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epnp.cpp
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3  | http://www.mrpt.org/ |
4  | |
5  | Copyright (c) 2005-2018, Individual contributors, see AUTHORS file |
6  | See: http://www.mrpt.org/Authors - All rights reserved. |
7  | Released under BSD License. See details in http://www.mrpt.org/License |
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9 
10 #include "vision-precomp.h" // Precompiled headers
11 #include <mrpt/config.h>
12 #include <iostream>
13 
14 // Opencv 2.3 had a broken <opencv/eigen.h> in Ubuntu 14.04 Trusty => Disable
15 // PNP classes
16 #include <mrpt/config.h>
17 #if MRPT_HAS_OPENCV && MRPT_OPENCV_VERSION_NUM < 0x240
18 #undef MRPT_HAS_OPENCV
19 #define MRPT_HAS_OPENCV 0
20 #endif
21 
22 #if MRPT_HAS_OPENCV
23 #include <mrpt/otherlibs/do_opencv_includes.h>
24 using namespace cv;
25 
26 #include "epnp.h"
27 
28 mrpt::vision::pnp::epnp::epnp(
29  const cv::Mat& cameraMatrix, const cv::Mat& opoints, const cv::Mat& ipoints)
30 {
31  if (cameraMatrix.depth() == CV_32F)
32  init_camera_parameters<float>(cameraMatrix);
33  else
34  init_camera_parameters<double>(cameraMatrix);
35 
36  number_of_correspondences = std::max(
37  opoints.checkVector(3, CV_32F), opoints.checkVector(3, CV_64F));
38 
39  pws.resize(3 * number_of_correspondences);
40  us.resize(2 * number_of_correspondences);
41 
42  if (opoints.depth() == ipoints.depth())
43  {
44  if (opoints.depth() == CV_32F)
45  init_points<float, float>(opoints, ipoints);
46  else
47  init_points<double, double>(opoints, ipoints);
48  }
49  else if (opoints.depth() == CV_32F)
50  init_points<float, double>(opoints, ipoints);
51  else
52  init_points<double, float>(opoints, ipoints);
53 
54  alphas.resize(4 * number_of_correspondences);
55  pcs.resize(3 * number_of_correspondences);
56 
57  max_nr = 0;
58  A1 = nullptr;
59  A2 = nullptr;
60 }
61 
62 mrpt::vision::pnp::epnp::~epnp()
63 {
64  if (A1) delete[] A1;
65  if (A2) delete[] A2;
66 }
67 
68 void mrpt::vision::pnp::epnp::choose_control_points(void)
69 {
70  // Take C0 as the reference points centroid:
71  cws[0][0] = cws[0][1] = cws[0][2] = 0;
72  for (int i = 0; i < number_of_correspondences; i++)
73  for (int j = 0; j < 3; j++) cws[0][j] += pws[3 * i + j];
74 
75  for (int j = 0; j < 3; j++) cws[0][j] /= number_of_correspondences;
76 
77  // Take C1, C2, and C3 from PCA on the reference points:
78  CvMat* PW0 = cvCreateMat(number_of_correspondences, 3, CV_64F);
79 
80  double pw0tpw0[3 * 3], dc[3], uct[3 * 3];
81  CvMat PW0tPW0 = cvMat(3, 3, CV_64F, pw0tpw0);
82  CvMat DC = cvMat(3, 1, CV_64F, dc);
83  CvMat UCt = cvMat(3, 3, CV_64F, uct);
84 
85  for (int i = 0; i < number_of_correspondences; i++)
86  for (int j = 0; j < 3; j++)
87  PW0->data.db[3 * i + j] = pws[3 * i + j] - cws[0][j];
88 
89  cvMulTransposed(PW0, &PW0tPW0, 1);
90  cvSVD(&PW0tPW0, &DC, &UCt, 0, CV_SVD_MODIFY_A | CV_SVD_U_T);
91 
92  cvReleaseMat(&PW0);
93 
94  for (int i = 1; i < 4; i++)
95  {
96  double k = sqrt(dc[i - 1] / number_of_correspondences);
97  for (int j = 0; j < 3; j++)
98  cws[i][j] = cws[0][j] + k * uct[3 * (i - 1) + j];
99  }
100 }
101 
102 void mrpt::vision::pnp::epnp::compute_barycentric_coordinates(void)
103 {
104  double cc[3 * 3], cc_inv[3 * 3];
105  CvMat CC = cvMat(3, 3, CV_64F, cc);
106  CvMat CC_inv = cvMat(3, 3, CV_64F, cc_inv);
107 
108  for (int i = 0; i < 3; i++)
109  for (int j = 1; j < 4; j++) cc[3 * i + j - 1] = cws[j][i] - cws[0][i];
110 
111  cvInvert(&CC, &CC_inv, CV_SVD);
112  double* ci = cc_inv;
113  for (int i = 0; i < number_of_correspondences; i++)
114  {
115  double* pi = &pws[0] + 3 * i;
116  double* a = &alphas[0] + 4 * i;
117 
118  for (int j = 0; j < 3; j++)
119  a[1 + j] = ci[3 * j] * (pi[0] - cws[0][0]) +
120  ci[3 * j + 1] * (pi[1] - cws[0][1]) +
121  ci[3 * j + 2] * (pi[2] - cws[0][2]);
122  a[0] = 1.0f - a[1] - a[2] - a[3];
123  }
124 }
125 
126 void mrpt::vision::pnp::epnp::fill_M(
127  CvMat* M, const int row, const double* as, const double u, const double v)
128 {
129  double* M1 = M->data.db + row * 12;
130  double* M2 = M1 + 12;
131 
132  for (int i = 0; i < 4; i++)
133  {
134  M1[3 * i] = as[i] * fu;
135  M1[3 * i + 1] = 0.0;
136  M1[3 * i + 2] = as[i] * (uc - u);
137 
138  M2[3 * i] = 0.0;
139  M2[3 * i + 1] = as[i] * fv;
140  M2[3 * i + 2] = as[i] * (vc - v);
141  }
142 }
143 
144 void mrpt::vision::pnp::epnp::compute_ccs(const double* betas, const double* ut)
145 {
146  for (int i = 0; i < 4; i++) ccs[i][0] = ccs[i][1] = ccs[i][2] = 0.0f;
147 
148  for (int i = 0; i < 4; i++)
149  {
150  const double* v = ut + 12 * (11 - i);
151  for (int j = 0; j < 4; j++)
152  for (int k = 0; k < 3; k++) ccs[j][k] += betas[i] * v[3 * j + k];
153  }
154 }
155 
156 void mrpt::vision::pnp::epnp::compute_pcs(void)
157 {
158  for (int i = 0; i < number_of_correspondences; i++)
159  {
160  double* a = &alphas[0] + 4 * i;
161  double* pc = &pcs[0] + 3 * i;
162 
163  for (int j = 0; j < 3; j++)
164  pc[j] = a[0] * ccs[0][j] + a[1] * ccs[1][j] + a[2] * ccs[2][j] +
165  a[3] * ccs[3][j];
166  }
167 }
168 
169 void mrpt::vision::pnp::epnp::compute_pose(cv::Mat& R, cv::Mat& t)
170 {
171  choose_control_points();
172  compute_barycentric_coordinates();
173 
174  CvMat* M = cvCreateMat(2 * number_of_correspondences, 12, CV_64F);
175 
176  for (int i = 0; i < number_of_correspondences; i++)
177  fill_M(M, 2 * i, &alphas[0] + 4 * i, us[2 * i], us[2 * i + 1]);
178 
179  double mtm[12 * 12], d[12], ut[12 * 12];
180  CvMat MtM = cvMat(12, 12, CV_64F, mtm);
181  CvMat D = cvMat(12, 1, CV_64F, d);
182  CvMat Ut = cvMat(12, 12, CV_64F, ut);
183 
184  cvMulTransposed(M, &MtM, 1);
185  cvSVD(&MtM, &D, &Ut, 0, CV_SVD_MODIFY_A | CV_SVD_U_T);
186  cvReleaseMat(&M);
187 
188  double l_6x10[6 * 10], rho[6];
189  CvMat L_6x10 = cvMat(6, 10, CV_64F, l_6x10);
190  CvMat Rho = cvMat(6, 1, CV_64F, rho);
191 
192  compute_L_6x10(ut, l_6x10);
193  compute_rho(rho);
194 
195  double Betas[4][4], rep_errors[4];
196  double Rs[4][3][3], ts[4][3];
197 
198  find_betas_approx_1(&L_6x10, &Rho, Betas[1]);
199  gauss_newton(&L_6x10, &Rho, Betas[1]);
200  rep_errors[1] = compute_R_and_t(ut, Betas[1], Rs[1], ts[1]);
201 
202  find_betas_approx_2(&L_6x10, &Rho, Betas[2]);
203  gauss_newton(&L_6x10, &Rho, Betas[2]);
204  rep_errors[2] = compute_R_and_t(ut, Betas[2], Rs[2], ts[2]);
205 
206  find_betas_approx_3(&L_6x10, &Rho, Betas[3]);
207  gauss_newton(&L_6x10, &Rho, Betas[3]);
208  rep_errors[3] = compute_R_and_t(ut, Betas[3], Rs[3], ts[3]);
209 
210  int N = 1;
211  if (rep_errors[2] < rep_errors[1]) N = 2;
212  if (rep_errors[3] < rep_errors[N]) N = 3;
213 
214  cv::Mat(3, 1, CV_64F, ts[N]).copyTo(t);
215  cv::Mat(3, 3, CV_64F, Rs[N]).copyTo(R);
216 }
217 
218 void mrpt::vision::pnp::epnp::copy_R_and_t(
219  const double R_src[3][3], const double t_src[3], double R_dst[3][3],
220  double t_dst[3])
221 {
222  for (int i = 0; i < 3; i++)
223  {
224  for (int j = 0; j < 3; j++) R_dst[i][j] = R_src[i][j];
225  t_dst[i] = t_src[i];
226  }
227 }
228 
229 double mrpt::vision::pnp::epnp::dist2(const double* p1, const double* p2)
230 {
231  return (p1[0] - p2[0]) * (p1[0] - p2[0]) +
232  (p1[1] - p2[1]) * (p1[1] - p2[1]) +
233  (p1[2] - p2[2]) * (p1[2] - p2[2]);
234 }
235 
236 double mrpt::vision::pnp::epnp::dot(const double* v1, const double* v2)
237 {
238  return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
239 }
240 
241 void mrpt::vision::pnp::epnp::estimate_R_and_t(double R[3][3], double t[3])
242 {
243  double pc0[3], pw0[3];
244 
245  pc0[0] = pc0[1] = pc0[2] = 0.0;
246  pw0[0] = pw0[1] = pw0[2] = 0.0;
247 
248  for (int i = 0; i < number_of_correspondences; i++)
249  {
250  const double* pc = &pcs[3 * i];
251  const double* pw = &pws[3 * i];
252 
253  for (int j = 0; j < 3; j++)
254  {
255  pc0[j] += pc[j];
256  pw0[j] += pw[j];
257  }
258  }
259  for (int j = 0; j < 3; j++)
260  {
261  pc0[j] /= number_of_correspondences;
262  pw0[j] /= number_of_correspondences;
263  }
264 
265  double abt[3 * 3], abt_d[3], abt_u[3 * 3], abt_v[3 * 3];
266  CvMat ABt = cvMat(3, 3, CV_64F, abt);
267  CvMat ABt_D = cvMat(3, 1, CV_64F, abt_d);
268  CvMat ABt_U = cvMat(3, 3, CV_64F, abt_u);
269  CvMat ABt_V = cvMat(3, 3, CV_64F, abt_v);
270 
271  cvSetZero(&ABt);
272  for (int i = 0; i < number_of_correspondences; i++)
273  {
274  double* pc = &pcs[3 * i];
275  double* pw = &pws[3 * i];
276 
277  for (int j = 0; j < 3; j++)
278  {
279  abt[3 * j] += (pc[j] - pc0[j]) * (pw[0] - pw0[0]);
280  abt[3 * j + 1] += (pc[j] - pc0[j]) * (pw[1] - pw0[1]);
281  abt[3 * j + 2] += (pc[j] - pc0[j]) * (pw[2] - pw0[2]);
282  }
283  }
284 
285  cvSVD(&ABt, &ABt_D, &ABt_U, &ABt_V, CV_SVD_MODIFY_A);
286 
287  for (int i = 0; i < 3; i++)
288  for (int j = 0; j < 3; j++) R[i][j] = dot(abt_u + 3 * i, abt_v + 3 * j);
289 
290  const double det =
291  R[0][0] * R[1][1] * R[2][2] + R[0][1] * R[1][2] * R[2][0] +
292  R[0][2] * R[1][0] * R[2][1] - R[0][2] * R[1][1] * R[2][0] -
293  R[0][1] * R[1][0] * R[2][2] - R[0][0] * R[1][2] * R[2][1];
294 
295  if (det < 0)
296  {
297  R[2][0] = -R[2][0];
298  R[2][1] = -R[2][1];
299  R[2][2] = -R[2][2];
300  }
301 
302  t[0] = pc0[0] - dot(R[0], pw0);
303  t[1] = pc0[1] - dot(R[1], pw0);
304  t[2] = pc0[2] - dot(R[2], pw0);
305 }
306 
307 void mrpt::vision::pnp::epnp::solve_for_sign(void)
308 {
309  if (pcs[2] < 0.0)
310  {
311  for (int i = 0; i < 4; i++)
312  for (int j = 0; j < 3; j++) ccs[i][j] = -ccs[i][j];
313 
314  for (int i = 0; i < number_of_correspondences; i++)
315  {
316  pcs[3 * i] = -pcs[3 * i];
317  pcs[3 * i + 1] = -pcs[3 * i + 1];
318  pcs[3 * i + 2] = -pcs[3 * i + 2];
319  }
320  }
321 }
322 
323 double mrpt::vision::pnp::epnp::compute_R_and_t(
324  const double* ut, const double* betas, double R[3][3], double t[3])
325 {
326  compute_ccs(betas, ut);
327  compute_pcs();
328 
329  solve_for_sign();
330 
331  estimate_R_and_t(R, t);
332 
333  return reprojection_error(R, t);
334 }
335 
336 double mrpt::vision::pnp::epnp::reprojection_error(
337  const double R[3][3], const double t[3])
338 {
339  double sum2 = 0.0;
340 
341  for (int i = 0; i < number_of_correspondences; i++)
342  {
343  double* pw = &pws[3 * i];
344  double Xc = dot(R[0], pw) + t[0];
345  double Yc = dot(R[1], pw) + t[1];
346  double inv_Zc = 1.0 / (dot(R[2], pw) + t[2]);
347  double ue = uc + fu * Xc * inv_Zc;
348  double ve = vc + fv * Yc * inv_Zc;
349  double u = us[2 * i], v = us[2 * i + 1];
350 
351  sum2 += sqrt((u - ue) * (u - ue) + (v - ve) * (v - ve));
352  }
353 
354  return sum2 / number_of_correspondences;
355 }
356 
357 // betas10 = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44]
358 // betas_approx_1 = [B11 B12 B13 B14]
359 
360 void mrpt::vision::pnp::epnp::find_betas_approx_1(
361  const CvMat* L_6x10, const CvMat* Rho, double* betas)
362 {
363  double l_6x4[6 * 4], b4[4];
364  CvMat L_6x4 = cvMat(6, 4, CV_64F, l_6x4);
365  CvMat B4 = cvMat(4, 1, CV_64F, b4);
366 
367  for (int i = 0; i < 6; i++)
368  {
369  cvmSet(&L_6x4, i, 0, cvmGet(L_6x10, i, 0));
370  cvmSet(&L_6x4, i, 1, cvmGet(L_6x10, i, 1));
371  cvmSet(&L_6x4, i, 2, cvmGet(L_6x10, i, 3));
372  cvmSet(&L_6x4, i, 3, cvmGet(L_6x10, i, 6));
373  }
374 
375  cvSolve(&L_6x4, Rho, &B4, CV_SVD);
376 
377  if (b4[0] < 0)
378  {
379  betas[0] = sqrt(-b4[0]);
380  betas[1] = -b4[1] / betas[0];
381  betas[2] = -b4[2] / betas[0];
382  betas[3] = -b4[3] / betas[0];
383  }
384  else
385  {
386  betas[0] = sqrt(b4[0]);
387  betas[1] = b4[1] / betas[0];
388  betas[2] = b4[2] / betas[0];
389  betas[3] = b4[3] / betas[0];
390  }
391 }
392 
393 // betas10 = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44]
394 // betas_approx_2 = [B11 B12 B22 ]
395 
396 void mrpt::vision::pnp::epnp::find_betas_approx_2(
397  const CvMat* L_6x10, const CvMat* Rho, double* betas)
398 {
399  double l_6x3[6 * 3], b3[3];
400  CvMat L_6x3 = cvMat(6, 3, CV_64F, l_6x3);
401  CvMat B3 = cvMat(3, 1, CV_64F, b3);
402 
403  for (int i = 0; i < 6; i++)
404  {
405  cvmSet(&L_6x3, i, 0, cvmGet(L_6x10, i, 0));
406  cvmSet(&L_6x3, i, 1, cvmGet(L_6x10, i, 1));
407  cvmSet(&L_6x3, i, 2, cvmGet(L_6x10, i, 2));
408  }
409 
410  cvSolve(&L_6x3, Rho, &B3, CV_SVD);
411 
412  if (b3[0] < 0)
413  {
414  betas[0] = sqrt(-b3[0]);
415  betas[1] = (b3[2] < 0) ? sqrt(-b3[2]) : 0.0;
416  }
417  else
418  {
419  betas[0] = sqrt(b3[0]);
420  betas[1] = (b3[2] > 0) ? sqrt(b3[2]) : 0.0;
421  }
422 
423  if (b3[1] < 0) betas[0] = -betas[0];
424 
425  betas[2] = 0.0;
426  betas[3] = 0.0;
427 }
428 
429 // betas10 = [B11 B12 B22 B13 B23 B33 B14 B24 B34 B44]
430 // betas_approx_3 = [B11 B12 B22 B13 B23 ]
431 
432 void mrpt::vision::pnp::epnp::find_betas_approx_3(
433  const CvMat* L_6x10, const CvMat* Rho, double* betas)
434 {
435  double l_6x5[6 * 5], b5[5];
436  CvMat L_6x5 = cvMat(6, 5, CV_64F, l_6x5);
437  CvMat B5 = cvMat(5, 1, CV_64F, b5);
438 
439  for (int i = 0; i < 6; i++)
440  {
441  cvmSet(&L_6x5, i, 0, cvmGet(L_6x10, i, 0));
442  cvmSet(&L_6x5, i, 1, cvmGet(L_6x10, i, 1));
443  cvmSet(&L_6x5, i, 2, cvmGet(L_6x10, i, 2));
444  cvmSet(&L_6x5, i, 3, cvmGet(L_6x10, i, 3));
445  cvmSet(&L_6x5, i, 4, cvmGet(L_6x10, i, 4));
446  }
447 
448  cvSolve(&L_6x5, Rho, &B5, CV_SVD);
449 
450  if (b5[0] < 0)
451  {
452  betas[0] = sqrt(-b5[0]);
453  betas[1] = (b5[2] < 0) ? sqrt(-b5[2]) : 0.0;
454  }
455  else
456  {
457  betas[0] = sqrt(b5[0]);
458  betas[1] = (b5[2] > 0) ? sqrt(b5[2]) : 0.0;
459  }
460  if (b5[1] < 0) betas[0] = -betas[0];
461  betas[2] = b5[3] / betas[0];
462  betas[3] = 0.0;
463 }
464 
465 void mrpt::vision::pnp::epnp::compute_L_6x10(const double* ut, double* l_6x10)
466 {
467  const double* v[4];
468 
469  v[0] = ut + 12 * 11;
470  v[1] = ut + 12 * 10;
471  v[2] = ut + 12 * 9;
472  v[3] = ut + 12 * 8;
473 
474  double dv[4][6][3];
475 
476  for (int i = 0; i < 4; i++)
477  {
478  int a = 0, b = 1;
479  for (int j = 0; j < 6; j++)
480  {
481  dv[i][j][0] = v[i][3 * a] - v[i][3 * b];
482  dv[i][j][1] = v[i][3 * a + 1] - v[i][3 * b + 1];
483  dv[i][j][2] = v[i][3 * a + 2] - v[i][3 * b + 2];
484 
485  b++;
486  if (b > 3)
487  {
488  a++;
489  b = a + 1;
490  }
491  }
492  }
493 
494  for (int i = 0; i < 6; i++)
495  {
496  double* row = l_6x10 + 10 * i;
497 
498  row[0] = dot(dv[0][i], dv[0][i]);
499  row[1] = 2.0f * dot(dv[0][i], dv[1][i]);
500  row[2] = dot(dv[1][i], dv[1][i]);
501  row[3] = 2.0f * dot(dv[0][i], dv[2][i]);
502  row[4] = 2.0f * dot(dv[1][i], dv[2][i]);
503  row[5] = dot(dv[2][i], dv[2][i]);
504  row[6] = 2.0f * dot(dv[0][i], dv[3][i]);
505  row[7] = 2.0f * dot(dv[1][i], dv[3][i]);
506  row[8] = 2.0f * dot(dv[2][i], dv[3][i]);
507  row[9] = dot(dv[3][i], dv[3][i]);
508  }
509 }
510 
511 void mrpt::vision::pnp::epnp::compute_rho(double* rho)
512 {
513  rho[0] = dist2(cws[0], cws[1]);
514  rho[1] = dist2(cws[0], cws[2]);
515  rho[2] = dist2(cws[0], cws[3]);
516  rho[3] = dist2(cws[1], cws[2]);
517  rho[4] = dist2(cws[1], cws[3]);
518  rho[5] = dist2(cws[2], cws[3]);
519 }
520 
521 void mrpt::vision::pnp::epnp::compute_A_and_b_gauss_newton(
522  const double* l_6x10, const double* rho, const double betas[4], CvMat* A,
523  CvMat* b)
524 {
525  for (int i = 0; i < 6; i++)
526  {
527  const double* rowL = l_6x10 + i * 10;
528  double* rowA = A->data.db + i * 4;
529 
530  rowA[0] = 2 * rowL[0] * betas[0] + rowL[1] * betas[1] +
531  rowL[3] * betas[2] + rowL[6] * betas[3];
532  rowA[1] = rowL[1] * betas[0] + 2 * rowL[2] * betas[1] +
533  rowL[4] * betas[2] + rowL[7] * betas[3];
534  rowA[2] = rowL[3] * betas[0] + rowL[4] * betas[1] +
535  2 * rowL[5] * betas[2] + rowL[8] * betas[3];
536  rowA[3] = rowL[6] * betas[0] + rowL[7] * betas[1] + rowL[8] * betas[2] +
537  2 * rowL[9] * betas[3];
538 
539  cvmSet(
540  b, i, 0,
541  rho[i] -
542  (rowL[0] * betas[0] * betas[0] + rowL[1] * betas[0] * betas[1] +
543  rowL[2] * betas[1] * betas[1] + rowL[3] * betas[0] * betas[2] +
544  rowL[4] * betas[1] * betas[2] + rowL[5] * betas[2] * betas[2] +
545  rowL[6] * betas[0] * betas[3] + rowL[7] * betas[1] * betas[3] +
546  rowL[8] * betas[2] * betas[3] +
547  rowL[9] * betas[3] * betas[3]));
548  }
549 }
550 
551 void mrpt::vision::pnp::epnp::gauss_newton(
552  const CvMat* L_6x10, const CvMat* Rho, double betas[4])
553 {
554  const int iterations_number = 5;
555 
556  double a[6 * 4], b[6], x[4];
557  CvMat A = cvMat(6, 4, CV_64F, a);
558  CvMat B = cvMat(6, 1, CV_64F, b);
559  CvMat X = cvMat(4, 1, CV_64F, x);
560 
561  for (int k = 0; k < iterations_number; k++)
562  {
563  compute_A_and_b_gauss_newton(
564  L_6x10->data.db, Rho->data.db, betas, &A, &B);
565  qr_solve(&A, &B, &X);
566  for (int i = 0; i < 4; i++) betas[i] += x[i];
567  }
568 }
569 
570 void mrpt::vision::pnp::epnp::qr_solve(CvMat* A, CvMat* b, CvMat* X)
571 {
572  const int nr = A->rows;
573  const int nc = A->cols;
574 
575  if (max_nr != 0 && max_nr < nr)
576  {
577  delete[] A1;
578  delete[] A2;
579  }
580  if (max_nr < nr)
581  {
582  max_nr = nr;
583  A1 = new double[nr];
584  A2 = new double[nr];
585  }
586 
587  double *pA = A->data.db, *ppAkk = pA;
588  for (int k = 0; k < nc; k++)
589  {
590  double *ppAik1 = ppAkk, eta = fabs(*ppAik1);
591  for (int i = k + 1; i < nr; i++)
592  {
593  double elt = fabs(*ppAik1);
594  if (eta < elt) eta = elt;
595  ppAik1 += nc;
596  }
597  if (eta == 0)
598  {
599  A1[k] = A2[k] = 0.0;
600  // cerr << "God damnit, A is singular, this shouldn't happen." <<
601  // endl;
602  return;
603  }
604  else
605  {
606  double *ppAik2 = ppAkk, sum2 = 0.0, inv_eta = 1. / eta;
607  for (int i = k; i < nr; i++)
608  {
609  *ppAik2 *= inv_eta;
610  sum2 += *ppAik2 * *ppAik2;
611  ppAik2 += nc;
612  }
613  double sigma = sqrt(sum2);
614  if (*ppAkk < 0) sigma = -sigma;
615  *ppAkk += sigma;
616  A1[k] = sigma * *ppAkk;
617  A2[k] = -eta * sigma;
618  for (int j = k + 1; j < nc; j++)
619  {
620  double *ppAik = ppAkk, sum = 0;
621  for (int i = k; i < nr; i++)
622  {
623  sum += *ppAik * ppAik[j - k];
624  ppAik += nc;
625  }
626  double tau = sum / A1[k];
627  ppAik = ppAkk;
628  for (int i = k; i < nr; i++)
629  {
630  ppAik[j - k] -= tau * *ppAik;
631  ppAik += nc;
632  }
633  }
634  }
635  ppAkk += nc + 1;
636  }
637 
638  // b <- Qt b
639  double *ppAjj = pA, *pb = b->data.db;
640  for (int j = 0; j < nc; j++)
641  {
642  double *ppAij = ppAjj, tau = 0;
643  for (int i = j; i < nr; i++)
644  {
645  tau += *ppAij * pb[i];
646  ppAij += nc;
647  }
648  tau /= A1[j];
649  ppAij = ppAjj;
650  for (int i = j; i < nr; i++)
651  {
652  pb[i] -= tau * *ppAij;
653  ppAij += nc;
654  }
655  ppAjj += nc + 1;
656  }
657 
658  // X = R-1 b
659  double* pX = X->data.db;
660  pX[nc - 1] = pb[nc - 1] / A2[nc - 1];
661  for (int i = nc - 2; i >= 0; i--)
662  {
663  double *ppAij = pA + i * nc + (i + 1), sum = 0;
664 
665  for (int j = i + 1; j < nc; j++)
666  {
667  sum += *ppAij * pX[j];
668  ppAij++;
669  }
670  pX[i] = (pb[i] - sum) / A2[i];
671  }
672 }
673 #endif
mrpt::vision::pnp::epnp::compute_pcs
void compute_pcs(void)
Internal function.
mrpt::math::sum
CONTAINER::Scalar sum(const CONTAINER &v)
Computes the sum of all the elements.
Definition: ops_containers.h:211
mrpt::vision::pnp::epnp::find_betas_approx_1
void find_betas_approx_1(const CvMat *L_6x10, const CvMat *Rho, double *betas)
Internal function.
mrpt::vision::pnp::epnp::copy_R_and_t
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])
Copy function of output result.
epnp.h
Efficient PnP - Eigen Wrapper for OpenCV calib3d implementation.
mrpt::vision::pnp::epnp::choose_control_points
void choose_control_points(void)
Function to select 4 control points from n points.
mrpt::vision::pnp::epnp::compute_rho
void compute_rho(double *rho)
Get distances between all object points taken 2 at a time(nC2)
mrpt::vision::pnp::epnp::compute_barycentric_coordinates
void compute_barycentric_coordinates(void)
Convert from object space to relative object space (Barycentric coordinates)
t
GLdouble GLdouble t
Definition: glext.h:3689
mrpt::vision::pnp::epnp::compute_A_and_b_gauss_newton
void compute_A_and_b_gauss_newton(const double *l_6x10, const double *rho, const double cb[4], CvMat *A, CvMat *b)
Internal function.
mrpt::vision::pnp::epnp::solve_for_sign
void solve_for_sign(void)
Internal function.
mrpt::vision::pnp::epnp::qr_solve
void qr_solve(CvMat *A, CvMat *b, CvMat *X)
QR optimization algorithm.
R
const float R
Definition: CKinematicChain.cpp:138
mrpt::vision::pnp::epnp::find_betas_approx_2
void find_betas_approx_2(const CvMat *L_6x10, const CvMat *Rho, double *betas)
Internal function.
vision-precomp.h
mrpt::vision::pnp::epnp::fill_M
void fill_M(CvMat *M, const int row, const double *alphas, const double u, const double v)
Generate the Matrix M.
mrpt::vision::pnp::epnp::compute_L_6x10
void compute_L_6x10(const double *ut, double *l_6x10)
Internal function.
mrpt::vision::pnp::epnp::compute_pose
void compute_pose(cv::Mat &R, cv::Mat &t)
OpenCV wrapper to compute pose.
mrpt::vision::pnp::epnp::~epnp
~epnp()
Destructor for EPnP class.
v
const GLdouble * v
Definition: glext.h:3678
v1
GLfloat GLfloat v1
Definition: glext.h:4105
mrpt::vision::pnp::epnp::dist2
double dist2(const double *p1, const double *p2)
Squared distance between two vectors.
v2
GLfloat GLfloat GLfloat v2
Definition: glext.h:4107
b
GLubyte GLubyte b
Definition: glext.h:6279
mrpt::vision::pnp::epnp::dot
double dot(const double *v1, const double *v2)
Dot product of two OpenCV vectors.
mrpt::vision::pnp::epnp::compute_ccs
void compute_ccs(const double *betas, const double *ut)
Internal function.
mrpt::vision::pnp::epnp::reprojection_error
double reprojection_error(const double R[3][3], const double t[3])
Function to compute reprojection error.
mrpt::vision::pnp::epnp::estimate_R_and_t
void estimate_R_and_t(double R[3][3], double t[3])
Helper function to @func compute_R_and_t()
row
GLenum GLenum GLvoid * row
Definition: glext.h:3576
mrpt::vision::pnp::epnp::find_betas_approx_3
void find_betas_approx_3(const CvMat *L_6x10, const CvMat *Rho, double *betas)
Internal function.
mrpt::obs::gnss::A1
double A1
Definition: gnss_messages_novatel.h:461
mrpt::obs::gnss::b3
double b3
Definition: gnss_messages_novatel.h:455
mrpt::vision::pnp::epnp::compute_R_and_t
double compute_R_and_t(const double *ut, const double *betas, double R[3][3], double t[3])
Function to compute pose.
cv
Definition: checkerboard_cam_calib.cpp:57
det
EIGEN_STRONG_INLINE Scalar det() const
Definition: eigen_plugins.h:595
mrpt::vision::pnp::epnp::gauss_newton
void gauss_newton(const CvMat *L_6x10, const CvMat *Rho, double current_betas[4])
Gauss Newton iterative algorithm.
mrpt::vision::pnp::epnp::epnp
epnp(const cv::Mat &cameraMatrix, const cv::Mat &opoints, const cv::Mat &ipoints)
Constructor for EPnP class.
x
GLenum GLint x
Definition: glext.h:3538
a
GLubyte GLubyte GLubyte a
Definition: glext.h:6279


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