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sac_model_circle3d.hpp
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#ifndef PCL_SAMPLE_CONSENSUS_IMPL_SAC_MODEL_CIRCLE_3D_HPP_
#define PCL_SAMPLE_CONSENSUS_IMPL_SAC_MODEL_CIRCLE_3D_HPP_
#include <limits>
#include <unsupported/Eigen/NonLinearOptimization> // for LevenbergMarquardt
#include <pcl/sample_consensus/sac_model_circle3d.h>
#include <pcl/common/concatenate.h>
//////////////////////////////////////////////////////////////////////////
template <typename PointT> bool
pcl::SampleConsensusModelCircle3D<PointT>::isSampleGood (
const Indices &samples) const
{
if (samples.size () != sample_size_)
{
PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::isSampleGood] Wrong number of samples (is %lu, should be %lu)!\n", samples.size (), sample_size_);
return (false);
}
// Double precision here follows computeModelCoefficients, which means we
// can't use getVector3fMap-accessor to make our lives easier.
Eigen::Vector3d p0 ((*input_)[samples[0]].x, (*input_)[samples[0]].y, (*input_)[samples[0]].z);
Eigen::Vector3d p1 ((*input_)[samples[1]].x, (*input_)[samples[1]].y, (*input_)[samples[1]].z);
Eigen::Vector3d p2 ((*input_)[samples[2]].x, (*input_)[samples[2]].y, (*input_)[samples[2]].z);
// Check if the squared norm of the cross-product is non-zero, otherwise
// common_helper_vec, which plays an important role in computeModelCoefficients,
// would likely be ill-formed.
if ((p1 - p0).cross(p1 - p2).squaredNorm() < Eigen::NumTraits<float>::dummy_precision ())
{
PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::isSampleGood] Sample points too similar or collinear!\n");
return (false);
}
return (true);
}
//////////////////////////////////////////////////////////////////////////
template <typename PointT> bool
pcl::SampleConsensusModelCircle3D<PointT>::computeModelCoefficients (const Indices &samples, Eigen::VectorXf &model_coefficients) const
{
if (samples.size () != sample_size_)
{
PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::computeModelCoefficients] Invalid set of samples given (%lu)!\n", samples.size ());
return (false);
}
model_coefficients.resize (model_size_); //needing 7 coefficients: centerX, centerY, centerZ, radius, normalX, normalY, normalZ
Eigen::Vector3d p0 ((*input_)[samples[0]].x, (*input_)[samples[0]].y, (*input_)[samples[0]].z);
Eigen::Vector3d p1 ((*input_)[samples[1]].x, (*input_)[samples[1]].y, (*input_)[samples[1]].z);
Eigen::Vector3d p2 ((*input_)[samples[2]].x, (*input_)[samples[2]].y, (*input_)[samples[2]].z);
Eigen::Vector3d helper_vec01 = p0 - p1;
Eigen::Vector3d helper_vec02 = p0 - p2;
Eigen::Vector3d helper_vec10 = p1 - p0;
Eigen::Vector3d helper_vec12 = p1 - p2;
Eigen::Vector3d helper_vec20 = p2 - p0;
Eigen::Vector3d helper_vec21 = p2 - p1;
Eigen::Vector3d common_helper_vec = helper_vec01.cross (helper_vec12);
// The same check is implemented in isSampleGood, so be sure to look there too
// if you find the need to change something here.
if (common_helper_vec.squaredNorm() < Eigen::NumTraits<float>::dummy_precision ())
{
PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::computeModelCoefficients] Sample points too similar or collinear!\n");
return (false);
}
double commonDividend = 2.0 * common_helper_vec.squaredNorm ();
double alpha = (helper_vec12.squaredNorm () * helper_vec01.dot (helper_vec02)) / commonDividend;
double beta = (helper_vec02.squaredNorm () * helper_vec10.dot (helper_vec12)) / commonDividend;
double gamma = (helper_vec01.squaredNorm () * helper_vec20.dot (helper_vec21)) / commonDividend;
Eigen::Vector3d circle_center = alpha * p0 + beta * p1 + gamma * p2;
Eigen::Vector3d circle_radiusVector = circle_center - p0;
double circle_radius = circle_radiusVector.norm ();
Eigen::Vector3d circle_normal = common_helper_vec.normalized ();
model_coefficients[0] = static_cast<float> (circle_center[0]);
model_coefficients[1] = static_cast<float> (circle_center[1]);
model_coefficients[2] = static_cast<float> (circle_center[2]);
model_coefficients[3] = static_cast<float> (circle_radius);
model_coefficients[4] = static_cast<float> (circle_normal[0]);
model_coefficients[5] = static_cast<float> (circle_normal[1]);
model_coefficients[6] = static_cast<float> (circle_normal[2]);
PCL_DEBUG ("[pcl::SampleConsensusModelCircle3D::computeModelCoefficients] Model is (%g,%g,%g,%g,%g,%g,%g).\n",
model_coefficients[0], model_coefficients[1], model_coefficients[2], model_coefficients[3],
model_coefficients[4], model_coefficients[5], model_coefficients[6]);
return (true);
}
//////////////////////////////////////////////////////////////////////////
template <typename PointT> void
pcl::SampleConsensusModelCircle3D<PointT>::getDistancesToModel (const Eigen::VectorXf &model_coefficients, std::vector<double> &distances) const
{
// Check if the model is valid given the user constraints
if (!isModelValid (model_coefficients))
{
distances.clear ();
return;
}
distances.resize (indices_->size ());
// Iterate through the 3d points and calculate the distances from them to the sphere
for (std::size_t i = 0; i < indices_->size (); ++i)
// Calculate the distance from the point to the circle:
// 1. calculate intersection point of the plane in which the circle lies and the
// line from the sample point with the direction of the plane normal (projected point)
// 2. calculate the intersection point of the line from the circle center to the projected point
// with the circle
// 3. calculate distance from corresponding point on the circle to the sample point
{
// what i have:
// P : Sample Point
Eigen::Vector3d P ((*input_)[(*indices_)[i]].x, (*input_)[(*indices_)[i]].y, (*input_)[(*indices_)[i]].z);
// C : Circle Center
Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
// N : Circle (Plane) Normal
Eigen::Vector3d N (model_coefficients[4], model_coefficients[5], model_coefficients[6]);
// r : Radius
double r = model_coefficients[3];
Eigen::Vector3d helper_vectorPC = P - C;
// 1.1. get line parameter
double lambda = (helper_vectorPC.dot (N)) / N.squaredNorm ();
// Projected Point on plane
Eigen::Vector3d P_proj = P + lambda * N;
Eigen::Vector3d helper_vectorP_projC = P_proj - C;
// K : Point on Circle
Eigen::Vector3d K = C + r * helper_vectorP_projC.normalized ();
Eigen::Vector3d distanceVector = P - K;
distances[i] = distanceVector.norm ();
}
}
//////////////////////////////////////////////////////////////////////////
template <typename PointT> void
pcl::SampleConsensusModelCircle3D<PointT>::selectWithinDistance (
const Eigen::VectorXf &model_coefficients, const double threshold,
Indices &inliers)
{
// Check if the model is valid given the user constraints
if (!isModelValid (model_coefficients))
{
inliers.clear ();
return;
}
inliers.clear ();
inliers.reserve (indices_->size ());
const auto squared_threshold = threshold * threshold;
// Iterate through the 3d points and calculate the distances from them to the sphere
for (std::size_t i = 0; i < indices_->size (); ++i)
{
// what i have:
// P : Sample Point
Eigen::Vector3d P ((*input_)[(*indices_)[i]].x, (*input_)[(*indices_)[i]].y, (*input_)[(*indices_)[i]].z);
// C : Circle Center
Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
// N : Circle (Plane) Normal
Eigen::Vector3d N (model_coefficients[4], model_coefficients[5], model_coefficients[6]);
// r : Radius
double r = model_coefficients[3];
Eigen::Vector3d helper_vectorPC = P - C;
// 1.1. get line parameter
double lambda = (-(helper_vectorPC.dot (N))) / N.dot (N);
// Projected Point on plane
Eigen::Vector3d P_proj = P + lambda * N;
Eigen::Vector3d helper_vectorP_projC = P_proj - C;
// K : Point on Circle
Eigen::Vector3d K = C + r * helper_vectorP_projC.normalized ();
Eigen::Vector3d distanceVector = P - K;
if (distanceVector.squaredNorm () < squared_threshold)
{
// Returns the indices of the points whose distances are smaller than the threshold
inliers.push_back ((*indices_)[i]);
}
}
}
//////////////////////////////////////////////////////////////////////////
template <typename PointT> std::size_t
pcl::SampleConsensusModelCircle3D<PointT>::countWithinDistance (
const Eigen::VectorXf &model_coefficients, const double threshold) const
{
// Check if the model is valid given the user constraints
if (!isModelValid (model_coefficients))
return (0);
std::size_t nr_p = 0;
const auto squared_threshold = threshold * threshold;
// Iterate through the 3d points and calculate the distances from them to the sphere
for (std::size_t i = 0; i < indices_->size (); ++i)
{
// what i have:
// P : Sample Point
Eigen::Vector3d P ((*input_)[(*indices_)[i]].x, (*input_)[(*indices_)[i]].y, (*input_)[(*indices_)[i]].z);
// C : Circle Center
Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
// N : Circle (Plane) Normal
Eigen::Vector3d N (model_coefficients[4], model_coefficients[5], model_coefficients[6]);
// r : Radius
double r = model_coefficients[3];
Eigen::Vector3d helper_vectorPC = P - C;
// 1.1. get line parameter
double lambda = (-(helper_vectorPC.dot (N))) / N.dot (N);
// Projected Point on plane
Eigen::Vector3d P_proj = P + lambda * N;
Eigen::Vector3d helper_vectorP_projC = P_proj - C;
// K : Point on Circle
Eigen::Vector3d K = C + r * helper_vectorP_projC.normalized ();
Eigen::Vector3d distanceVector = P - K;
if (distanceVector.squaredNorm () < squared_threshold)
nr_p++;
}
return (nr_p);
}
//////////////////////////////////////////////////////////////////////////
template <typename PointT> void
pcl::SampleConsensusModelCircle3D<PointT>::optimizeModelCoefficients (
const Indices &inliers,
const Eigen::VectorXf &model_coefficients,
Eigen::VectorXf &optimized_coefficients) const
{
optimized_coefficients = model_coefficients;
// Needs a set of valid model coefficients
if (!isModelValid (model_coefficients))
{
PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::optimizeModelCoefficients] Given model is invalid!\n");
return;
}
// Need more than the minimum sample size to make a difference
if (inliers.size () <= sample_size_)
{
PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::optimizeModelCoefficients] Not enough inliers to refine/optimize the model's coefficients (%lu)! Returning the same coefficients.\n", inliers.size ());
return;
}
OptimizationFunctor functor (this, inliers);
Eigen::NumericalDiff<OptimizationFunctor> num_diff (functor);
Eigen::LevenbergMarquardt<Eigen::NumericalDiff<OptimizationFunctor>, double> lm (num_diff);
Eigen::VectorXd coeff;
int info = lm.minimize (coeff);
for (Eigen::Index i = 0; i < coeff.size (); ++i)
optimized_coefficients[i] = static_cast<float> (coeff[i]);
// Compute the L2 norm of the residuals
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",
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]);
}
//////////////////////////////////////////////////////////////////////////
template <typename PointT> void
pcl::SampleConsensusModelCircle3D<PointT>::projectPoints (
const Indices &inliers, const Eigen::VectorXf &model_coefficients,
PointCloud &projected_points, bool copy_data_fields) const
{
// Needs a valid set of model coefficients
if (!isModelValid (model_coefficients))
{
PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::projectPoints] Given model is invalid!\n");
return;
}
projected_points.header = input_->header;
projected_points.is_dense = input_->is_dense;
// Copy all the data fields from the input cloud to the projected one?
if (copy_data_fields)
{
// Allocate enough space and copy the basics
projected_points.resize (input_->size ());
projected_points.width = input_->width;
projected_points.height = input_->height;
using FieldList = typename pcl::traits::fieldList<PointT>::type;
// Iterate over each point
for (std::size_t i = 0; i < projected_points.size (); ++i)
// Iterate over each dimension
pcl::for_each_type <FieldList> (NdConcatenateFunctor <PointT, PointT> ((*input_)[i], projected_points[i]));
// Iterate through the 3d points and calculate the distances from them to the plane
for (std::size_t i = 0; i < inliers.size (); ++i)
{
// what i have:
// P : Sample Point
Eigen::Vector3d P ((*input_)[inliers[i]].x, (*input_)[inliers[i]].y, (*input_)[inliers[i]].z);
// C : Circle Center
Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
// N : Circle (Plane) Normal
Eigen::Vector3d N (model_coefficients[4], model_coefficients[5], model_coefficients[6]);
// r : Radius
double r = model_coefficients[3];
Eigen::Vector3d helper_vectorPC = P - C;
// 1.1. get line parameter
//float lambda = (helper_vectorPC.dot(N)) / N.squaredNorm() ;
double lambda = (-(helper_vectorPC.dot (N))) / N.dot (N);
// Projected Point on plane
Eigen::Vector3d P_proj = P + lambda * N;
Eigen::Vector3d helper_vectorP_projC = P_proj - C;
// K : Point on Circle
Eigen::Vector3d K = C + r * helper_vectorP_projC.normalized ();
projected_points[i].x = static_cast<float> (K[0]);
projected_points[i].y = static_cast<float> (K[1]);
projected_points[i].z = static_cast<float> (K[2]);
}
}
else
{
// Allocate enough space and copy the basics
projected_points.resize (inliers.size ());
projected_points.width = inliers.size ();
projected_points.height = 1;
using FieldList = typename pcl::traits::fieldList<PointT>::type;
// Iterate over each point
for (std::size_t i = 0; i < inliers.size (); ++i)
// Iterate over each dimension
pcl::for_each_type <FieldList> (NdConcatenateFunctor <PointT, PointT> ((*input_)[inliers[i]], projected_points[i]));
// Iterate through the 3d points and calculate the distances from them to the plane
for (std::size_t i = 0; i < inliers.size (); ++i)
{
// what i have:
// P : Sample Point
Eigen::Vector3d P ((*input_)[inliers[i]].x, (*input_)[inliers[i]].y, (*input_)[inliers[i]].z);
// C : Circle Center
Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
// N : Circle (Plane) Normal
Eigen::Vector3d N (model_coefficients[4], model_coefficients[5], model_coefficients[6]);
// r : Radius
double r = model_coefficients[3];
Eigen::Vector3d helper_vectorPC = P - C;
// 1.1. get line parameter
double lambda = (-(helper_vectorPC.dot (N))) / N.dot (N);
// Projected Point on plane
Eigen::Vector3d P_proj = P + lambda * N;
Eigen::Vector3d helper_vectorP_projC = P_proj - C;
// K : Point on Circle
Eigen::Vector3d K = C + r * helper_vectorP_projC.normalized ();
projected_points[i].x = static_cast<float> (K[0]);
projected_points[i].y = static_cast<float> (K[1]);
projected_points[i].z = static_cast<float> (K[2]);
}
}
}
//////////////////////////////////////////////////////////////////////////
template <typename PointT> bool
pcl::SampleConsensusModelCircle3D<PointT>::doSamplesVerifyModel (
const std::set<index_t> &indices,
const Eigen::VectorXf &model_coefficients,
const double threshold) const
{
// Needs a valid model coefficients
if (!isModelValid (model_coefficients))
{
PCL_ERROR ("[pcl::SampleConsensusModelCircle3D::doSamplesVerifyModel] Given model is invalid!\n");
return (false);
}
const auto squared_threshold = threshold * threshold;
for (const auto &index : indices)
{
// Calculate the distance from the point to the sphere as the difference between
//dist(point,sphere_origin) and sphere_radius
// what i have:
// P : Sample Point
Eigen::Vector3d P ((*input_)[index].x, (*input_)[index].y, (*input_)[index].z);
// C : Circle Center
Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
// N : Circle (Plane) Normal
Eigen::Vector3d N (model_coefficients[4], model_coefficients[5], model_coefficients[6]);
// r : Radius
double r = model_coefficients[3];
Eigen::Vector3d helper_vectorPC = P - C;
// 1.1. get line parameter
double lambda = (-(helper_vectorPC.dot (N))) / N.dot (N);
// Projected Point on plane
Eigen::Vector3d P_proj = P + lambda * N;
Eigen::Vector3d helper_vectorP_projC = P_proj - C;
// K : Point on Circle
Eigen::Vector3d K = C + r * helper_vectorP_projC.normalized ();
Eigen::Vector3d distanceVector = P - K;
if (distanceVector.squaredNorm () > squared_threshold)
return (false);
}
return (true);
}
//////////////////////////////////////////////////////////////////////////
template <typename PointT> bool
pcl::SampleConsensusModelCircle3D<PointT>::isModelValid (const Eigen::VectorXf &model_coefficients) const
{
if (!SampleConsensusModel<PointT>::isModelValid (model_coefficients))
return (false);
if (radius_min_ != std::numeric_limits<double>::lowest() && model_coefficients[3] < radius_min_)
{
PCL_DEBUG ("[pcl::SampleConsensusModelCircle3D::isModelValid] Radius of circle is too small: should be larger than %g, but is %g.\n",
radius_min_, model_coefficients[3]);
return (false);
}
if (radius_max_ != std::numeric_limits<double>::max() && model_coefficients[3] > radius_max_)
{
PCL_DEBUG ("[pcl::SampleConsensusModelCircle3D::isModelValid] Radius of circle is too big: should be smaller than %g, but is %g.\n",
radius_max_, model_coefficients[3]);
return (false);
}
return (true);
}
#define PCL_INSTANTIATE_SampleConsensusModelCircle3D(T) template class PCL_EXPORTS pcl::SampleConsensusModelCircle3D<T>;
#endif // PCL_SAMPLE_CONSENSUS_IMPL_SAC_MODEL_CIRCLE3D_HPP_
pcl::SampleConsensusModelCircle3D::isModelValid
bool isModelValid(const Eigen::VectorXf &model_coefficients) const override
Check whether a model is valid given the user constraints.
Definition sac_model_circle3d.hpp:460
pcl::SampleConsensusModelCircle3D::doSamplesVerifyModel
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.
Definition sac_model_circle3d.hpp:414
pcl::SampleConsensusModelCircle3D::isSampleGood
bool isSampleGood(const Indices &samples) const override
Check if a sample of indices results in a good sample of points indices.
Definition sac_model_circle3d.hpp:50
pcl::SampleConsensusModelCircle3D::projectPoints
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.
Definition sac_model_circle3d.hpp:312
pcl::SampleConsensusModelCircle3D::countWithinDistance
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.
Definition sac_model_circle3d.hpp:234
pcl::SampleConsensusModelCircle3D::getDistancesToModel
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.
Definition sac_model_circle3d.hpp:139
pcl::SampleConsensusModelCircle3D::optimizeModelCoefficients
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.
Definition sac_model_circle3d.hpp:276
pcl::SampleConsensusModelCircle3D::PointCloud
typename SampleConsensusModel< PointT >::PointCloud PointCloud
Definition sac_model_circle3d.h:69
pcl::SampleConsensusModelCircle3D::selectWithinDistance
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.
Definition sac_model_circle3d.hpp:186
pcl::SampleConsensusModelCircle3D::computeModelCoefficients
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...
Definition sac_model_circle3d.hpp:79
pcl::SampleConsensusModel
SampleConsensusModel represents the base model class.
Definition sac_model.h:71
pcl::K
@ K
Definition norms.h:54
pcl::Indices
IndicesAllocator<> Indices
Type used for indices in PCL.
Definition types.h:133