Point Cloud Library (PCL)  1.12.0
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 <cfloat> // for DBL_MAX
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  // Get the values at the three points
59  Eigen::Vector3d p0 ((*input_)[samples[0]].x, (*input_)[samples[0]].y, (*input_)[samples[0]].z);
60  Eigen::Vector3d p1 ((*input_)[samples[1]].x, (*input_)[samples[1]].y, (*input_)[samples[1]].z);
61  Eigen::Vector3d p2 ((*input_)[samples[2]].x, (*input_)[samples[2]].y, (*input_)[samples[2]].z);
62 
63  // calculate vectors between points
64  p1 -= p0;
65  p2 -= p0;
66 
67  return (p1.dot (p2) < 0.000001);
68 }
69 
70 //////////////////////////////////////////////////////////////////////////
71 template <typename PointT> bool
72 pcl::SampleConsensusModelCircle3D<PointT>::computeModelCoefficients (const Indices &samples, Eigen::VectorXf &model_coefficients) const
73 {
74  // Need 3 samples
75  if (samples.size () != sample_size_)
76  {
77  PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::computeModelCoefficients] Invalid set of samples given (%lu)!\n", samples.size ());
78  return (false);
79  }
80 
81  model_coefficients.resize (model_size_); //needing 7 coefficients: centerX, centerY, centerZ, radius, normalX, normalY, normalZ
82 
83  Eigen::Vector3d p0 ((*input_)[samples[0]].x, (*input_)[samples[0]].y, (*input_)[samples[0]].z);
84  Eigen::Vector3d p1 ((*input_)[samples[1]].x, (*input_)[samples[1]].y, (*input_)[samples[1]].z);
85  Eigen::Vector3d p2 ((*input_)[samples[2]].x, (*input_)[samples[2]].y, (*input_)[samples[2]].z);
86 
87 
88  Eigen::Vector3d helper_vec01 = p0 - p1;
89  Eigen::Vector3d helper_vec02 = p0 - p2;
90  Eigen::Vector3d helper_vec10 = p1 - p0;
91  Eigen::Vector3d helper_vec12 = p1 - p2;
92  Eigen::Vector3d helper_vec20 = p2 - p0;
93  Eigen::Vector3d helper_vec21 = p2 - p1;
94 
95  Eigen::Vector3d common_helper_vec = helper_vec01.cross (helper_vec12);
96 
97  double commonDividend = 2.0 * common_helper_vec.squaredNorm ();
98 
99  double alpha = (helper_vec12.squaredNorm () * helper_vec01.dot (helper_vec02)) / commonDividend;
100  double beta = (helper_vec02.squaredNorm () * helper_vec10.dot (helper_vec12)) / commonDividend;
101  double gamma = (helper_vec01.squaredNorm () * helper_vec20.dot (helper_vec21)) / commonDividend;
102 
103  Eigen::Vector3d circle_center = alpha * p0 + beta * p1 + gamma * p2;
104 
105  Eigen::Vector3d circle_radiusVector = circle_center - p0;
106  double circle_radius = circle_radiusVector.norm ();
107  Eigen::Vector3d circle_normal = common_helper_vec.normalized ();
108 
109  model_coefficients[0] = static_cast<float> (circle_center[0]);
110  model_coefficients[1] = static_cast<float> (circle_center[1]);
111  model_coefficients[2] = static_cast<float> (circle_center[2]);
112  model_coefficients[3] = static_cast<float> (circle_radius);
113  model_coefficients[4] = static_cast<float> (circle_normal[0]);
114  model_coefficients[5] = static_cast<float> (circle_normal[1]);
115  model_coefficients[6] = static_cast<float> (circle_normal[2]);
116 
117  PCL_DEBUG ("[pcl::SampleConsensusModelCircle3D::computeModelCoefficients] Model is (%g,%g,%g,%g,%g,%g,%g).\n",
118  model_coefficients[0], model_coefficients[1], model_coefficients[2], model_coefficients[3],
119  model_coefficients[4], model_coefficients[5], model_coefficients[6]);
120  return (true);
121 }
122 
123 //////////////////////////////////////////////////////////////////////////
124 template <typename PointT> void
125 pcl::SampleConsensusModelCircle3D<PointT>::getDistancesToModel (const Eigen::VectorXf &model_coefficients, std::vector<double> &distances) const
126 {
127  // Check if the model is valid given the user constraints
128  if (!isModelValid (model_coefficients))
129  {
130  distances.clear ();
131  return;
132  }
133  distances.resize (indices_->size ());
134 
135  // Iterate through the 3d points and calculate the distances from them to the sphere
136  for (std::size_t i = 0; i < indices_->size (); ++i)
137  // Calculate the distance from the point to the circle:
138  // 1. calculate intersection point of the plane in which the circle lies and the
139  // line from the sample point with the direction of the plane normal (projected point)
140  // 2. calculate the intersection point of the line from the circle center to the projected point
141  // with the circle
142  // 3. calculate distance from corresponding point on the circle to the sample point
143  {
144  // what i have:
145  // P : Sample Point
146  Eigen::Vector3d P ((*input_)[(*indices_)[i]].x, (*input_)[(*indices_)[i]].y, (*input_)[(*indices_)[i]].z);
147  // C : Circle Center
148  Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
149  // N : Circle (Plane) Normal
150  Eigen::Vector3d N (model_coefficients[4], model_coefficients[5], model_coefficients[6]);
151  // r : Radius
152  double r = model_coefficients[3];
153 
154  Eigen::Vector3d helper_vectorPC = P - C;
155  // 1.1. get line parameter
156  double lambda = (helper_vectorPC.dot (N)) / N.squaredNorm ();
157 
158  // Projected Point on plane
159  Eigen::Vector3d P_proj = P + lambda * N;
160  Eigen::Vector3d helper_vectorP_projC = P_proj - C;
161 
162  // K : Point on Circle
163  Eigen::Vector3d K = C + r * helper_vectorP_projC.normalized ();
164  Eigen::Vector3d distanceVector = P - K;
165 
166  distances[i] = distanceVector.norm ();
167  }
168 }
169 
170 //////////////////////////////////////////////////////////////////////////
171 template <typename PointT> void
173  const Eigen::VectorXf &model_coefficients, const double threshold,
174  Indices &inliers)
175 {
176  // Check if the model is valid given the user constraints
177  if (!isModelValid (model_coefficients))
178  {
179  inliers.clear ();
180  return;
181  }
182  inliers.clear ();
183  inliers.reserve (indices_->size ());
184 
185  const auto squared_threshold = threshold * threshold;
186  // Iterate through the 3d points and calculate the distances from them to the sphere
187  for (std::size_t i = 0; i < indices_->size (); ++i)
188  {
189  // what i have:
190  // P : Sample Point
191  Eigen::Vector3d P ((*input_)[(*indices_)[i]].x, (*input_)[(*indices_)[i]].y, (*input_)[(*indices_)[i]].z);
192  // C : Circle Center
193  Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
194  // N : Circle (Plane) Normal
195  Eigen::Vector3d N (model_coefficients[4], model_coefficients[5], model_coefficients[6]);
196  // r : Radius
197  double r = model_coefficients[3];
198 
199  Eigen::Vector3d helper_vectorPC = P - C;
200  // 1.1. get line parameter
201  double lambda = (-(helper_vectorPC.dot (N))) / N.dot (N);
202  // Projected Point on plane
203  Eigen::Vector3d P_proj = P + lambda * N;
204  Eigen::Vector3d helper_vectorP_projC = P_proj - C;
205 
206  // K : Point on Circle
207  Eigen::Vector3d K = C + r * helper_vectorP_projC.normalized ();
208  Eigen::Vector3d distanceVector = P - K;
209 
210  if (distanceVector.squaredNorm () < squared_threshold)
211  {
212  // Returns the indices of the points whose distances are smaller than the threshold
213  inliers.push_back ((*indices_)[i]);
214  }
215  }
216 }
217 
218 //////////////////////////////////////////////////////////////////////////
219 template <typename PointT> std::size_t
221  const Eigen::VectorXf &model_coefficients, const double threshold) const
222 {
223  // Check if the model is valid given the user constraints
224  if (!isModelValid (model_coefficients))
225  return (0);
226  std::size_t nr_p = 0;
227 
228  const auto squared_threshold = threshold * threshold;
229  // Iterate through the 3d points and calculate the distances from them to the sphere
230  for (std::size_t i = 0; i < indices_->size (); ++i)
231  {
232  // what i have:
233  // P : Sample Point
234  Eigen::Vector3d P ((*input_)[(*indices_)[i]].x, (*input_)[(*indices_)[i]].y, (*input_)[(*indices_)[i]].z);
235  // C : Circle Center
236  Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
237  // N : Circle (Plane) Normal
238  Eigen::Vector3d N (model_coefficients[4], model_coefficients[5], model_coefficients[6]);
239  // r : Radius
240  double r = model_coefficients[3];
241 
242  Eigen::Vector3d helper_vectorPC = P - C;
243  // 1.1. get line parameter
244  double lambda = (-(helper_vectorPC.dot (N))) / N.dot (N);
245 
246  // Projected Point on plane
247  Eigen::Vector3d P_proj = P + lambda * N;
248  Eigen::Vector3d helper_vectorP_projC = P_proj - C;
249 
250  // K : Point on Circle
251  Eigen::Vector3d K = C + r * helper_vectorP_projC.normalized ();
252  Eigen::Vector3d distanceVector = P - K;
253 
254  if (distanceVector.squaredNorm () < squared_threshold)
255  nr_p++;
256  }
257  return (nr_p);
258 }
259 
260 //////////////////////////////////////////////////////////////////////////
261 template <typename PointT> void
263  const Indices &inliers,
264  const Eigen::VectorXf &model_coefficients,
265  Eigen::VectorXf &optimized_coefficients) const
266 {
267  optimized_coefficients = model_coefficients;
268 
269  // Needs a set of valid model coefficients
270  if (!isModelValid (model_coefficients))
271  {
272  PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::optimizeModelCoefficients] Given model is invalid!\n");
273  return;
274  }
275 
276  // Need more than the minimum sample size to make a difference
277  if (inliers.size () <= sample_size_)
278  {
279  PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::optimizeModelCoefficients] Not enough inliers to refine/optimize the model's coefficients (%lu)! Returning the same coefficients.\n", inliers.size ());
280  return;
281  }
282 
283  OptimizationFunctor functor (this, inliers);
284  Eigen::NumericalDiff<OptimizationFunctor> num_diff (functor);
285  Eigen::LevenbergMarquardt<Eigen::NumericalDiff<OptimizationFunctor>, double> lm (num_diff);
286  Eigen::VectorXd coeff;
287  int info = lm.minimize (coeff);
288  for (Eigen::Index i = 0; i < coeff.size (); ++i)
289  optimized_coefficients[i] = static_cast<float> (coeff[i]);
290 
291  // Compute the L2 norm of the residuals
292  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",
293  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]);
294 }
295 
296 //////////////////////////////////////////////////////////////////////////
297 template <typename PointT> void
299  const Indices &inliers, const Eigen::VectorXf &model_coefficients,
300  PointCloud &projected_points, bool copy_data_fields) const
301 {
302  // Needs a valid set of model coefficients
303  if (!isModelValid (model_coefficients))
304  {
305  PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::projectPoints] Given model is invalid!\n");
306  return;
307  }
308 
309  projected_points.header = input_->header;
310  projected_points.is_dense = input_->is_dense;
311 
312  // Copy all the data fields from the input cloud to the projected one?
313  if (copy_data_fields)
314  {
315  // Allocate enough space and copy the basics
316  projected_points.resize (input_->size ());
317  projected_points.width = input_->width;
318  projected_points.height = input_->height;
319 
320  using FieldList = typename pcl::traits::fieldList<PointT>::type;
321  // Iterate over each point
322  for (std::size_t i = 0; i < projected_points.size (); ++i)
323  // Iterate over each dimension
324  pcl::for_each_type <FieldList> (NdConcatenateFunctor <PointT, PointT> ((*input_)[i], projected_points[i]));
325 
326  // Iterate through the 3d points and calculate the distances from them to the plane
327  for (std::size_t i = 0; i < inliers.size (); ++i)
328  {
329  // what i have:
330  // P : Sample Point
331  Eigen::Vector3d P ((*input_)[inliers[i]].x, (*input_)[inliers[i]].y, (*input_)[inliers[i]].z);
332  // C : Circle Center
333  Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
334  // N : Circle (Plane) Normal
335  Eigen::Vector3d N (model_coefficients[4], model_coefficients[5], model_coefficients[6]);
336  // r : Radius
337  double r = model_coefficients[3];
338 
339  Eigen::Vector3d helper_vectorPC = P - C;
340  // 1.1. get line parameter
341  //float lambda = (helper_vectorPC.dot(N)) / N.squaredNorm() ;
342  double lambda = (-(helper_vectorPC.dot (N))) / N.dot (N);
343  // Projected Point on plane
344  Eigen::Vector3d P_proj = P + lambda * N;
345  Eigen::Vector3d helper_vectorP_projC = P_proj - C;
346 
347  // K : Point on Circle
348  Eigen::Vector3d K = C + r * helper_vectorP_projC.normalized ();
349 
350  projected_points[i].x = static_cast<float> (K[0]);
351  projected_points[i].y = static_cast<float> (K[1]);
352  projected_points[i].z = static_cast<float> (K[2]);
353  }
354  }
355  else
356  {
357  // Allocate enough space and copy the basics
358  projected_points.resize (inliers.size ());
359  projected_points.width = inliers.size ();
360  projected_points.height = 1;
361 
362  using FieldList = typename pcl::traits::fieldList<PointT>::type;
363  // Iterate over each point
364  for (std::size_t i = 0; i < inliers.size (); ++i)
365  // Iterate over each dimension
366  pcl::for_each_type <FieldList> (NdConcatenateFunctor <PointT, PointT> ((*input_)[inliers[i]], projected_points[i]));
367 
368  // Iterate through the 3d points and calculate the distances from them to the plane
369  for (std::size_t i = 0; i < inliers.size (); ++i)
370  {
371  // what i have:
372  // P : Sample Point
373  Eigen::Vector3d P ((*input_)[inliers[i]].x, (*input_)[inliers[i]].y, (*input_)[inliers[i]].z);
374  // C : Circle Center
375  Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
376  // N : Circle (Plane) Normal
377  Eigen::Vector3d N (model_coefficients[4], model_coefficients[5], model_coefficients[6]);
378  // r : Radius
379  double r = model_coefficients[3];
380 
381  Eigen::Vector3d helper_vectorPC = P - C;
382  // 1.1. get line parameter
383  double lambda = (-(helper_vectorPC.dot (N))) / N.dot (N);
384  // Projected Point on plane
385  Eigen::Vector3d P_proj = P + lambda * N;
386  Eigen::Vector3d helper_vectorP_projC = P_proj - C;
387 
388  // K : Point on Circle
389  Eigen::Vector3d K = C + r * helper_vectorP_projC.normalized ();
390 
391  projected_points[i].x = static_cast<float> (K[0]);
392  projected_points[i].y = static_cast<float> (K[1]);
393  projected_points[i].z = static_cast<float> (K[2]);
394  }
395  }
396 }
397 
398 //////////////////////////////////////////////////////////////////////////
399 template <typename PointT> bool
401  const std::set<index_t> &indices,
402  const Eigen::VectorXf &model_coefficients,
403  const double threshold) const
404 {
405  // Needs a valid model coefficients
406  if (!isModelValid (model_coefficients))
407  {
408  PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::doSamplesVerifyModel] Given model is invalid!\n");
409  return (false);
410  }
411 
412  const auto squared_threshold = threshold * threshold;
413  for (const auto &index : indices)
414  {
415  // Calculate the distance from the point to the sphere as the difference between
416  //dist(point,sphere_origin) and sphere_radius
417 
418  // what i have:
419  // P : Sample Point
420  Eigen::Vector3d P ((*input_)[index].x, (*input_)[index].y, (*input_)[index].z);
421  // C : Circle Center
422  Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
423  // N : Circle (Plane) Normal
424  Eigen::Vector3d N (model_coefficients[4], model_coefficients[5], model_coefficients[6]);
425  // r : Radius
426  double r = model_coefficients[3];
427  Eigen::Vector3d helper_vectorPC = P - C;
428  // 1.1. get line parameter
429  double lambda = (-(helper_vectorPC.dot (N))) / N.dot (N);
430  // Projected Point on plane
431  Eigen::Vector3d P_proj = P + lambda * N;
432  Eigen::Vector3d helper_vectorP_projC = P_proj - C;
433 
434  // K : Point on Circle
435  Eigen::Vector3d K = C + r * helper_vectorP_projC.normalized ();
436  Eigen::Vector3d distanceVector = P - K;
437 
438  if (distanceVector.squaredNorm () > squared_threshold)
439  return (false);
440  }
441  return (true);
442 }
443 
444 //////////////////////////////////////////////////////////////////////////
445 template <typename PointT> bool
446 pcl::SampleConsensusModelCircle3D<PointT>::isModelValid (const Eigen::VectorXf &model_coefficients) const
447 {
448  if (!SampleConsensusModel<PointT>::isModelValid (model_coefficients))
449  return (false);
450 
451  if (radius_min_ != -DBL_MAX && model_coefficients[3] < radius_min_)
452  {
453  PCL_DEBUG ("[pcl::SampleConsensusModelCircle3D::isModelValid] Radius of circle is too small: should be larger than %g, but is %g.\n",
454  radius_min_, model_coefficients[3]);
455  return (false);
456  }
457  if (radius_max_ != DBL_MAX && model_coefficients[3] > radius_max_)
458  {
459  PCL_DEBUG ("[pcl::SampleConsensusModelCircle3D::isModelValid] Radius of circle is too big: should be smaller than %g, but is %g.\n",
460  radius_max_, model_coefficients[3]);
461  return (false);
462  }
463 
464  return (true);
465 }
466 
467 #define PCL_INSTANTIATE_SampleConsensusModelCircle3D(T) template class PCL_EXPORTS pcl::SampleConsensusModelCircle3D<T>;
468 
469 #endif // PCL_SAMPLE_CONSENSUS_IMPL_SAC_MODEL_CIRCLE3D_HPP_
470 
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:70
@ 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