Point Cloud Library (PCL)  1.9.0-dev
mls.hpp
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39 
40 #ifndef PCL_SURFACE_IMPL_MLS_H_
41 #define PCL_SURFACE_IMPL_MLS_H_
42 
43 #include <pcl/point_traits.h>
44 #include <pcl/surface/mls.h>
45 #include <pcl/common/io.h>
46 #include <pcl/common/copy_point.h>
47 #include <pcl/common/centroid.h>
48 #include <pcl/common/eigen.h>
49 #include <pcl/common/geometry.h>
50 #include <boost/bind.hpp>
51 
52 #ifdef _OPENMP
53 #include <omp.h>
54 #endif
55 
56 //////////////////////////////////////////////////////////////////////////////////////////////
57 template <typename PointInT, typename PointOutT> void
59 {
60  // Reset or initialize the collection of indices
61  corresponding_input_indices_.reset (new PointIndices);
62 
63  // Check if normals have to be computed/saved
64  if (compute_normals_)
65  {
66  normals_.reset (new NormalCloud);
67  // Copy the header
68  normals_->header = input_->header;
69  // Clear the fields in case the method exits before computation
70  normals_->width = normals_->height = 0;
71  normals_->points.clear ();
72  }
73 
74  // Copy the header
75  output.header = input_->header;
76  output.width = output.height = 0;
77  output.points.clear ();
78 
79  if (search_radius_ <= 0 || sqr_gauss_param_ <= 0)
80  {
81  PCL_ERROR ("[pcl::%s::process] Invalid search radius (%f) or Gaussian parameter (%f)!\n", getClassName ().c_str (), search_radius_, sqr_gauss_param_);
82  return;
83  }
84 
85  // Check if distinct_cloud_ was set
86  if (upsample_method_ == DISTINCT_CLOUD && !distinct_cloud_)
87  {
88  PCL_ERROR ("[pcl::%s::process] Upsample method was set to DISTINCT_CLOUD, but no distinct cloud was specified.\n", getClassName ().c_str ());
89  return;
90  }
91 
92  if (!initCompute ())
93  return;
94 
95  // Initialize the spatial locator
96  if (!tree_)
97  {
98  KdTreePtr tree;
99  if (input_->isOrganized ())
100  tree.reset (new pcl::search::OrganizedNeighbor<PointInT> ());
101  else
102  tree.reset (new pcl::search::KdTree<PointInT> (false));
103  setSearchMethod (tree);
104  }
105 
106  // Send the surface dataset to the spatial locator
107  tree_->setInputCloud (input_);
108 
109  switch (upsample_method_)
110  {
111  // Initialize random number generator if necessary
112  case (RANDOM_UNIFORM_DENSITY):
113  {
114  rng_alg_.seed (static_cast<unsigned> (std::time (0)));
115  float tmp = static_cast<float> (search_radius_ / 2.0f);
116  boost::uniform_real<float> uniform_distrib (-tmp, tmp);
117  rng_uniform_distribution_.reset (new boost::variate_generator<boost::mt19937&, boost::uniform_real<float> > (rng_alg_, uniform_distrib));
118 
119  break;
120  }
121  case (VOXEL_GRID_DILATION):
122  case (DISTINCT_CLOUD):
123  {
124  if (!cache_mls_results_)
125  PCL_WARN ("The cache mls results is forced when using upsampling method VOXEL_GRID_DILATION or DISTINCT_CLOUD.\n");
126 
127  cache_mls_results_ = true;
128  break;
129  }
130  default:
131  break;
132  }
133 
134  if (cache_mls_results_)
135  {
136  mls_results_.resize (input_->size ());
137  }
138  else
139  {
140  mls_results_.resize (1); // Need to have a reference to a single dummy result.
141  }
142 
143  // Perform the actual surface reconstruction
144  performProcessing (output);
145 
146  if (compute_normals_)
147  {
148  normals_->height = 1;
149  normals_->width = static_cast<uint32_t> (normals_->size ());
150 
151  for (unsigned int i = 0; i < output.size (); ++i)
152  {
153  typedef typename pcl::traits::fieldList<PointOutT>::type FieldList;
154  pcl::for_each_type<FieldList> (SetIfFieldExists<PointOutT, float> (output.points[i], "normal_x", normals_->points[i].normal_x));
155  pcl::for_each_type<FieldList> (SetIfFieldExists<PointOutT, float> (output.points[i], "normal_y", normals_->points[i].normal_y));
156  pcl::for_each_type<FieldList> (SetIfFieldExists<PointOutT, float> (output.points[i], "normal_z", normals_->points[i].normal_z));
157  pcl::for_each_type<FieldList> (SetIfFieldExists<PointOutT, float> (output.points[i], "curvature", normals_->points[i].curvature));
158  }
159 
160  }
161 
162  // Set proper widths and heights for the clouds
163  output.height = 1;
164  output.width = static_cast<uint32_t> (output.size ());
165 
166  deinitCompute ();
167 }
168 
169 //////////////////////////////////////////////////////////////////////////////////////////////
170 template <typename PointInT, typename PointOutT> void
172  const std::vector<int> &nn_indices,
173  PointCloudOut &projected_points,
174  NormalCloud &projected_points_normals,
175  PointIndices &corresponding_input_indices,
176  MLSResult &mls_result) const
177 {
178  // Note: this method is const because it needs to be thread-safe
179  // (MovingLeastSquaresOMP calls it from multiple threads)
180 
181  mls_result.computeMLSSurface<PointInT> (*input_, index, nn_indices, search_radius_, order_);
182 
183  switch (upsample_method_)
184  {
185  case (NONE):
186  {
187  MLSResult::MLSProjectionResults proj = mls_result.projectQueryPoint (projection_method_, nr_coeff_);
188  addProjectedPointNormal (index, proj.point, proj.normal, mls_result.curvature, projected_points, projected_points_normals, corresponding_input_indices);
189  break;
190  }
191 
192  case (SAMPLE_LOCAL_PLANE):
193  {
194  // Uniformly sample a circle around the query point using the radius and step parameters
195  for (float u_disp = -static_cast<float> (upsampling_radius_); u_disp <= upsampling_radius_; u_disp += static_cast<float> (upsampling_step_))
196  for (float v_disp = -static_cast<float> (upsampling_radius_); v_disp <= upsampling_radius_; v_disp += static_cast<float> (upsampling_step_))
197  if (u_disp * u_disp + v_disp * v_disp < upsampling_radius_ * upsampling_radius_)
198  {
200  addProjectedPointNormal (index, proj.point, proj.normal, mls_result.curvature, projected_points, projected_points_normals, corresponding_input_indices);
201  }
202  break;
203  }
204 
205  case (RANDOM_UNIFORM_DENSITY):
206  {
207  // Compute the local point density and add more samples if necessary
208  int num_points_to_add = static_cast<int> (floor (desired_num_points_in_radius_ / 2.0 / static_cast<double> (nn_indices.size ())));
209 
210  // Just add the query point, because the density is good
211  if (num_points_to_add <= 0)
212  {
213  // Just add the current point
214  MLSResult::MLSProjectionResults proj = mls_result.projectQueryPoint (projection_method_, nr_coeff_);
215  addProjectedPointNormal (index, proj.point, proj.normal, mls_result.curvature, projected_points, projected_points_normals, corresponding_input_indices);
216  }
217  else
218  {
219  // Sample the local plane
220  for (int num_added = 0; num_added < num_points_to_add;)
221  {
222  double u = (*rng_uniform_distribution_) ();
223  double v = (*rng_uniform_distribution_) ();
224 
225  // Check if inside circle; if not, try another coin flip
226  if (u * u + v * v > search_radius_ * search_radius_ / 4)
227  continue;
228 
230  if (order_ > 1 && mls_result.num_neighbors >= 5 * nr_coeff_)
231  proj = mls_result.projectPointSimpleToPolynomialSurface (u, v);
232  else
233  proj = mls_result.projectPointToMLSPlane (u, v);
234 
235  addProjectedPointNormal (index, proj.point, proj.normal, mls_result.curvature, projected_points, projected_points_normals, corresponding_input_indices);
236 
237  num_added++;
238  }
239  }
240  break;
241  }
242 
243  default:
244  break;
245  }
246 }
247 
248 template <typename PointInT, typename PointOutT> void
250  const Eigen::Vector3d &point,
251  const Eigen::Vector3d &normal,
252  double curvature,
253  PointCloudOut &projected_points,
254  NormalCloud &projected_points_normals,
255  PointIndices &corresponding_input_indices) const
256 {
257  PointOutT aux;
258  aux.x = static_cast<float> (point[0]);
259  aux.y = static_cast<float> (point[1]);
260  aux.z = static_cast<float> (point[2]);
261 
262  // Copy additional point information if available
263  copyMissingFields (input_->points[index], aux);
264 
265  projected_points.push_back (aux);
266  corresponding_input_indices.indices.push_back (index);
267 
268  if (compute_normals_)
269  {
270  pcl::Normal aux_normal;
271  aux_normal.normal_x = static_cast<float> (normal[0]);
272  aux_normal.normal_y = static_cast<float> (normal[1]);
273  aux_normal.normal_z = static_cast<float> (normal[2]);
274  aux_normal.curvature = curvature;
275  projected_points_normals.push_back (aux_normal);
276  }
277 }
278 
279 //////////////////////////////////////////////////////////////////////////////////////////////
280 template <typename PointInT, typename PointOutT> void
282 {
283  // Compute the number of coefficients
284  nr_coeff_ = (order_ + 1) * (order_ + 2) / 2;
285 
286 #ifdef _OPENMP
287  // (Maximum) number of threads
288  const unsigned int threads = threads_ == 0 ? 1 : threads_;
289  // Create temporaries for each thread in order to avoid synchronization
290  typename PointCloudOut::CloudVectorType projected_points (threads);
291  typename NormalCloud::CloudVectorType projected_points_normals (threads);
292  std::vector<PointIndices> corresponding_input_indices (threads);
293 #endif
294 
295  // For all points
296 #ifdef _OPENMP
297 #pragma omp parallel for schedule (dynamic,1000) num_threads (threads)
298 #endif
299  for (int cp = 0; cp < static_cast<int> (indices_->size ()); ++cp)
300  {
301  // Allocate enough space to hold the results of nearest neighbor searches
302  // \note resize is irrelevant for a radiusSearch ().
303  std::vector<int> nn_indices;
304  std::vector<float> nn_sqr_dists;
305 
306  // Get the initial estimates of point positions and their neighborhoods
307  if (searchForNeighbors ((*indices_)[cp], nn_indices, nn_sqr_dists))
308  {
309  // Check the number of nearest neighbors for normal estimation (and later for polynomial fit as well)
310  if (nn_indices.size () >= 3)
311  {
312  // This thread's ID (range 0 to threads-1)
313 #ifdef _OPENMP
314  const int tn = omp_get_thread_num ();
315  // Size of projected points before computeMLSPointNormal () adds points
316  size_t pp_size = projected_points[tn].size ();
317 #else
318  PointCloudOut projected_points;
319  NormalCloud projected_points_normals;
320 #endif
321 
322  // Get a plane approximating the local surface's tangent and project point onto it
323  const int index = (*indices_)[cp];
324 
325  size_t mls_result_index = 0;
326  if (cache_mls_results_)
327  mls_result_index = index; // otherwise we give it a dummy location.
328 
329 #ifdef _OPENMP
330  computeMLSPointNormal (index, nn_indices, projected_points[tn], projected_points_normals[tn], corresponding_input_indices[tn], mls_results_[mls_result_index]);
331 
332  // Copy all information from the input cloud to the output points (not doing any interpolation)
333  for (size_t pp = pp_size; pp < projected_points[tn].size (); ++pp)
334  copyMissingFields (input_->points[(*indices_)[cp]], projected_points[tn][pp]);
335 #else
336  computeMLSPointNormal (index, nn_indices, projected_points, projected_points_normals, *corresponding_input_indices_, mls_results_[mls_result_index]);
337 
338  // Append projected points to output
339  output.insert (output.end (), projected_points.begin (), projected_points.end ());
340  if (compute_normals_)
341  normals_->insert (normals_->end (), projected_points_normals.begin (), projected_points_normals.end ());
342 #endif
343  }
344  }
345  }
346 
347 #ifdef _OPENMP
348  // Combine all threads' results into the output vectors
349  for (unsigned int tn = 0; tn < threads; ++tn)
350  {
351  output.insert (output.end (), projected_points[tn].begin (), projected_points[tn].end ());
352  corresponding_input_indices_->indices.insert (corresponding_input_indices_->indices.end (),
353  corresponding_input_indices[tn].indices.begin (), corresponding_input_indices[tn].indices.end ());
354  if (compute_normals_)
355  normals_->insert (normals_->end (), projected_points_normals[tn].begin (), projected_points_normals[tn].end ());
356  }
357 #endif
358 
359  // Perform the distinct-cloud or voxel-grid upsampling
360  performUpsampling (output);
361 }
362 
363 //////////////////////////////////////////////////////////////////////////////////////////////
364 template <typename PointInT, typename PointOutT> void
366 {
367 
368  if (upsample_method_ == DISTINCT_CLOUD)
369  {
370  corresponding_input_indices_.reset (new PointIndices);
371  for (size_t dp_i = 0; dp_i < distinct_cloud_->size (); ++dp_i) // dp_i = distinct_point_i
372  {
373  // Distinct cloud may have nan points, skip them
374  if (!pcl_isfinite (distinct_cloud_->points[dp_i].x))
375  continue;
376 
377  // Get 3D position of point
378  //Eigen::Vector3f pos = distinct_cloud_->points[dp_i].getVector3fMap ();
379  std::vector<int> nn_indices;
380  std::vector<float> nn_dists;
381  tree_->nearestKSearch (distinct_cloud_->points[dp_i], 1, nn_indices, nn_dists);
382  int input_index = nn_indices.front ();
383 
384  // If the closest point did not have a valid MLS fitting result
385  // OR if it is too far away from the sampled point
386  if (mls_results_[input_index].valid == false)
387  continue;
388 
389  Eigen::Vector3d add_point = distinct_cloud_->points[dp_i].getVector3fMap ().template cast<double> ();
390  MLSResult::MLSProjectionResults proj = mls_results_[input_index].projectPoint (add_point, projection_method_, 5 * nr_coeff_);
391  addProjectedPointNormal (input_index, proj.point, proj.normal, mls_results_[input_index].curvature, output, *normals_, *corresponding_input_indices_);
392  }
393  }
394 
395  // For the voxel grid upsampling method, generate the voxel grid and dilate it
396  // Then, project the newly obtained points to the MLS surface
397  if (upsample_method_ == VOXEL_GRID_DILATION)
398  {
399  corresponding_input_indices_.reset (new PointIndices);
400 
401  MLSVoxelGrid voxel_grid (input_, indices_, voxel_size_);
402  for (int iteration = 0; iteration < dilation_iteration_num_; ++iteration)
403  voxel_grid.dilate ();
404 
405  for (typename MLSVoxelGrid::HashMap::iterator m_it = voxel_grid.voxel_grid_.begin (); m_it != voxel_grid.voxel_grid_.end (); ++m_it)
406  {
407  // Get 3D position of point
408  Eigen::Vector3f pos;
409  voxel_grid.getPosition (m_it->first, pos);
410 
411  PointInT p;
412  p.x = pos[0];
413  p.y = pos[1];
414  p.z = pos[2];
415 
416  std::vector<int> nn_indices;
417  std::vector<float> nn_dists;
418  tree_->nearestKSearch (p, 1, nn_indices, nn_dists);
419  int input_index = nn_indices.front ();
420 
421  // If the closest point did not have a valid MLS fitting result
422  // OR if it is too far away from the sampled point
423  if (mls_results_[input_index].valid == false)
424  continue;
425 
426  Eigen::Vector3d add_point = p.getVector3fMap ().template cast<double> ();
427  MLSResult::MLSProjectionResults proj = mls_results_[input_index].projectPoint (add_point, projection_method_, 5 * nr_coeff_);
428  addProjectedPointNormal (input_index, proj.point, proj.normal, mls_results_[input_index].curvature, output, *normals_, *corresponding_input_indices_);
429  }
430  }
431 }
432 
433 //////////////////////////////////////////////////////////////////////////////////////////////
434 pcl::MLSResult::MLSResult (const Eigen::Vector3d &a_query_point,
435  const Eigen::Vector3d &a_mean,
436  const Eigen::Vector3d &a_plane_normal,
437  const Eigen::Vector3d &a_u,
438  const Eigen::Vector3d &a_v,
439  const Eigen::VectorXd &a_c_vec,
440  const int a_num_neighbors,
441  const float a_curvature,
442  const int a_order) :
443  query_point (a_query_point), mean (a_mean), plane_normal (a_plane_normal), u_axis (a_u), v_axis (a_v), c_vec (a_c_vec), num_neighbors (a_num_neighbors),
444  curvature (a_curvature), order (a_order), valid (true)
445 {}
446 
447 void
448 pcl::MLSResult::getMLSCoordinates (const Eigen::Vector3d &pt, double &u, double &v, double &w) const
449 {
450  Eigen::Vector3d delta = pt - mean;
451  u = delta.dot (u_axis);
452  v = delta.dot (v_axis);
453  w = delta.dot (plane_normal);
454 }
455 
456 void
457 pcl::MLSResult::getMLSCoordinates (const Eigen::Vector3d &pt, double &u, double &v) const
458 {
459  Eigen::Vector3d delta = pt - mean;
460  u = delta.dot (u_axis);
461  v = delta.dot (v_axis);
462 }
463 
464 double
465 pcl::MLSResult::getPolynomialValue (const double u, const double v) const
466 {
467  // Compute the polynomial's terms at the current point
468  // Example for second order: z = a + b*y + c*y^2 + d*x + e*x*y + f*x^2
469  double u_pow, v_pow, result;
470  int j = 0;
471  u_pow = 1;
472  result = 0;
473  for (int ui = 0; ui <= order; ++ui)
474  {
475  v_pow = 1;
476  for (int vi = 0; vi <= order - ui; ++vi)
477  {
478  result += c_vec[j++] * u_pow * v_pow;
479  v_pow *= v;
480  }
481  u_pow *= u;
482  }
483 
484  return (result);
485 }
486 
488 pcl::MLSResult::getPolynomialPartialDerivative (const double u, const double v) const
489 {
490  // Compute the displacement along the normal using the fitted polynomial
491  // and compute the partial derivatives needed for estimating the normal
493  Eigen::VectorXd u_pow (order + 2), v_pow (order + 2);
494  int j = 0;
495 
496  d.z = d.z_u = d.z_v = d.z_uu = d.z_vv = d.z_uv = 0;
497  u_pow (0) = v_pow (0) = 1;
498  for (int ui = 0; ui <= order; ++ui)
499  {
500  for (int vi = 0; vi <= order - ui; ++vi)
501  {
502  // Compute displacement along normal
503  d.z += u_pow (ui) * v_pow (vi) * c_vec[j];
504 
505  // Compute partial derivatives
506  if (ui >= 1)
507  d.z_u += c_vec[j] * ui * u_pow (ui - 1) * v_pow (vi);
508 
509  if (vi >= 1)
510  d.z_v += c_vec[j] * vi * u_pow (ui) * v_pow (vi - 1);
511 
512  if (ui >= 1 && vi >= 1)
513  d.z_uv += c_vec[j] * ui * u_pow (ui - 1) * vi * v_pow (vi - 1);
514 
515  if (ui >= 2)
516  d.z_uu += c_vec[j] * ui * (ui - 1) * u_pow (ui - 2) * v_pow (vi);
517 
518  if (vi >= 2)
519  d.z_vv += c_vec[j] * vi * (vi - 1) * u_pow (ui) * v_pow (vi - 2);
520 
521  if (ui == 0)
522  v_pow (vi + 1) = v_pow (vi) * v;
523 
524  ++j;
525  }
526  u_pow (ui + 1) = u_pow (ui) * u;
527  }
528 
529  return (d);
530 }
531 
532 Eigen::Vector2f
533 pcl::MLSResult::calculatePrincipleCurvatures (const double u, const double v) const
534 {
535  Eigen::Vector2f k (1e-5, 1e-5);
536 
537  // Note: this use the Monge Patch to derive the Gaussian curvature and Mean Curvature found here http://mathworld.wolfram.com/MongePatch.html
538  // Then:
539  // k1 = H + sqrt(H^2 - K)
540  // k1 = H - sqrt(H^2 - K)
541  if (order > 1 && c_vec.size () >= (order + 1) * (order + 2) / 2 && pcl_isfinite (c_vec[0]))
542  {
544  double Z = 1 + d.z_u * d.z_u + d.z_v * d.z_v;
545  double Zlen = std::sqrt (Z);
546  double K = (d.z_uu * d.z_vv - d.z_uv * d.z_uv) / (Z * Z);
547  double H = ((1.0 + d.z_v * d.z_v) * d.z_uu - 2.0 * d.z_u * d.z_v * d.z_uv + (1.0 + d.z_u * d.z_u) * d.z_vv) / (2.0 * Zlen * Zlen * Zlen);
548  double disc2 = H * H - K;
549  assert (disc2 >= 0.0);
550  double disc = std::sqrt (disc2);
551  k[0] = H + disc;
552  k[1] = H - disc;
553 
554  if (std::abs (k[0]) > std::abs (k[1])) std::swap (k[0], k[1]);
555  }
556  else
557  {
558  PCL_ERROR ("No Polynomial fit data, unable to calculate the principle curvatures!\n");
559  }
560 
561  return (k);
562 }
563 
565 pcl::MLSResult::projectPointOrthogonalToPolynomialSurface (const double u, const double v, const double w) const
566 {
567  double gu = u;
568  double gv = v;
569  double gw = 0;
570 
571  MLSProjectionResults result;
572  result.normal = plane_normal;
573  if (order > 1 && c_vec.size () >= (order + 1) * (order + 2) / 2 && pcl_isfinite (c_vec[0]))
574  {
576  gw = d.z;
577  double err_total;
578  double dist1 = std::abs (gw - w);
579  double dist2;
580  do
581  {
582  double e1 = (gu - u) + d.z_u * gw - d.z_u * w;
583  double e2 = (gv - v) + d.z_v * gw - d.z_v * w;
584 
585  double F1u = 1 + d.z_uu * gw + d.z_u * d.z_u - d.z_uu * w;
586  double F1v = d.z_uv * gw + d.z_u * d.z_v - d.z_uv * w;
587 
588  double F2u = d.z_uv * gw + d.z_v * d.z_u - d.z_uv * w;
589  double F2v = 1 + d.z_vv * gw + d.z_v * d.z_v - d.z_vv * w;
590 
591  Eigen::MatrixXd J (2, 2);
592  J (0, 0) = F1u;
593  J (0, 1) = F1v;
594  J (1, 0) = F2u;
595  J (1, 1) = F2v;
596 
597  Eigen::Vector2d err (e1, e2);
598  Eigen::Vector2d update = J.inverse () * err;
599  gu -= update (0);
600  gv -= update (1);
601 
602  d = getPolynomialPartialDerivative (gu, gv);
603  gw = d.z;
604  dist2 = std::sqrt ((gu - u) * (gu - u) + (gv - v) * (gv - v) + (gw - w) * (gw - w));
605 
606  err_total = std::sqrt (e1 * e1 + e2 * e2);
607 
608  } while (err_total > 1e-8 && dist2 < dist1);
609 
610  if (dist2 > dist1) // the optimization was diverging reset the coordinates for simple projection
611  {
612  gu = u;
613  gv = v;
615  gw = d.z;
616  }
617 
618  result.u = gu;
619  result.v = gv;
620  result.normal -= (d.z_u * u_axis + d.z_v * v_axis);
621  result.normal.normalize ();
622  }
623 
624  result.point = mean + gu * u_axis + gv * v_axis + gw * plane_normal;
625 
626  return (result);
627 }
628 
630 pcl::MLSResult::projectPointToMLSPlane (const double u, const double v) const
631 {
632  MLSProjectionResults result;
633  result.u = u;
634  result.v = v;
635  result.normal = plane_normal;
636  result.point = mean + u * u_axis + v * v_axis;
637 
638  return (result);
639 }
640 
642 pcl::MLSResult::projectPointSimpleToPolynomialSurface (const double u, const double v) const
643 {
644  MLSProjectionResults result;
645  double w = 0;
646 
647  result.u = u;
648  result.v = v;
649  result.normal = plane_normal;
650 
651  if (order > 1 && c_vec.size () >= (order + 1) * (order + 2) / 2 && pcl_isfinite (c_vec[0]))
652  {
654  w = d.z;
655  result.normal -= (d.z_u * u_axis + d.z_v * v_axis);
656  result.normal.normalize ();
657  }
658 
659  result.point = mean + u * u_axis + v * v_axis + w * plane_normal;
660 
661  return (result);
662 }
663 
665 pcl::MLSResult::projectPoint (const Eigen::Vector3d &pt, ProjectionMethod method, int required_neighbors) const
666 {
667  double u, v, w;
668  getMLSCoordinates (pt, u, v, w);
669 
671  if (order > 1 && num_neighbors >= required_neighbors && pcl_isfinite (c_vec[0]) && method != NONE)
672  {
673  if (method == ORTHOGONAL)
675  else // SIMPLE
677  }
678  else
679  {
680  proj = projectPointToMLSPlane (u, v);
681  }
682 
683  return (proj);
684 }
685 
687 pcl::MLSResult::projectQueryPoint (ProjectionMethod method, int required_neighbors) const
688 {
690  if (order > 1 && num_neighbors >= required_neighbors && pcl_isfinite (c_vec[0]) && method != NONE)
691  {
692  if (method == ORTHOGONAL)
693  {
694  double u, v, w;
695  getMLSCoordinates (query_point, u, v, w);
697  }
698  else // SIMPLE
699  {
700  // Projection onto MLS surface along Darboux normal to the height at (0,0)
701  proj.point = mean + (c_vec[0] * plane_normal);
702 
703  // Compute tangent vectors using the partial derivates evaluated at (0,0) which is c_vec[order_+1] and c_vec[1]
704  proj.normal = plane_normal - c_vec[order + 1] * u_axis - c_vec[1] * v_axis;
705  proj.normal.normalize ();
706  }
707  }
708  else
709  {
710  proj.normal = plane_normal;
711  proj.point = mean;
712  }
713 
714  return (proj);
715 }
716 
717 template <typename PointT> void
719  int index,
720  const std::vector<int> &nn_indices,
721  double search_radius,
722  int polynomial_order,
723  boost::function<double(const double)> weight_func)
724 {
725  // Compute the plane coefficients
726  EIGEN_ALIGN16 Eigen::Matrix3d covariance_matrix;
727  Eigen::Vector4d xyz_centroid;
728 
729  // Estimate the XYZ centroid
730  pcl::compute3DCentroid (cloud, nn_indices, xyz_centroid);
731 
732  // Compute the 3x3 covariance matrix
733  pcl::computeCovarianceMatrix (cloud, nn_indices, xyz_centroid, covariance_matrix);
734  EIGEN_ALIGN16 Eigen::Vector3d::Scalar eigen_value;
735  EIGEN_ALIGN16 Eigen::Vector3d eigen_vector;
736  Eigen::Vector4d model_coefficients (0, 0, 0, 0);
737  pcl::eigen33 (covariance_matrix, eigen_value, eigen_vector);
738  model_coefficients.head<3> ().matrix () = eigen_vector;
739  model_coefficients[3] = -1 * model_coefficients.dot (xyz_centroid);
740 
741  // Projected query point
742  valid = true;
743  query_point = cloud.points[index].getVector3fMap ().template cast<double> ();
744  double distance = query_point.dot (model_coefficients.head<3> ()) + model_coefficients[3];
745  mean = query_point - distance * model_coefficients.head<3> ();
746 
747  curvature = covariance_matrix.trace ();
748  // Compute the curvature surface change
749  if (curvature != 0)
750  curvature = std::abs (eigen_value / curvature);
751 
752  // Get a copy of the plane normal easy access
753  plane_normal = model_coefficients.head<3> ();
754 
755  // Local coordinate system (Darboux frame)
756  v_axis = plane_normal.unitOrthogonal ();
757  u_axis = plane_normal.cross (v_axis);
758 
759  // Perform polynomial fit to update point and normal
760  ////////////////////////////////////////////////////
761  num_neighbors = static_cast<int> (nn_indices.size ());
762  order = polynomial_order;
763  if (order > 1)
764  {
765  int nr_coeff = (order + 1) * (order + 2) / 2;
766 
767  if (num_neighbors >= nr_coeff)
768  {
769  // Note: The max_sq_radius parameter is only used if weight_func was not defined
770  double max_sq_radius = 1;
771  if (weight_func == 0)
772  {
773  max_sq_radius = search_radius * search_radius;
774  weight_func = boost::bind (&pcl::MLSResult::computeMLSWeight, this, _1, max_sq_radius);
775  }
776 
777  // Allocate matrices and vectors to hold the data used for the polynomial fit
778  Eigen::VectorXd weight_vec (num_neighbors);
779  Eigen::MatrixXd P (nr_coeff, num_neighbors);
780  Eigen::VectorXd f_vec (num_neighbors);
781  Eigen::MatrixXd P_weight; // size will be (nr_coeff_, nn_indices.size ());
782  Eigen::MatrixXd P_weight_Pt (nr_coeff, nr_coeff);
783 
784  // Update neighborhood, since point was projected, and computing relative
785  // positions. Note updating only distances for the weights for speed
786  std::vector<Eigen::Vector3d, Eigen::aligned_allocator<Eigen::Vector3d> > de_meaned (num_neighbors);
787  for (size_t ni = 0; ni < (size_t) num_neighbors; ++ni)
788  {
789  de_meaned[ni][0] = cloud.points[nn_indices[ni]].x - mean[0];
790  de_meaned[ni][1] = cloud.points[nn_indices[ni]].y - mean[1];
791  de_meaned[ni][2] = cloud.points[nn_indices[ni]].z - mean[2];
792  weight_vec (ni) = weight_func (de_meaned[ni].dot (de_meaned[ni]));
793  }
794 
795  // Go through neighbors, transform them in the local coordinate system,
796  // save height and the evaluation of the polynome's terms
797  double u_coord, v_coord, u_pow, v_pow;
798  for (size_t ni = 0; ni < (size_t) num_neighbors; ++ni)
799  {
800  // Transforming coordinates
801  u_coord = de_meaned[ni].dot (u_axis);
802  v_coord = de_meaned[ni].dot (v_axis);
803  f_vec (ni) = de_meaned[ni].dot (plane_normal);
804 
805  // Compute the polynomial's terms at the current point
806  int j = 0;
807  u_pow = 1;
808  for (int ui = 0; ui <= order; ++ui)
809  {
810  v_pow = 1;
811  for (int vi = 0; vi <= order - ui; ++vi)
812  {
813  P (j++, ni) = u_pow * v_pow;
814  v_pow *= v_coord;
815  }
816  u_pow *= u_coord;
817  }
818  }
819 
820  // Computing coefficients
821  P_weight = P * weight_vec.asDiagonal ();
822  P_weight_Pt = P_weight * P.transpose ();
823  c_vec = P_weight * f_vec;
824  P_weight_Pt.llt ().solveInPlace (c_vec);
825  }
826  }
827 }
828 
829 //////////////////////////////////////////////////////////////////////////////////////////////
830 template <typename PointInT, typename PointOutT>
832  IndicesPtr &indices,
833  float voxel_size) :
834  voxel_grid_ (), bounding_min_ (), bounding_max_ (), data_size_ (), voxel_size_ (voxel_size)
835 {
836  pcl::getMinMax3D (*cloud, *indices, bounding_min_, bounding_max_);
837 
838  Eigen::Vector4f bounding_box_size = bounding_max_ - bounding_min_;
839  double max_size = (std::max) ((std::max)(bounding_box_size.x (), bounding_box_size.y ()), bounding_box_size.z ());
840  // Put initial cloud in voxel grid
841  data_size_ = static_cast<uint64_t> (1.5 * max_size / voxel_size_);
842  for (unsigned int i = 0; i < indices->size (); ++i)
843  if (pcl_isfinite (cloud->points[(*indices)[i]].x))
844  {
845  Eigen::Vector3i pos;
846  getCellIndex (cloud->points[(*indices)[i]].getVector3fMap (), pos);
847 
848  uint64_t index_1d;
849  getIndexIn1D (pos, index_1d);
850  Leaf leaf;
851  voxel_grid_[index_1d] = leaf;
852  }
853 }
854 
855 //////////////////////////////////////////////////////////////////////////////////////////////
856 template <typename PointInT, typename PointOutT> void
858 {
859  HashMap new_voxel_grid = voxel_grid_;
860  for (typename MLSVoxelGrid::HashMap::iterator m_it = voxel_grid_.begin (); m_it != voxel_grid_.end (); ++m_it)
861  {
862  Eigen::Vector3i index;
863  getIndexIn3D (m_it->first, index);
864 
865  // Now dilate all of its voxels
866  for (int x = -1; x <= 1; ++x)
867  for (int y = -1; y <= 1; ++y)
868  for (int z = -1; z <= 1; ++z)
869  if (x != 0 || y != 0 || z != 0)
870  {
871  Eigen::Vector3i new_index;
872  new_index = index + Eigen::Vector3i (x, y, z);
873 
874  uint64_t index_1d;
875  getIndexIn1D (new_index, index_1d);
876  Leaf leaf;
877  new_voxel_grid[index_1d] = leaf;
878  }
879  }
880  voxel_grid_ = new_voxel_grid;
881 }
882 
883 
884 /////////////////////////////////////////////////////////////////////////////////////////////
885 template <typename PointInT, typename PointOutT> void
887  PointOutT &point_out) const
888 {
889  PointOutT temp = point_out;
890  copyPoint (point_in, point_out);
891  point_out.x = temp.x;
892  point_out.y = temp.y;
893  point_out.z = temp.z;
894 }
895 
896 #define PCL_INSTANTIATE_MovingLeastSquares(T,OutT) template class PCL_EXPORTS pcl::MovingLeastSquares<T,OutT>;
897 #define PCL_INSTANTIATE_MovingLeastSquaresOMP(T,OutT) template class PCL_EXPORTS pcl::MovingLeastSquaresOMP<T,OutT>;
898 
899 #endif // PCL_SURFACE_IMPL_MLS_H_
A point structure representing normal coordinates and the surface curvature estimate.
Data structure used to store the MLS polynomial partial derivatives.
Definition: mls.h:68
bool valid
If True, the mls results data is valid, otherwise False.
Definition: mls.h:222
Eigen::Vector3d plane_normal
The normal of the local plane of the query point.
Definition: mls.h:215
double z_u
The partial derivative dz/du.
Definition: mls.h:71
MLSResult()
Definition: mls.h:91
search::KdTree is a wrapper class which inherits the pcl::KdTree class for performing search function...
Definition: kdtree.h:62
A helper functor that can set a specific value in a field if the field exists.
Definition: point_traits.h:298
std::vector< PointCloud< PointT >, Eigen::aligned_allocator< PointCloud< PointT > > > CloudVectorType
Definition: point_cloud.h:427
size_t size() const
Definition: point_cloud.h:448
std::vector< PointT, Eigen::aligned_allocator< PointT > > points
The point data.
Definition: point_cloud.h:410
Eigen::VectorXd c_vec
The polynomial coefficients Example: z = c_vec[0] + c_vec[1]*v + c_vec[2]*v^2 + c_vec[3]*u + c_vec[4]...
Definition: mls.h:218
struct pcl::PointXYZIEdge EIGEN_ALIGN16
double u
The u-coordinate of the projected point in local MLS frame.
Definition: mls.h:83
virtual void performProcessing(PointCloudOut &output)
Abstract surface reconstruction method.
Definition: mls.hpp:281
MLSProjectionResults projectPointOrthogonalToPolynomialSurface(const double u, const double v, const double w) const
Project a point orthogonal to the polynomial surface.
Definition: mls.hpp:565
boost::shared_ptr< std::vector< int > > IndicesPtr
Definition: pcl_base.h:60
MLSProjectionResults projectPointToMLSPlane(const double u, const double v) const
Project a point onto the MLS plane.
Definition: mls.hpp:630
ProjectionMethod
Definition: mls.h:60
double z_vv
The partial derivative d^2z/dv^2.
Definition: mls.h:74
iterator end()
Definition: point_cloud.h:443
Eigen::Vector4f bounding_max_
Definition: mls.h:650
std::vector< int > indices
Definition: PointIndices.h:19
void push_back(const PointT &pt)
Insert a new point in the cloud, at the end of the container.
Definition: point_cloud.h:480
double z_uv
The partial derivative d^2z/dudv.
Definition: mls.h:75
void computeMLSSurface(const pcl::PointCloud< PointT > &cloud, int index, const std::vector< int > &nn_indices, double search_radius, int polynomial_order=2, boost::function< double(const double)> weight_func=0)
Smooth a given point and its neighborghood using Moving Least Squares.
Definition: mls.hpp:718
Project to the closest point on the polynonomial surface.
Definition: mls.h:64
uint32_t height
The point cloud height (if organized as an image-structure).
Definition: point_cloud.h:415
int order
The order of the polynomial.
Definition: mls.h:221
Eigen::Vector4f bounding_min_
Definition: mls.h:650
double z_uu
The partial derivative d^2z/du^2.
Definition: mls.h:73
double getPolynomialValue(const double u, const double v) const
Calculate the polynomial.
Definition: mls.hpp:465
Data structure used to store the MLS projection results.
Definition: mls.h:79
Eigen::Vector3d point
The projected point.
Definition: mls.h:85
uint32_t width
The point cloud width (if organized as an image-structure).
Definition: point_cloud.h:413
double v
The u-coordinate of the projected point in local MLS frame.
Definition: mls.h:84
double z_v
The partial derivative dz/dv.
Definition: mls.h:72
Eigen::Vector3d normal
The projected point&#39;s normal.
Definition: mls.h:86
MLSProjectionResults projectPoint(const Eigen::Vector3d &pt, ProjectionMethod method, int required_neighbors=0) const
Project a point using the specified method.
Definition: mls.hpp:665
void getIndexIn3D(uint64_t index_1d, Eigen::Vector3i &index_3d) const
Definition: mls.h:623
PolynomialPartialDerivative getPolynomialPartialDerivative(const double u, const double v) const
Calculate the polynomial&#39;s first and second partial derivatives.
Definition: mls.hpp:488
unsigned int computeCovarianceMatrix(const pcl::PointCloud< PointT > &cloud, const Eigen::Matrix< Scalar, 4, 1 > &centroid, Eigen::Matrix< Scalar, 3, 3 > &covariance_matrix)
Compute the 3x3 covariance matrix of a given set of points.
Data structure used to store the results of the MLS fitting.
Definition: mls.h:58
pcl::search::Search< PointInT >::Ptr KdTreePtr
Definition: mls.h:263
int num_neighbors
The number of neighbors used to create the mls surface.
Definition: mls.h:219
void performUpsampling(PointCloudOut &output)
Perform upsampling for the distinct-cloud and voxel-grid methods.
Definition: mls.hpp:365
void getMinMax3D(const pcl::PointCloud< PointT > &cloud, PointT &min_pt, PointT &max_pt)
Get the minimum and maximum values on each of the 3 (x-y-z) dimensions in a given pointcloud...
Definition: common.hpp:242
Eigen::Vector3d u_axis
The axis corresponding to the u-coordinates of the local plane of the query point.
Definition: mls.h:216
Eigen::Vector3d mean
The mean point of all the neighbors.
Definition: mls.h:214
void process(PointCloudOut &output)
Base method for surface reconstruction for all points given in <setInputCloud (), setIndices ()> ...
Definition: mls.hpp:58
Eigen::Vector3d v_axis
The axis corresponding to the v-coordinates of the local plane of the query point.
Definition: mls.h:217
Project to the mls plane.
Definition: mls.h:62
PointCloudIn::ConstPtr PointCloudInConstPtr
Definition: mls.h:273
PointCloud represents the base class in PCL for storing collections of 3D points. ...
Eigen::Vector3d query_point
The query point about which the mls surface was generated.
Definition: mls.h:213
pcl::PCLHeader header
The point cloud header.
Definition: point_cloud.h:407
void eigen33(const Matrix &mat, typename Matrix::Scalar &eigenvalue, Vector &eigenvector)
determines the eigenvector and eigenvalue of the smallest eigenvalue of the symmetric positive semi d...
Definition: eigen.hpp:251
Definition: norms.h:55
A minimalistic implementation of a voxel grid, necessary for the point cloud upsampling.
Definition: mls.h:603
MLSVoxelGrid(PointCloudInConstPtr &cloud, IndicesPtr &indices, float voxel_size)
Definition: mls.hpp:831
void getIndexIn1D(const Eigen::Vector3i &index, uint64_t &index_1d) const
Definition: mls.h:616
void getMLSCoordinates(const Eigen::Vector3d &pt, double &u, double &v, double &w) const
Given a point calculate it&#39;s 3D location in the MLS frame.
Definition: mls.hpp:448
OrganizedNeighbor is a class for optimized nearest neigbhor search in organized point clouds...
Definition: organized.h:62
void getPosition(const uint64_t &index_1d, Eigen::Vector3f &point) const
Definition: mls.h:640
float curvature
The curvature at the query point.
Definition: mls.h:220
iterator begin()
Definition: point_cloud.h:442
MLSProjectionResults projectPointSimpleToPolynomialSurface(const double u, const double v) const
Project a point along the MLS plane normal to the polynomial surface.
Definition: mls.hpp:642
MLSProjectionResults projectQueryPoint(ProjectionMethod method, int required_neighbors=0) const
Project the query point used to generate the mls surface about using the specified method...
Definition: mls.hpp:687
double z
The z component of the polynomial evaluated at z(u, v).
Definition: mls.h:70
unsigned int compute3DCentroid(ConstCloudIterator< PointT > &cloud_iterator, Eigen::Matrix< Scalar, 4, 1 > &centroid)
Compute the 3D (X-Y-Z) centroid of a set of points and return it as a 3D vector.
Definition: centroid.hpp:50
void getCellIndex(const Eigen::Vector3f &p, Eigen::Vector3i &index) const
Definition: mls.h:633
iterator insert(iterator position, const PointT &pt)
Insert a new point in the cloud, given an iterator.
Definition: point_cloud.h:494
void copyMissingFields(const PointInT &point_in, PointOutT &point_out) const
Definition: mls.hpp:886
void addProjectedPointNormal(int index, const Eigen::Vector3d &point, const Eigen::Vector3d &normal, double curvature, PointCloudOut &projected_points, NormalCloud &projected_points_normals, PointIndices &corresponding_input_indices) const
This is a helper function for add projected points.
Definition: mls.hpp:249
void copyPoint(const PointInT &point_in, PointOutT &point_out)
Copy the fields of a source point into a target point.
Definition: copy_point.hpp:138
void computeMLSPointNormal(int index, const std::vector< int > &nn_indices, PointCloudOut &projected_points, NormalCloud &projected_points_normals, PointIndices &corresponding_input_indices, MLSResult &mls_result) const
Smooth a given point and its neighborghood using Moving Least Squares.
Definition: mls.hpp:171
Eigen::Vector2f calculatePrincipleCurvatures(const double u, const double v) const
Calculate the principle curvatures using the polynomial surface.
Definition: mls.hpp:533
std::map< uint64_t, Leaf > HashMap
Definition: mls.h:648