first version of ePnP code

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());

modules/calib3d/src/epnp.cpp

+#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;
+}

modules/calib3d/src/epnp.h

+#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