double * v2)
+{
+ return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
+}
+
+double epnp::reprojection_error(const double R[3][3], const double t[3])
+{
+ double sum2 = 0.0;
+
+ for(int i = 0; i < number_of_correspondences; i++) {
+ double * pw = pws + 3 * i;
+ double Xc = dot(R[0], pw) + t[0];
+ double Yc = dot(R[1], pw) + t[1];
+ double inv_Zc = 1.0 / (dot(R[2], pw) + t[2]);
+ double ue = uc + fu * Xc * inv_Zc;
+ double ve = vc + fv * Yc * inv_Zc;
+ double u = us[2 * i], v = us[2 * i + 1];
+
+ sum2 += sqrt( (u - ue) * (u - ue) + (v - ve) * (v - ve) );
+ }
+
+ return sum2 / number_of_correspondences;
+}
+
+void epnp::estimate_R_and_t(double R[3][3], double t[3])
+{
+ double pc0[3], pw0[3];
+
+ pc0[0] = pc0[1] = pc0[2] = 0.0;
+ pw0[0] = pw0[1] = pw0[2] = 0.0;
+
+ for(int i = 0; i < number_of_correspondences; i++) {
+ const double * pc = pcs + 3 * i;
+ const double * pw = pws + 3 * i;
+
+ for(int j = 0; j < 3; j++) {
+ pc0[j] += pc[j];
+ pw0[j] += pw[j];
+ }
+ }
+ for(int j = 0; j < 3; j++) {
+ pc0[j] /= number_of_correspondences;
+ pw0[j] /= number_of_correspondences;
+ }
+
+ double abt[3 * 3], abt_d[3], abt_u[3 * 3], abt_v[3 * 3];
+ CvMat ABt = cvMat(3, 3, CV_64F, abt);
+ CvMat ABt_D = cvMat(3, 1, CV_64F, abt_d);
+ CvMat ABt_U = cvMat(3, 3, CV_64F, abt_u);
+ CvMat ABt_V = cvMat(3, 3, CV_64F, abt_v);
+
+ cvSetZero(&ABt);
+ for(int i = 0; i < number_of_correspondences; i++) {
+ double * pc = pcs + 3 * i;
+ double * pw = pws + 3 * i;
+
+ for(int j = 0; j < 3; j++) {
+ abt[3 * j ] += (pc[j] - pc0[j]) * (pw[0] - pw0[0]);
+ abt[3 * j + 1] += (pc[j] - pc0[j]) * (pw[1] - pw0[1]);
+ abt[3 * j + 2] += (pc[j] - pc0[j]) * (pw[2] - pw0[2]);
+ }
+ }
+
+ cvSVD(&ABt, &ABt_D, &ABt_U, &ABt_V, CV_SVD_MODIFY_A);
+
+ for(int i = 0; i < 3; i++)
+ for(int j = 0; j < 3; j++)
+ R[i][j] = dot(abt_u + 3 * i, abt_v + 3 * j);
+
+ const double det =
+ R[0][0] * R[1][1] * R[2][2] + R[0][1] * R[1][2] * R[2][0] + R[0][2] * R[1][0] * R[2][1] -
+ R[0][2] * R[1][1] * R[2][0] - R[0][1] * R[1][0] * R[2][2] - R[0][0] * R[1][2] * R[2][1];
+
+ if (det < 0) {
+ R[2][0] = -R[2][0];
+ R[2][1] = -R[2][1];
+ R[2][2] = -R[2][2];
+ }
+
+ t[0] = pc0[0] - dot(R[0], pw0);
+ t[1] = pc0[1] - dot(R[1], pw0);
+ t[2] = pc0[2] - dot(R[2], pw0);
+}
+
+void epnp::print_pose(const double R[3][3], const double t[3])
+{
+ cout << R[0][0] << " " << R[0][1] << " " << R[0][2] << " " << t[0] << endl;
+ cout << R[1][0] << " " << R[1][1] << " " << R[1][2] << " " << t[1] << endl;
+ cout << R[2][0] << " " << R[2][1] << " " << R[2][2] << " " << t[2] << endl;
+}
+
+void epnp::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];
+
+ for(int i = 0; i < number_of_correspondences; i++) {
+ pcs[3 * i ] = -pcs[3 * i];
+ pcs[3 * i + 1] = -pcs[3 * i + 1];
+ pcs[3 * i + 2] = -pcs[3 * i + 2];
+ }
+ }
+}
+
+double epnp::compute_R_and_t(const double * ut, const double * betas,
+ double R[3][3], double t[3])
+{
+ compute_ccs(betas, ut);
+ compute_pcs();
+
+ solve_for_sign();
+
+ estimate_R_and_t(R, t);
+
+ return reprojection_error(R, t);
+}
+
+// betas10 = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44]
+// betas_approx_1 = [B11 B12 B13 B14]
+
+void epnp::find_betas_approx_1(const CvMat * L_6x10, const CvMat * Rho,
+ double * betas)
+{
+ double l_6x4[6 * 4], b4[4];
+ CvMat L_6x4 = cvMat(6, 4, CV_64F, l_6x4);
+ CvMat B4 = cvMat(4, 1, CV_64F, b4);
+
+ for(int i = 0; i < 6; i++) {
+ cvmSet(&L_6x4, i, 0, cvmGet(L_6x10, i, 0));
+ cvmSet(&L_6x4, i, 1, cvmGet(L_6x10, i, 1));
+ cvmSet(&L_6x4, i, 2, cvmGet(L_6x10, i, 3));
+ cvmSet(&L_6x4, i, 3, cvmGet(L_6x10, i, 6));
+ }
+
+ cvSolve(&L_6x4, Rho, &B4, CV_SVD);
+
+ if (b4[0] < 0) {
+ betas[0] = sqrt(-b4[0]);
+ betas[1] = -b4[1] / betas[0];
+ betas[2] = -b4[2] / betas[0];
+ betas[3] = -b4[3] / betas[0];
+ } else {
+ betas[0] = sqrt(b4[0]);
+ betas[1] = b4[1] / betas[0];
+ betas[2] = b4[2] / betas[0];
+ betas[3] = b4[3] / betas[0];
+ }
+}
+
+// betas10 = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44]
+// betas_approx_2 = [B11 B12 B22 ]
+
+void epnp::find_betas_approx_2(const CvMat * L_6x10, const CvMat * Rho,
+ double * betas)
+{
+ double l_6x3[6 * 3], b3[3];
+ CvMat L_6x3 = cvMat(6, 3, CV_64F, l_6x3);
+ CvMat B3 = cvMat(3, 1, CV_64F, b3);
+
+ for(int i = 0; i < 6; i++) {
+ cvmSet(&L_6x3, i, 0, cvmGet(L_6x10, i, 0));
+ cvmSet(&L_6x3, i, 1, cvmGet(L_6x10, i, 1));
+ cvmSet(&L_6x3, i, 2, cvmGet(L_6x10, i, 2));
+ }
+
+ cvSolve(&L_6x3, Rho, &B3, CV_SVD);
+
+ if (b3[0] < 0) {
+ betas[0] = sqrt(-b3[0]);
+ betas[1] = (b3[2] < 0) ? sqrt(-b3[2]) : 0.0;
+ } else {
+ betas[0] = sqrt(b3[0]);
+ betas[1] = (b3[2] > 0) ? sqrt(b3[2]) : 0.0;
+ }
+
+ if (b3[1] < 0) betas[0] = -betas[0];
+
+ betas[2] = 0.0;
+ betas[3] = 0.0;
+}
+
+// betas10 = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44]
+// betas_approx_3 = [B11 B12 B22 B13 B23 ]
+
+void epnp::find_betas_approx_3(const CvMat * L_6x10, const CvMat * Rho,
+ double * betas)
+{
+ double l_6x5[6 * 5], b5[5];
+ CvMat L_6x5 = cvMat(6, 5, CV_64F, l_6x5);
+ CvMat B5 = cvMat(5, 1, CV_64F, b5);
+
+ for(int i = 0; i < 6; i++) {
+ cvmSet(&L_6x5, i, 0, cvmGet(L_6x10, i, 0));
+ cvmSet(&L_6x5, i, 1, cvmGet(L_6x10, i, 1));
+ cvmSet(&L_6x5, i, 2, cvmGet(L_6x10, i, 2));
+ cvmSet(&L_6x5, i, 3, cvmGet(L_6x10, i, 3));
+ cvmSet(&L_6x5, i, 4, cvmGet(L_6x10, i, 4));
+ }
+
+ cvSolve(&L_6x5, Rho, &B5, CV_SVD);
+
+ if (b5[0] < 0) {
+ betas[0] = sqrt(-b5[0]);
+ betas[1] = (b5[2] < 0) ? sqrt(-b5[2]) : 0.0;
+ } else {
+ betas[0] = sqrt(b5[0]);
+ betas[1] = (b5[2] > 0) ? sqrt(b5[2]) : 0.0;
+ }
+ if (b5[1] < 0) betas[0] = -betas[0];
+ betas[2] = b5[3] / betas[0];
+ betas[3] = 0.0;
+}
+
+void epnp::compute_L_6x10(const double * ut, double * l_6x10)
+{
+ const double * v[4];
+
+ v[0] = ut + 12 * 11;
+ v[1] = ut + 12 * 10;
+ v[2] = ut + 12 * 9;
+ v[3] = ut + 12 * 8;
+
+ double dv[4][6][3];
+
+ for(int i = 0; i < 4; i++) {
+ int a = 0, b = 1;
+ for(int j = 0; j < 6; j++) {
+ dv[i][j][0] = v[i][3 * a ] - v[i][3 * b];
+ dv[i][j][1] = v[i][3 * a + 1] - v[i][3 * b + 1];
+ dv[i][j][2] = v[i][3 * a + 2] - v[i][3 * b + 2];
+
+ b++;
+ if (b > 3) {
+ a++;
+ b = a + 1;
+ }
+ }
+ }
+
+ for(int i = 0; i < 6; i++) {
+ double * row = l_6x10 + 10 * i;
+
+ row[0] = dot(dv[0][i], dv[0][i]);
+ row[1] = 2.0f * dot(dv[0][i], dv[1][i]);
+ row[2] = dot(dv[1][i], dv[1][i]);
+ row[3] = 2.0f * dot(dv[0][i], dv[2][i]);
+ row[4] = 2.0f * dot(dv[1][i], dv[2][i]);
+ row[5] = dot(dv[2][i], dv[2][i]);
+ row[6] = 2.0f * dot(dv[0][i], dv[3][i]);
+ row[7] = 2.0f * dot(dv[1][i], dv[3][i]);
+ row[8] = 2.0f * dot(dv[2][i], dv[3][i]);
+ row[9] = dot(dv[3][i], dv[3][i]);
+ }
+}
+
+void epnp::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]);
+}
+
+void epnp::compute_A_and_b_gauss_newton(const double * l_6x10, const double * rho,
+ double betas[4], CvMat * A, CvMat * b)
+{
+ for(int i = 0; i < 6; i++) {
+ const double * rowL = l_6x10 + i * 10;
+ double * rowA = A->data.db + i * 4;
+
+ rowA[0] = 2 * rowL[0] * betas[0] + rowL[1] * betas[1] + rowL[3] * betas[2] + rowL[6] * betas[3];
+ rowA[1] = rowL[1] * betas[0] + 2 * rowL[2] * betas[1] + rowL[4] * betas[2] + rowL[7] * betas[3];
+ rowA[2] = rowL[3] * betas[0] + rowL[4] * betas[1] + 2 * rowL[5] * betas[2] + rowL[8] * betas[3];
+ rowA[3] = rowL[6] * betas[0] + rowL[7] * betas[1] + rowL[8] * betas[2] + 2 * rowL[9] * betas[3];
+
+ cvmSet(b, i, 0, rho[i] -
+ (
+ rowL[0] * betas[0] * betas[0] +
+ rowL[1] * betas[0] * betas[1] +
+ rowL[2] * betas[1] * betas[1] +
+ rowL[3] * betas[0] * betas[2] +
+ rowL[4] * betas[1] * betas[2] +
+ rowL[5] * betas[2] * betas[2] +
+ rowL[6] * betas[0] * betas[3] +
+ rowL[7] * betas[1] * betas[3] +
+ rowL[8] * betas[2] * betas[3] +
+ rowL[9] * betas[3] * betas[3]
+ ));
+ }
+}
+
+void epnp::gauss_newton(const CvMat * L_6x10, const CvMat * Rho,
+ double betas[4])
+{
+ const int iterations_number = 5;
+
+ double a[6*4], b[6], x[4];
+ CvMat A = cvMat(6, 4, CV_64F, a);
+ CvMat B = cvMat(6, 1, CV_64F, b);
+ CvMat X = cvMat(4, 1, CV_64F, x);
+
+ for(int k = 0; k < iterations_number; k++) {
+ compute_A_and_b_gauss_newton(L_6x10->data.db, Rho->data.db,
+ betas, &A, &B);
+ qr_solve(&A, &B, &X);
+
+ for(int i = 0; i < 4; i++)
+ betas[i] += x[i];
+ }
+}
+
+void epnp::qr_solve(CvMat * A, CvMat * b, CvMat * X)
+{
+ static int max_nr = 0;
+ static double * A1, * A2;
+
+ const int nr = A->rows;
+ const int nc = A->cols;
+
+ if (max_nr != 0 && max_nr < nr) {
+ delete [] A1;
+ delete [] A2;
+ }
+ if (max_nr < nr) {
+ max_nr = nr;
+ A1 = new double[nr];
+ A2 = new double[nr];
+ }
+
+ double * pA = A->data.db, * ppAkk = pA;
+ for(int k = 0; k < nc; k++) {
+ double * ppAik = ppAkk, eta = fabs(*ppAik);
+ for(int i = k + 1; i < nr; i++) {
+ double elt = fabs(*ppAik);
+ if (eta < elt) eta = elt;
+ ppAik += nc;
+ }
+
+ if (eta == 0) {
+ A1[k] = A2[k] = 0.0;
+ cerr << "God damnit, A is singular, this shouldn't happen." << endl;
+ return;
+ } else {
+ double * ppAik = ppAkk, sum = 0.0, inv_eta = 1. / eta;
+ for(int i = k; i < nr; i++) {
+ *ppAik *= inv_eta;
+ sum += *ppAik * *ppAik;
+ ppAik += nc;
+ }
+ double sigma = sqrt(sum);
+ 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;
+ }
+
+ // b <- Qt b
+ double * ppAjj = pA, * pb = b->data.db;
+ for(int j = 0; j < nc; j++) {
+ double * ppAij = ppAjj, tau = 0;
+ for(int i = j; i < nr; i++) {
+ tau += *ppAij * pb[i];
+ ppAij += nc;
+ }
+ tau /= A1[j];
+ ppAij = ppAjj;
+ for(int i = j; i < nr; i++) {
+ pb[i] -= tau * *ppAij;
+ ppAij += nc;
+ }
+ ppAjj += nc + 1;
+ }
+
+ // X = R-1 b
+ double * pX = X->data.db;
+ pX[nc - 1] = pb[nc - 1] / A2[nc - 1];
+ for(int i = nc - 2; i >= 0; i--) {
+ double * ppAij = pA + i * nc + (i + 1), sum = 0;
+
+ for(int j = i + 1; j < nc; j++) {
+ sum += *ppAij * pX[j];
+ ppAij++;
+ }
+ pX[i] = (pb[i] - sum) / A2[i];
+ }
+}
+
+
+
+void epnp::relative_error(double & rot_err, double & transl_err,
+ const double Rtrue[3][3], const double ttrue[3],
+ const double Rest[3][3], const double test[3])
+{
+ double qtrue[4], qest[4];
+
+ mat_to_quat(Rtrue, qtrue);
+ mat_to_quat(Rest, qest);
+
+ double rot_err1 = sqrt((qtrue[0] - qest[0]) * (qtrue[0] - qest[0]) +
+ (qtrue[1] - qest[1]) * (qtrue[1] - qest[1]) +
+ (qtrue[2] - qest[2]) * (qtrue[2] - qest[2]) +
+ (qtrue[3] - qest[3]) * (qtrue[3] - qest[3]) ) /
+ sqrt(qtrue[0] * qtrue[0] + qtrue[1] * qtrue[1] + qtrue[2] * qtrue[2] + qtrue[3] * qtrue[3]);
+
+ double rot_err2 = sqrt((qtrue[0] + qest[0]) * (qtrue[0] + qest[0]) +
+ (qtrue[1] + qest[1]) * (qtrue[1] + qest[1]) +
+ (qtrue[2] + qest[2]) * (qtrue[2] + qest[2]) +
+ (qtrue[3] + qest[3]) * (qtrue[3] + qest[3]) ) /
+ sqrt(qtrue[0] * qtrue[0] + qtrue[1] * qtrue[1] + qtrue[2] * qtrue[2] + qtrue[3] * qtrue[3]);
+
+ rot_err = min(rot_err1, rot_err2);
+
+ transl_err =
+ sqrt((ttrue[0] - test[0]) * (ttrue[0] - test[0]) +
+ (ttrue[1] - test[1]) * (ttrue[1] - test[1]) +
+ (ttrue[2] - test[2]) * (ttrue[2] - test[2])) /
+ sqrt(ttrue[0] * ttrue[0] + ttrue[1] * ttrue[1] + ttrue[2] * ttrue[2]);
+}
+
+void epnp::mat_to_quat(const double R[3][3], double q[4])
+{
+ double tr = R[0][0] + R[1][1] + R[2][2];
+ double n4;
+
+ if (tr > 0.0f) {
+ q[0] = R[1][2] - R[2][1];
+ q[1] = R[2][0] - R[0][2];
+ q[2] = R[0][1] - R[1][0];
+ q[3] = tr + 1.0f;
+ n4 = q[3];
+ } else if ( (R[0][0] > R[1][1]) && (R[0][0] > R[2][2]) ) {
+ q[0] = 1.0f + R[0][0] - R[1][1] - R[2][2];
+ q[1] = R[1][0] + R[0][1];
+ q[2] = R[2][0] + R[0][2];
+ q[3] = R[1][2] - R[2][1];
+ n4 = q[0];
+ } else if (R[1][1] > R[2][2]) {
+ q[0] = R[1][0] + R[0][1];
+ q[1] = 1.0f + R[1][1] - R[0][0] - R[2][2];
+ q[2] = R[2][1] + R[1][2];
+ q[3] = R[2][0] - R[0][2];
+ n4 = q[1];
+ } else {
+ q[0] = R[2][0] + R[0][2];
+ q[1] = R[2][1] + R[1][2];
+ q[2] = 1.0f + R[2][2] - R[0][0] - R[1][1];
+ q[3] = R[0][1] - R[1][0];
+ n4 = q[2];
+ }
+ double scale = 0.5f / double(sqrt(n4));
+
+ q[0] *= scale;
+ q[1] *= scale;
+ q[2] *= scale;
+ q[3] *= scale;
+}
diff --git a/modules/calib3d/src/epnp.h b/modules/calib3d/src/epnp.h
new file mode 100644
index 000000000..a7c8cfeee
--- /dev/null
+++ b/modules/calib3d/src/epnp.h
@@ -0,0 +1,73 @@
+#ifndef epnp_h
+#define epnp_h
+
+#include "precomp.hpp"
+
+class epnp {
+ public:
+ epnp(void);
+ ~epnp();
+
+ void set_internal_parameters(const double uc, const double vc,
+ const double fu, const double fv);
+
+ void set_maximum_number_of_correspondences(const int n);
+ void reset_correspondences(void);
+ void add_correspondence(const double X, const double Y, const double Z,
+ const double u, const double v);
+
+ double compute_pose(double R[3][3], double T[3]);
+
+ void relative_error(double & rot_err, double & transl_err,
+ const double Rtrue[3][3], const double ttrue[3],
+ const double Rest[3][3], const double test[3]);
+
+ void print_pose(const double R[3][3], const double t[3]);
+ double reprojection_error(const double R[3][3], const double t[3]);
+
+ private:
+ void choose_control_points(void);
+ void compute_barycentric_coordinates(void);
+ 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 * ut);
+ void compute_pcs(void);
+
+ void solve_for_sign(void);
+
+ void find_betas_approx_1(const CvMat * L_6x10, const CvMat * Rho, double * betas);
+ void find_betas_approx_2(const CvMat * L_6x10, const CvMat * Rho, double * betas);
+ void find_betas_approx_3(const CvMat * L_6x10, const CvMat * Rho, double * betas);
+ void qr_solve(CvMat * A, CvMat * b, CvMat * X);
+
+ double dot(const double * v1, const double * v2);
+ double dist2(const double * p1, const double * p2);
+
+ void compute_rho(double * rho);
+ void compute_L_6x10(const double * ut, double * l_6x10);
+
+ void gauss_newton(const CvMat * L_6x10, const CvMat * Rho, double current_betas[4]);
+ void compute_A_and_b_gauss_newton(const double * l_6x10, const double * rho,
+ double cb[4], CvMat * A, CvMat * b);
+
+ 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]);
+
+ void copy_R_and_t(const double R_dst[3][3], const double t_dst[3],
+ double R_src[3][3], double t_src[3]);
+
+ void mat_to_quat(const double R[3][3], double q[4]);
+
+
+ double uc, vc, fu, fv;
+
+ double * pws, * us, * alphas, * pcs;
+ int maximum_number_of_correspondences;
+ int number_of_correspondences;
+
+ double cws[4][3], ccs[4][3];
+ double cws_determinant;
+};
+
+#endif