Point Cloud Library (PCL)  1.14.0-dev
sac_model_circle3d.hpp
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38 
39 #ifndef PCL_SAMPLE_CONSENSUS_IMPL_SAC_MODEL_CIRCLE_3D_HPP_
40 #define PCL_SAMPLE_CONSENSUS_IMPL_SAC_MODEL_CIRCLE_3D_HPP_
41 
42 #include <limits>
43 
44 #include <unsupported/Eigen/NonLinearOptimization> // for LevenbergMarquardt
45 #include <pcl/sample_consensus/sac_model_circle3d.h>
46 #include <pcl/common/concatenate.h>
47 
48 //////////////////////////////////////////////////////////////////////////
49 template <typename PointT> bool
51  const Indices &samples) const
52 {
53  if (samples.size () != sample_size_)
54  {
55  PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::isSampleGood] Wrong number of samples (is %lu, should be %lu)!\n", samples.size (), sample_size_);
56  return (false);
57  }
58 
59  // Double precision here follows computeModelCoefficients, which means we
60  // can't use getVector3fMap-accessor to make our lives easier.
61  Eigen::Vector3d p0 ((*input_)[samples[0]].x, (*input_)[samples[0]].y, (*input_)[samples[0]].z);
62  Eigen::Vector3d p1 ((*input_)[samples[1]].x, (*input_)[samples[1]].y, (*input_)[samples[1]].z);
63  Eigen::Vector3d p2 ((*input_)[samples[2]].x, (*input_)[samples[2]].y, (*input_)[samples[2]].z);
64 
65  // Check if the squared norm of the cross-product is non-zero, otherwise
66  // common_helper_vec, which plays an important role in computeModelCoefficients,
67  // would likely be ill-formed.
68  if ((p1 - p0).cross(p1 - p2).squaredNorm() < Eigen::NumTraits<float>::dummy_precision ())
69  {
70  PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::isSampleGood] Sample points too similar or collinear!\n");
71  return (false);
72  }
73 
74  return (true);
75 }
76 
77 //////////////////////////////////////////////////////////////////////////
78 template <typename PointT> bool
79 pcl::SampleConsensusModelCircle3D<PointT>::computeModelCoefficients (const Indices &samples, Eigen::VectorXf &model_coefficients) const
80 {
81  if (samples.size () != sample_size_)
82  {
83  PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::computeModelCoefficients] Invalid set of samples given (%lu)!\n", samples.size ());
84  return (false);
85  }
86 
87  model_coefficients.resize (model_size_); //needing 7 coefficients: centerX, centerY, centerZ, radius, normalX, normalY, normalZ
88 
89  Eigen::Vector3d p0 ((*input_)[samples[0]].x, (*input_)[samples[0]].y, (*input_)[samples[0]].z);
90  Eigen::Vector3d p1 ((*input_)[samples[1]].x, (*input_)[samples[1]].y, (*input_)[samples[1]].z);
91  Eigen::Vector3d p2 ((*input_)[samples[2]].x, (*input_)[samples[2]].y, (*input_)[samples[2]].z);
92 
93 
94  Eigen::Vector3d helper_vec01 = p0 - p1;
95  Eigen::Vector3d helper_vec02 = p0 - p2;
96  Eigen::Vector3d helper_vec10 = p1 - p0;
97  Eigen::Vector3d helper_vec12 = p1 - p2;
98  Eigen::Vector3d helper_vec20 = p2 - p0;
99  Eigen::Vector3d helper_vec21 = p2 - p1;
100 
101  Eigen::Vector3d common_helper_vec = helper_vec01.cross (helper_vec12);
102 
103  // The same check is implemented in isSampleGood, so be sure to look there too
104  // if you find the need to change something here.
105  if (common_helper_vec.squaredNorm() < Eigen::NumTraits<float>::dummy_precision ())
106  {
107  PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::computeModelCoefficients] Sample points too similar or collinear!\n");
108  return (false);
109  }
110 
111  double commonDividend = 2.0 * common_helper_vec.squaredNorm ();
112 
113  double alpha = (helper_vec12.squaredNorm () * helper_vec01.dot (helper_vec02)) / commonDividend;
114  double beta = (helper_vec02.squaredNorm () * helper_vec10.dot (helper_vec12)) / commonDividend;
115  double gamma = (helper_vec01.squaredNorm () * helper_vec20.dot (helper_vec21)) / commonDividend;
116 
117  Eigen::Vector3d circle_center = alpha * p0 + beta * p1 + gamma * p2;
118 
119  Eigen::Vector3d circle_radiusVector = circle_center - p0;
120  double circle_radius = circle_radiusVector.norm ();
121  Eigen::Vector3d circle_normal = common_helper_vec.normalized ();
122 
123  model_coefficients[0] = static_cast<float> (circle_center[0]);
124  model_coefficients[1] = static_cast<float> (circle_center[1]);
125  model_coefficients[2] = static_cast<float> (circle_center[2]);
126  model_coefficients[3] = static_cast<float> (circle_radius);
127  model_coefficients[4] = static_cast<float> (circle_normal[0]);
128  model_coefficients[5] = static_cast<float> (circle_normal[1]);
129  model_coefficients[6] = static_cast<float> (circle_normal[2]);
130 
131  PCL_DEBUG ("[pcl::SampleConsensusModelCircle3D::computeModelCoefficients] Model is (%g,%g,%g,%g,%g,%g,%g).\n",
132  model_coefficients[0], model_coefficients[1], model_coefficients[2], model_coefficients[3],
133  model_coefficients[4], model_coefficients[5], model_coefficients[6]);
134  return (true);
135 }
136 
137 //////////////////////////////////////////////////////////////////////////
138 template <typename PointT> void
139 pcl::SampleConsensusModelCircle3D<PointT>::getDistancesToModel (const Eigen::VectorXf &model_coefficients, std::vector<double> &distances) const
140 {
141  // Check if the model is valid given the user constraints
142  if (!isModelValid (model_coefficients))
143  {
144  distances.clear ();
145  return;
146  }
147  distances.resize (indices_->size ());
148 
149  // Iterate through the 3d points and calculate the distances from them to the sphere
150  for (std::size_t i = 0; i < indices_->size (); ++i)
151  // Calculate the distance from the point to the circle:
152  // 1. calculate intersection point of the plane in which the circle lies and the
153  // line from the sample point with the direction of the plane normal (projected point)
154  // 2. calculate the intersection point of the line from the circle center to the projected point
155  // with the circle
156  // 3. calculate distance from corresponding point on the circle to the sample point
157  {
158  // what i have:
159  // P : Sample Point
160  Eigen::Vector3d P ((*input_)[(*indices_)[i]].x, (*input_)[(*indices_)[i]].y, (*input_)[(*indices_)[i]].z);
161  // C : Circle Center
162  Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
163  // N : Circle (Plane) Normal
164  Eigen::Vector3d N (model_coefficients[4], model_coefficients[5], model_coefficients[6]);
165  // r : Radius
166  double r = model_coefficients[3];
167 
168  Eigen::Vector3d helper_vectorPC = P - C;
169  // 1.1. get line parameter
170  double lambda = (helper_vectorPC.dot (N)) / N.squaredNorm ();
171 
172  // Projected Point on plane
173  Eigen::Vector3d P_proj = P + lambda * N;
174  Eigen::Vector3d helper_vectorP_projC = P_proj - C;
175 
176  // K : Point on Circle
177  Eigen::Vector3d K = C + r * helper_vectorP_projC.normalized ();
178  Eigen::Vector3d distanceVector = P - K;
179 
180  distances[i] = distanceVector.norm ();
181  }
182 }
183 
184 //////////////////////////////////////////////////////////////////////////
185 template <typename PointT> void
187  const Eigen::VectorXf &model_coefficients, const double threshold,
188  Indices &inliers)
189 {
190  // Check if the model is valid given the user constraints
191  if (!isModelValid (model_coefficients))
192  {
193  inliers.clear ();
194  return;
195  }
196  inliers.clear ();
197  inliers.reserve (indices_->size ());
198 
199  const auto squared_threshold = threshold * threshold;
200  // Iterate through the 3d points and calculate the distances from them to the sphere
201  for (std::size_t i = 0; i < indices_->size (); ++i)
202  {
203  // what i have:
204  // P : Sample Point
205  Eigen::Vector3d P ((*input_)[(*indices_)[i]].x, (*input_)[(*indices_)[i]].y, (*input_)[(*indices_)[i]].z);
206  // C : Circle Center
207  Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
208  // N : Circle (Plane) Normal
209  Eigen::Vector3d N (model_coefficients[4], model_coefficients[5], model_coefficients[6]);
210  // r : Radius
211  double r = model_coefficients[3];
212 
213  Eigen::Vector3d helper_vectorPC = P - C;
214  // 1.1. get line parameter
215  double lambda = (-(helper_vectorPC.dot (N))) / N.dot (N);
216  // Projected Point on plane
217  Eigen::Vector3d P_proj = P + lambda * N;
218  Eigen::Vector3d helper_vectorP_projC = P_proj - C;
219 
220  // K : Point on Circle
221  Eigen::Vector3d K = C + r * helper_vectorP_projC.normalized ();
222  Eigen::Vector3d distanceVector = P - K;
223 
224  if (distanceVector.squaredNorm () < squared_threshold)
225  {
226  // Returns the indices of the points whose distances are smaller than the threshold
227  inliers.push_back ((*indices_)[i]);
228  }
229  }
230 }
231 
232 //////////////////////////////////////////////////////////////////////////
233 template <typename PointT> std::size_t
235  const Eigen::VectorXf &model_coefficients, const double threshold) const
236 {
237  // Check if the model is valid given the user constraints
238  if (!isModelValid (model_coefficients))
239  return (0);
240  std::size_t nr_p = 0;
241 
242  const auto squared_threshold = threshold * threshold;
243  // Iterate through the 3d points and calculate the distances from them to the sphere
244  for (std::size_t i = 0; i < indices_->size (); ++i)
245  {
246  // what i have:
247  // P : Sample Point
248  Eigen::Vector3d P ((*input_)[(*indices_)[i]].x, (*input_)[(*indices_)[i]].y, (*input_)[(*indices_)[i]].z);
249  // C : Circle Center
250  Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
251  // N : Circle (Plane) Normal
252  Eigen::Vector3d N (model_coefficients[4], model_coefficients[5], model_coefficients[6]);
253  // r : Radius
254  double r = model_coefficients[3];
255 
256  Eigen::Vector3d helper_vectorPC = P - C;
257  // 1.1. get line parameter
258  double lambda = (-(helper_vectorPC.dot (N))) / N.dot (N);
259 
260  // Projected Point on plane
261  Eigen::Vector3d P_proj = P + lambda * N;
262  Eigen::Vector3d helper_vectorP_projC = P_proj - C;
263 
264  // K : Point on Circle
265  Eigen::Vector3d K = C + r * helper_vectorP_projC.normalized ();
266  Eigen::Vector3d distanceVector = P - K;
267 
268  if (distanceVector.squaredNorm () < squared_threshold)
269  nr_p++;
270  }
271  return (nr_p);
272 }
273 
274 //////////////////////////////////////////////////////////////////////////
275 template <typename PointT> void
277  const Indices &inliers,
278  const Eigen::VectorXf &model_coefficients,
279  Eigen::VectorXf &optimized_coefficients) const
280 {
281  optimized_coefficients = model_coefficients;
282 
283  // Needs a set of valid model coefficients
284  if (!isModelValid (model_coefficients))
285  {
286  PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::optimizeModelCoefficients] Given model is invalid!\n");
287  return;
288  }
289 
290  // Need more than the minimum sample size to make a difference
291  if (inliers.size () <= sample_size_)
292  {
293  PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::optimizeModelCoefficients] Not enough inliers to refine/optimize the model's coefficients (%lu)! Returning the same coefficients.\n", inliers.size ());
294  return;
295  }
296 
297  OptimizationFunctor functor (this, inliers);
298  Eigen::NumericalDiff<OptimizationFunctor> num_diff (functor);
299  Eigen::LevenbergMarquardt<Eigen::NumericalDiff<OptimizationFunctor>, double> lm (num_diff);
300  Eigen::VectorXd coeff;
301  int info = lm.minimize (coeff);
302  for (Eigen::Index i = 0; i < coeff.size (); ++i)
303  optimized_coefficients[i] = static_cast<float> (coeff[i]);
304 
305  // Compute the L2 norm of the residuals
306  PCL_DEBUG ("[pcl::SampleConsensusModelCircle3D::optimizeModelCoefficients] LM solver finished with exit code %i, having a residual norm of %g. \nInitial solution: %g %g %g %g %g %g %g \nFinal solution: %g %g %g %g %g %g %g\n",
307  info, lm.fvec.norm (), model_coefficients[0], model_coefficients[1], model_coefficients[2], model_coefficients[3], model_coefficients[4], model_coefficients[5], model_coefficients[6], optimized_coefficients[0], optimized_coefficients[1], optimized_coefficients[2], optimized_coefficients[3], optimized_coefficients[4], optimized_coefficients[5], optimized_coefficients[6]);
308 }
309 
310 //////////////////////////////////////////////////////////////////////////
311 template <typename PointT> void
313  const Indices &inliers, const Eigen::VectorXf &model_coefficients,
314  PointCloud &projected_points, bool copy_data_fields) const
315 {
316  // Needs a valid set of model coefficients
317  if (!isModelValid (model_coefficients))
318  {
319  PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::projectPoints] Given model is invalid!\n");
320  return;
321  }
322 
323  projected_points.header = input_->header;
324  projected_points.is_dense = input_->is_dense;
325 
326  // Copy all the data fields from the input cloud to the projected one?
327  if (copy_data_fields)
328  {
329  // Allocate enough space and copy the basics
330  projected_points.resize (input_->size ());
331  projected_points.width = input_->width;
332  projected_points.height = input_->height;
333 
334  using FieldList = typename pcl::traits::fieldList<PointT>::type;
335  // Iterate over each point
336  for (std::size_t i = 0; i < projected_points.size (); ++i)
337  // Iterate over each dimension
338  pcl::for_each_type <FieldList> (NdConcatenateFunctor <PointT, PointT> ((*input_)[i], projected_points[i]));
339 
340  // Iterate through the 3d points and calculate the distances from them to the plane
341  for (std::size_t i = 0; i < inliers.size (); ++i)
342  {
343  // what i have:
344  // P : Sample Point
345  Eigen::Vector3d P ((*input_)[inliers[i]].x, (*input_)[inliers[i]].y, (*input_)[inliers[i]].z);
346  // C : Circle Center
347  Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
348  // N : Circle (Plane) Normal
349  Eigen::Vector3d N (model_coefficients[4], model_coefficients[5], model_coefficients[6]);
350  // r : Radius
351  double r = model_coefficients[3];
352 
353  Eigen::Vector3d helper_vectorPC = P - C;
354  // 1.1. get line parameter
355  //float lambda = (helper_vectorPC.dot(N)) / N.squaredNorm() ;
356  double lambda = (-(helper_vectorPC.dot (N))) / N.dot (N);
357  // Projected Point on plane
358  Eigen::Vector3d P_proj = P + lambda * N;
359  Eigen::Vector3d helper_vectorP_projC = P_proj - C;
360 
361  // K : Point on Circle
362  Eigen::Vector3d K = C + r * helper_vectorP_projC.normalized ();
363 
364  projected_points[i].x = static_cast<float> (K[0]);
365  projected_points[i].y = static_cast<float> (K[1]);
366  projected_points[i].z = static_cast<float> (K[2]);
367  }
368  }
369  else
370  {
371  // Allocate enough space and copy the basics
372  projected_points.resize (inliers.size ());
373  projected_points.width = inliers.size ();
374  projected_points.height = 1;
375 
376  using FieldList = typename pcl::traits::fieldList<PointT>::type;
377  // Iterate over each point
378  for (std::size_t i = 0; i < inliers.size (); ++i)
379  // Iterate over each dimension
380  pcl::for_each_type <FieldList> (NdConcatenateFunctor <PointT, PointT> ((*input_)[inliers[i]], projected_points[i]));
381 
382  // Iterate through the 3d points and calculate the distances from them to the plane
383  for (std::size_t i = 0; i < inliers.size (); ++i)
384  {
385  // what i have:
386  // P : Sample Point
387  Eigen::Vector3d P ((*input_)[inliers[i]].x, (*input_)[inliers[i]].y, (*input_)[inliers[i]].z);
388  // C : Circle Center
389  Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
390  // N : Circle (Plane) Normal
391  Eigen::Vector3d N (model_coefficients[4], model_coefficients[5], model_coefficients[6]);
392  // r : Radius
393  double r = model_coefficients[3];
394 
395  Eigen::Vector3d helper_vectorPC = P - C;
396  // 1.1. get line parameter
397  double lambda = (-(helper_vectorPC.dot (N))) / N.dot (N);
398  // Projected Point on plane
399  Eigen::Vector3d P_proj = P + lambda * N;
400  Eigen::Vector3d helper_vectorP_projC = P_proj - C;
401 
402  // K : Point on Circle
403  Eigen::Vector3d K = C + r * helper_vectorP_projC.normalized ();
404 
405  projected_points[i].x = static_cast<float> (K[0]);
406  projected_points[i].y = static_cast<float> (K[1]);
407  projected_points[i].z = static_cast<float> (K[2]);
408  }
409  }
410 }
411 
412 //////////////////////////////////////////////////////////////////////////
413 template <typename PointT> bool
415  const std::set<index_t> &indices,
416  const Eigen::VectorXf &model_coefficients,
417  const double threshold) const
418 {
419  // Needs a valid model coefficients
420  if (!isModelValid (model_coefficients))
421  {
422  PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::doSamplesVerifyModel] Given model is invalid!\n");
423  return (false);
424  }
425 
426  const auto squared_threshold = threshold * threshold;
427  for (const auto &index : indices)
428  {
429  // Calculate the distance from the point to the sphere as the difference between
430  //dist(point,sphere_origin) and sphere_radius
431 
432  // what i have:
433  // P : Sample Point
434  Eigen::Vector3d P ((*input_)[index].x, (*input_)[index].y, (*input_)[index].z);
435  // C : Circle Center
436  Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
437  // N : Circle (Plane) Normal
438  Eigen::Vector3d N (model_coefficients[4], model_coefficients[5], model_coefficients[6]);
439  // r : Radius
440  double r = model_coefficients[3];
441  Eigen::Vector3d helper_vectorPC = P - C;
442  // 1.1. get line parameter
443  double lambda = (-(helper_vectorPC.dot (N))) / N.dot (N);
444  // Projected Point on plane
445  Eigen::Vector3d P_proj = P + lambda * N;
446  Eigen::Vector3d helper_vectorP_projC = P_proj - C;
447 
448  // K : Point on Circle
449  Eigen::Vector3d K = C + r * helper_vectorP_projC.normalized ();
450  Eigen::Vector3d distanceVector = P - K;
451 
452  if (distanceVector.squaredNorm () > squared_threshold)
453  return (false);
454  }
455  return (true);
456 }
457 
458 //////////////////////////////////////////////////////////////////////////
459 template <typename PointT> bool
460 pcl::SampleConsensusModelCircle3D<PointT>::isModelValid (const Eigen::VectorXf &model_coefficients) const
461 {
462  if (!SampleConsensusModel<PointT>::isModelValid (model_coefficients))
463  return (false);
464 
465  if (radius_min_ != std::numeric_limits<double>::lowest() && model_coefficients[3] < radius_min_)
466  {
467  PCL_DEBUG ("[pcl::SampleConsensusModelCircle3D::isModelValid] Radius of circle is too small: should be larger than %g, but is %g.\n",
468  radius_min_, model_coefficients[3]);
469  return (false);
470  }
471  if (radius_max_ != std::numeric_limits<double>::max() && model_coefficients[3] > radius_max_)
472  {
473  PCL_DEBUG ("[pcl::SampleConsensusModelCircle3D::isModelValid] Radius of circle is too big: should be smaller than %g, but is %g.\n",
474  radius_max_, model_coefficients[3]);
475  return (false);
476  }
477 
478  return (true);
479 }
480 
481 #define PCL_INSTANTIATE_SampleConsensusModelCircle3D(T) template class PCL_EXPORTS pcl::SampleConsensusModelCircle3D<T>;
482 
483 #endif // PCL_SAMPLE_CONSENSUS_IMPL_SAC_MODEL_CIRCLE3D_HPP_
484 
PointCloud represents the base class in PCL for storing collections of 3D points.
Definition: point_cloud.h:173
bool is_dense
True if no points are invalid (e.g., have NaN or Inf values in any of their floating point fields).
Definition: point_cloud.h:403
void resize(std::size_t count)
Resizes the container to contain count elements.
Definition: point_cloud.h:462
std::uint32_t width
The point cloud width (if organized as an image-structure).
Definition: point_cloud.h:398
pcl::PCLHeader header
The point cloud header.
Definition: point_cloud.h:392
std::uint32_t height
The point cloud height (if organized as an image-structure).
Definition: point_cloud.h:400
std::size_t size() const
Definition: point_cloud.h:443
bool isModelValid(const Eigen::VectorXf &model_coefficients) const override
Check whether a model is valid given the user constraints.
bool doSamplesVerifyModel(const std::set< index_t > &indices, const Eigen::VectorXf &model_coefficients, const double threshold) const override
Verify whether a subset of indices verifies the given 3d circle model coefficients.
bool isSampleGood(const Indices &samples) const override
Check if a sample of indices results in a good sample of points indices.
void projectPoints(const Indices &inliers, const Eigen::VectorXf &model_coefficients, PointCloud &projected_points, bool copy_data_fields=true) const override
Create a new point cloud with inliers projected onto the 3d circle model.
std::size_t countWithinDistance(const Eigen::VectorXf &model_coefficients, const double threshold) const override
Count all the points which respect the given model coefficients as inliers.
void getDistancesToModel(const Eigen::VectorXf &model_coefficients, std::vector< double > &distances) const override
Compute all distances from the cloud data to a given 3D circle model.
void optimizeModelCoefficients(const Indices &inliers, const Eigen::VectorXf &model_coefficients, Eigen::VectorXf &optimized_coefficients) const override
Recompute the 3d circle coefficients using the given inlier set and return them to the user.
void selectWithinDistance(const Eigen::VectorXf &model_coefficients, const double threshold, Indices &inliers) override
Compute all distances from the cloud data to a given 3D circle model.
bool computeModelCoefficients(const Indices &samples, Eigen::VectorXf &model_coefficients) const override
Check whether the given index samples can form a valid 2D circle model, compute the model coefficient...
SampleConsensusModel represents the base model class.
Definition: sac_model.h:71
@ K
Definition: norms.h:54
IndicesAllocator<> Indices
Type used for indices in PCL.
Definition: types.h:133
Helper functor structure for concatenate.
Definition: concatenate.h:50