Point Cloud Library (PCL)  1.12.0
rops_estimation.hpp
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39 
40 #ifndef PCL_ROPS_ESTIMATION_HPP_
41 #define PCL_ROPS_ESTIMATION_HPP_
42 
43 #include <pcl/features/rops_estimation.h>
44 
45 #include <array>
46 #include <numeric> // for accumulate
47 #include <Eigen/Eigenvalues> // for EigenSolver
48 
49 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
50 template <typename PointInT, typename PointOutT>
52  number_of_bins_ (5),
53  number_of_rotations_ (3),
54  support_radius_ (1.0f),
55  sqr_support_radius_ (1.0f),
56  step_ (22.5f),
57  triangles_ (0),
58  triangles_of_the_point_ (0)
59 {
60 }
61 
62 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
63 template <typename PointInT, typename PointOutT>
65 {
66  triangles_.clear ();
67  triangles_of_the_point_.clear ();
68 }
69 
70 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
71 template <typename PointInT, typename PointOutT> void
73 {
74  if (number_of_bins != 0)
75  number_of_bins_ = number_of_bins;
76 }
77 
78 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
79 template <typename PointInT, typename PointOutT> unsigned int
81 {
82  return (number_of_bins_);
83 }
84 
85 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
86 template <typename PointInT, typename PointOutT> void
88 {
89  if (number_of_rotations != 0)
90  {
91  number_of_rotations_ = number_of_rotations;
92  step_ = 90.0f / static_cast <float> (number_of_rotations_ + 1);
93  }
94 }
95 
96 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
97 template <typename PointInT, typename PointOutT> unsigned int
99 {
100  return (number_of_rotations_);
101 }
102 
103 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
104 template <typename PointInT, typename PointOutT> void
106 {
107  if (support_radius > 0.0f)
108  {
109  support_radius_ = support_radius;
110  sqr_support_radius_ = support_radius * support_radius;
111  }
112 }
113 
114 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
115 template <typename PointInT, typename PointOutT> float
117 {
118  return (support_radius_);
119 }
120 
121 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
122 template <typename PointInT, typename PointOutT> void
123 pcl::ROPSEstimation <PointInT, PointOutT>::setTriangles (const std::vector <pcl::Vertices>& triangles)
124 {
125  triangles_ = triangles;
126 }
127 
128 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
129 template <typename PointInT, typename PointOutT> void
130 pcl::ROPSEstimation <PointInT, PointOutT>::getTriangles (std::vector <pcl::Vertices>& triangles) const
131 {
132  triangles = triangles_;
133 }
134 
135 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
136 template <typename PointInT, typename PointOutT> void
138 {
139  if (triangles_.empty ())
140  {
141  output.clear ();
142  return;
143  }
144 
145  buildListOfPointsTriangles ();
146 
147  //feature size = number_of_rotations * number_of_axis_to_rotate_around * number_of_projections * number_of_central_moments
148  unsigned int feature_size = number_of_rotations_ * 3 * 3 * 5;
149  const auto number_of_points = indices_->size ();
150  output.clear ();
151  output.reserve (number_of_points);
152 
153  for (const auto& idx: *indices_)
154  {
155  std::set <unsigned int> local_triangles;
156  pcl::Indices local_points;
157  getLocalSurface ((*input_)[idx], local_triangles, local_points);
158 
159  Eigen::Matrix3f lrf_matrix;
160  computeLRF ((*input_)[idx], local_triangles, lrf_matrix);
161 
162  PointCloudIn transformed_cloud;
163  transformCloud ((*input_)[idx], lrf_matrix, local_points, transformed_cloud);
164 
165  std::array<PointInT, 3> axes;
166  axes[0].x = 1.0f; axes[0].y = 0.0f; axes[0].z = 0.0f;
167  axes[1].x = 0.0f; axes[1].y = 1.0f; axes[1].z = 0.0f;
168  axes[2].x = 0.0f; axes[2].y = 0.0f; axes[2].z = 1.0f;
169  std::vector <float> feature;
170  for (const auto &axis : axes)
171  {
172  float theta = step_;
173  do
174  {
175  //rotate local surface and get bounding box
176  PointCloudIn rotated_cloud;
177  Eigen::Vector3f min, max;
178  rotateCloud (axis, theta, transformed_cloud, rotated_cloud, min, max);
179 
180  //for each projection (XY, XZ and YZ) compute distribution matrix and central moments
181  for (unsigned int i_proj = 0; i_proj < 3; i_proj++)
182  {
183  Eigen::MatrixXf distribution_matrix;
184  distribution_matrix.resize (number_of_bins_, number_of_bins_);
185  getDistributionMatrix (i_proj, min, max, rotated_cloud, distribution_matrix);
186 
187  // TODO remove this needless copy due to API design
188  std::vector <float> moments;
189  computeCentralMoments (distribution_matrix, moments);
190 
191  feature.insert (feature.end (), moments.begin (), moments.end ());
192  }
193 
194  theta += step_;
195  } while (theta < 90.0f);
196  }
197 
198  const float norm = std::accumulate(
199  feature.cbegin(), feature.cend(), 0.f, [](const auto& sum, const auto& val) {
200  return sum + std::abs(val);
201  });
202  float invert_norm;
203  if (norm < std::numeric_limits <float>::epsilon ())
204  invert_norm = 1.0f;
205  else
206  invert_norm = 1.0f / norm;
207 
208  output.emplace_back ();
209  for (std::size_t i_dim = 0; i_dim < feature_size; i_dim++)
210  output.back().histogram[i_dim] = feature[i_dim] * invert_norm;
211  }
212 }
213 
214 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
215 template <typename PointInT, typename PointOutT> void
217 {
218  triangles_of_the_point_.clear ();
219 
220  std::vector <unsigned int> dummy;
221  dummy.reserve (100);
222  triangles_of_the_point_.resize (surface_->points. size (), dummy);
223 
224  for (std::size_t i_triangle = 0; i_triangle < triangles_.size (); i_triangle++)
225  for (const auto& vertex: triangles_[i_triangle].vertices)
226  triangles_of_the_point_[vertex].push_back (i_triangle);
227 }
228 
229 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
230 template <typename PointInT, typename PointOutT> void
231 pcl::ROPSEstimation <PointInT, PointOutT>::getLocalSurface (const PointInT& point, std::set <unsigned int>& local_triangles, pcl::Indices& local_points) const
232 {
233  std::vector <float> distances;
234  tree_->radiusSearch (point, support_radius_, local_points, distances);
235 
236  for (const auto& pt: local_points)
237  local_triangles.insert (triangles_of_the_point_[pt].begin (),
238  triangles_of_the_point_[pt].end ());
239 }
240 
241 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
242 template <typename PointInT, typename PointOutT> void
243 pcl::ROPSEstimation <PointInT, PointOutT>::computeLRF (const PointInT& point, const std::set <unsigned int>& local_triangles, Eigen::Matrix3f& lrf_matrix) const
244 {
245  std::size_t number_of_triangles = local_triangles.size ();
246 
247  std::vector<Eigen::Matrix3f, Eigen::aligned_allocator<Eigen::Matrix3f> > scatter_matrices;
248  std::vector <float> triangle_area (number_of_triangles), distance_weight (number_of_triangles);
249 
250  scatter_matrices.reserve (number_of_triangles);
251  triangle_area.clear ();
252  distance_weight.clear ();
253 
254  float total_area = 0.0f;
255  const float coeff = 1.0f / 12.0f;
256  const float coeff_1_div_3 = 1.0f / 3.0f;
257 
258  Eigen::Vector3f feature_point (point.x, point.y, point.z);
259 
260  for (const auto& triangle: local_triangles)
261  {
262  Eigen::Vector3f pt[3];
263  for (unsigned int i_vertex = 0; i_vertex < 3; i_vertex++)
264  {
265  const unsigned int index = triangles_[triangle].vertices[i_vertex];
266  pt[i_vertex] (0) = (*surface_)[index].x;
267  pt[i_vertex] (1) = (*surface_)[index].y;
268  pt[i_vertex] (2) = (*surface_)[index].z;
269  }
270 
271  const float curr_area = ((pt[1] - pt[0]).cross (pt[2] - pt[0])).norm ();
272  triangle_area.push_back (curr_area);
273  total_area += curr_area;
274 
275  distance_weight.push_back (std::pow (support_radius_ - (feature_point - (pt[0] + pt[1] + pt[2]) * coeff_1_div_3).norm (), 2.0f));
276 
277  Eigen::Matrix3f curr_scatter_matrix;
278  curr_scatter_matrix.setZero ();
279  for (const auto &i_pt : pt)
280  {
281  Eigen::Vector3f vec = i_pt - feature_point;
282  curr_scatter_matrix += vec * (vec.transpose ());
283  for (const auto &j_pt : pt)
284  curr_scatter_matrix += vec * ((j_pt - feature_point).transpose ());
285  }
286  scatter_matrices.emplace_back (coeff * curr_scatter_matrix);
287  }
288 
289  if (std::abs (total_area) < std::numeric_limits <float>::epsilon ())
290  total_area = 1.0f / total_area;
291  else
292  total_area = 1.0f;
293 
294  Eigen::Matrix3f overall_scatter_matrix;
295  overall_scatter_matrix.setZero ();
296  std::vector<float> total_weight (number_of_triangles);
297  const float denominator = 1.0f / 6.0f;
298  for (std::size_t i_triangle = 0; i_triangle < number_of_triangles; i_triangle++)
299  {
300  const float factor = distance_weight[i_triangle] * triangle_area[i_triangle] * total_area;
301  overall_scatter_matrix += factor * scatter_matrices[i_triangle];
302  total_weight[i_triangle] = factor * denominator;
303  }
304 
305  Eigen::Vector3f v1, v2, v3;
306  computeEigenVectors (overall_scatter_matrix, v1, v2, v3);
307 
308  float h1 = 0.0f;
309  float h3 = 0.0f;
310  std::size_t i_triangle = 0;
311  for (const auto& triangle: local_triangles)
312  {
313  Eigen::Vector3f pt[3];
314  for (unsigned int i_vertex = 0; i_vertex < 3; i_vertex++)
315  {
316  const unsigned int index = triangles_[triangle].vertices[i_vertex];
317  pt[i_vertex] (0) = (*surface_)[index].x;
318  pt[i_vertex] (1) = (*surface_)[index].y;
319  pt[i_vertex] (2) = (*surface_)[index].z;
320  }
321 
322  float factor1 = 0.0f;
323  float factor3 = 0.0f;
324  for (const auto &i_pt : pt)
325  {
326  Eigen::Vector3f vec = i_pt - feature_point;
327  factor1 += vec.dot (v1);
328  factor3 += vec.dot (v3);
329  }
330  h1 += total_weight[i_triangle] * factor1;
331  h3 += total_weight[i_triangle] * factor3;
332  i_triangle++;
333  }
334 
335  if (h1 < 0.0f) v1 = -v1;
336  if (h3 < 0.0f) v3 = -v3;
337 
338  v2 = v3.cross (v1);
339 
340  lrf_matrix.row (0) = v1;
341  lrf_matrix.row (1) = v2;
342  lrf_matrix.row (2) = v3;
343 }
344 
345 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
346 template <typename PointInT, typename PointOutT> void
348  Eigen::Vector3f& major_axis, Eigen::Vector3f& middle_axis, Eigen::Vector3f& minor_axis) const
349 {
350  Eigen::EigenSolver <Eigen::Matrix3f> eigen_solver;
351  eigen_solver.compute (matrix);
352 
353  Eigen::EigenSolver <Eigen::Matrix3f>::EigenvectorsType eigen_vectors;
354  Eigen::EigenSolver <Eigen::Matrix3f>::EigenvalueType eigen_values;
355  eigen_vectors = eigen_solver.eigenvectors ();
356  eigen_values = eigen_solver.eigenvalues ();
357 
358  unsigned int temp = 0;
359  unsigned int major_index = 0;
360  unsigned int middle_index = 1;
361  unsigned int minor_index = 2;
362 
363  if (eigen_values.real () (major_index) < eigen_values.real () (middle_index))
364  {
365  temp = major_index;
366  major_index = middle_index;
367  middle_index = temp;
368  }
369 
370  if (eigen_values.real () (major_index) < eigen_values.real () (minor_index))
371  {
372  temp = major_index;
373  major_index = minor_index;
374  minor_index = temp;
375  }
376 
377  if (eigen_values.real () (middle_index) < eigen_values.real () (minor_index))
378  {
379  temp = minor_index;
380  minor_index = middle_index;
381  middle_index = temp;
382  }
383 
384  major_axis = eigen_vectors.col (major_index).real ();
385  middle_axis = eigen_vectors.col (middle_index).real ();
386  minor_axis = eigen_vectors.col (minor_index).real ();
387 }
388 
389 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
390 template <typename PointInT, typename PointOutT> void
391 pcl::ROPSEstimation <PointInT, PointOutT>::transformCloud (const PointInT& point, const Eigen::Matrix3f& matrix, const pcl::Indices& local_points, PointCloudIn& transformed_cloud) const
392 {
393  const auto number_of_points = local_points.size ();
394  transformed_cloud.clear ();
395  transformed_cloud.reserve (number_of_points);
396 
397  for (const auto& idx: local_points)
398  {
399  Eigen::Vector3f transformed_point ((*surface_)[idx].x - point.x,
400  (*surface_)[idx].y - point.y,
401  (*surface_)[idx].z - point.z);
402 
403  transformed_point = matrix * transformed_point;
404 
405  PointInT new_point;
406  new_point.x = transformed_point (0);
407  new_point.y = transformed_point (1);
408  new_point.z = transformed_point (2);
409  transformed_cloud.emplace_back (new_point);
410  }
411 }
412 
413 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
414 template <typename PointInT, typename PointOutT> void
415 pcl::ROPSEstimation <PointInT, PointOutT>::rotateCloud (const PointInT& axis, const float angle, const PointCloudIn& cloud, PointCloudIn& rotated_cloud, Eigen::Vector3f& min, Eigen::Vector3f& max) const
416 {
417  Eigen::Matrix3f rotation_matrix;
418  const float x = axis.x;
419  const float y = axis.y;
420  const float z = axis.z;
421  const float rad = M_PI / 180.0f;
422  const float cosine = std::cos (angle * rad);
423  const float sine = std::sin (angle * rad);
424  rotation_matrix << cosine + (1 - cosine) * x * x, (1 - cosine) * x * y - sine * z, (1 - cosine) * x * z + sine * y,
425  (1 - cosine) * y * x + sine * z, cosine + (1 - cosine) * y * y, (1 - cosine) * y * z - sine * x,
426  (1 - cosine) * z * x - sine * y, (1 - cosine) * z * y + sine * x, cosine + (1 - cosine) * z * z;
427 
428  const auto number_of_points = cloud.size ();
429 
430  rotated_cloud.header = cloud.header;
431  rotated_cloud.width = number_of_points;
432  rotated_cloud.height = 1;
433  rotated_cloud.clear ();
434  rotated_cloud.reserve (number_of_points);
435 
436  min (0) = std::numeric_limits <float>::max ();
437  min (1) = std::numeric_limits <float>::max ();
438  min (2) = std::numeric_limits <float>::max ();
439  max (0) = -std::numeric_limits <float>::max ();
440  max (1) = -std::numeric_limits <float>::max ();
441  max (2) = -std::numeric_limits <float>::max ();
442 
443  for (const auto& pt: cloud.points)
444  {
445  Eigen::Vector3f point (pt.x, pt.y, pt.z);
446  point = rotation_matrix * point;
447 
448  PointInT rotated_point;
449  rotated_point.x = point (0);
450  rotated_point.y = point (1);
451  rotated_point.z = point (2);
452  rotated_cloud.emplace_back (rotated_point);
453 
454  for (int i = 0; i < 3; ++i)
455  {
456  min(i) = std::min(min(i), point(i));
457  max(i) = std::max(max(i), point(i));
458  }
459  }
460 }
461 
462 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
463 template <typename PointInT, typename PointOutT> void
464 pcl::ROPSEstimation <PointInT, PointOutT>::getDistributionMatrix (const unsigned int projection, const Eigen::Vector3f& min, const Eigen::Vector3f& max, const PointCloudIn& cloud, Eigen::MatrixXf& matrix) const
465 {
466  matrix.setZero ();
467 
468  const unsigned int coord[3][2] = {
469  {0, 1},
470  {0, 2},
471  {1, 2}};
472 
473  const float u_bin_length = (max (coord[projection][0]) - min (coord[projection][0])) / number_of_bins_;
474  const float v_bin_length = (max (coord[projection][1]) - min (coord[projection][1])) / number_of_bins_;
475 
476  for (const auto& pt: cloud.points)
477  {
478  Eigen::Vector3f point (pt.x, pt.y, pt.z);
479 
480  const float u_length = point (coord[projection][0]) - min[coord[projection][0]];
481  const float v_length = point (coord[projection][1]) - min[coord[projection][1]];
482 
483  const float u_ratio = u_length / u_bin_length;
484  unsigned int row = static_cast <unsigned int> (u_ratio);
485  if (row == number_of_bins_) row--;
486 
487  const float v_ratio = v_length / v_bin_length;
488  unsigned int col = static_cast <unsigned int> (v_ratio);
489  if (col == number_of_bins_) col--;
490 
491  matrix (row, col) += 1.0f;
492  }
493 
494  matrix /= std::max<float> (1, cloud.size ());
495 }
496 
497 //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
498 template <typename PointInT, typename PointOutT> void
499 pcl::ROPSEstimation <PointInT, PointOutT>::computeCentralMoments (const Eigen::MatrixXf& matrix, std::vector <float>& moments) const
500 {
501  float mean_i = 0.0f;
502  float mean_j = 0.0f;
503 
504  for (unsigned int i = 0; i < number_of_bins_; i++)
505  for (unsigned int j = 0; j < number_of_bins_; j++)
506  {
507  const float m = matrix (i, j);
508  mean_i += static_cast <float> (i + 1) * m;
509  mean_j += static_cast <float> (j + 1) * m;
510  }
511 
512  const unsigned int number_of_moments_to_compute = 4;
513  const float power[number_of_moments_to_compute][2] = {
514  {1.0f, 1.0f},
515  {2.0f, 1.0f},
516  {1.0f, 2.0f},
517  {2.0f, 2.0f}};
518 
519  float entropy = 0.0f;
520  moments.resize (number_of_moments_to_compute + 1, 0.0f);
521  for (unsigned int i = 0; i < number_of_bins_; i++)
522  {
523  const float i_factor = static_cast <float> (i + 1) - mean_i;
524  for (unsigned int j = 0; j < number_of_bins_; j++)
525  {
526  const float j_factor = static_cast <float> (j + 1) - mean_j;
527  const float m = matrix (i, j);
528  if (m > 0.0f)
529  entropy -= m * std::log (m);
530  for (unsigned int i_moment = 0; i_moment < number_of_moments_to_compute; i_moment++)
531  moments[i_moment] += std::pow (i_factor, power[i_moment][0]) * std::pow (j_factor, power[i_moment][1]) * m;
532  }
533  }
534 
535  moments[number_of_moments_to_compute] = entropy;
536 }
537 
538 #endif // PCL_ROPS_ESTIMATION_HPP_
void compute(PointCloudOut &output)
Base method for feature estimation for all points given in <setInputCloud (), setIndices ()> using th...
Definition: feature.hpp:194
This class implements the method for extracting RoPS features presented in the article "Rotational Pr...
__device__ __host__ __forceinline__ float norm(const float3 &v1, const float3 &v2)
IndicesAllocator<> Indices
Type used for indices in PCL.
Definition: types.h:133
#define M_PI
Definition: pcl_macros.h:201