mls.hpp
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#ifndef PCL_SURFACE_IMPL_MLS_H_
#define PCL_SURFACE_IMPL_MLS_H_
#include <pcl/point_traits.h>
#include <pcl/surface/mls.h>
#include <pcl/common/io.h>
#include <pcl/common/copy_point.h>
#include <pcl/common/centroid.h>
#include <pcl/common/eigen.h>
#include <pcl/common/geometry.h>
#ifdef _OPENMP
#include <omp.h>
#endif
//////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointInT, typename PointOutT> void
pcl::MovingLeastSquares<PointInT, PointOutT>::process (PointCloudOut &output)
{
// Reset or initialize the collection of indices
corresponding_input_indices_.reset (new PointIndices);
// Check if normals have to be computed/saved
if (compute_normals_)
{
normals_.reset (new NormalCloud);
// Copy the header
normals_->header = input_->header;
// Clear the fields in case the method exits before computation
normals_->width = normals_->height = 0;
normals_->points.clear ();
}
// Copy the header
output.header = input_->header;
output.width = output.height = 0;
output.points.clear ();
if (search_radius_ <= 0 || sqr_gauss_param_ <= 0)
{
PCL_ERROR ("[pcl::%s::process] Invalid search radius (%f) or Gaussian parameter (%f)!\n", getClassName ().c_str (), search_radius_, sqr_gauss_param_);
return;
}
// Check if distinct_cloud_ was set
if (upsample_method_ == DISTINCT_CLOUD && !distinct_cloud_)
{
PCL_ERROR ("[pcl::%s::process] Upsample method was set to DISTINCT_CLOUD, but no distinct cloud was specified.\n", getClassName ().c_str ());
return;
}
if (!initCompute ())
return;
// Initialize the spatial locator
if (!tree_)
{
KdTreePtr tree;
if (input_->isOrganized ())
tree.reset (new pcl::search::OrganizedNeighbor<PointInT> ());
else
tree.reset (new pcl::search::KdTree<PointInT> (false));
setSearchMethod (tree);
}
// Send the surface dataset to the spatial locator
tree_->setInputCloud (input_);
switch (upsample_method_)
{
// Initialize random number generator if necessary
case (RANDOM_UNIFORM_DENSITY):
{
std::random_device rd;
rng_.seed (rd());
const double tmp = search_radius_ / 2.0;
rng_uniform_distribution_.reset (new std::uniform_real_distribution<> (-tmp, tmp));
break;
}
case (VOXEL_GRID_DILATION):
case (DISTINCT_CLOUD):
{
if (!cache_mls_results_)
PCL_WARN ("The cache mls results is forced when using upsampling method VOXEL_GRID_DILATION or DISTINCT_CLOUD.\n");
cache_mls_results_ = true;
break;
}
default:
break;
}
if (cache_mls_results_)
{
mls_results_.resize (input_->size ());
}
else
{
mls_results_.resize (1); // Need to have a reference to a single dummy result.
}
// Perform the actual surface reconstruction
performProcessing (output);
if (compute_normals_)
{
normals_->height = 1;
normals_->width = static_cast<std::uint32_t> (normals_->size ());
for (std::size_t i = 0; i < output.size (); ++i)
{
using FieldList = typename pcl::traits::fieldList<PointOutT>::type;
pcl::for_each_type<FieldList> (SetIfFieldExists<PointOutT, float> (output.points[i], "normal_x", normals_->points[i].normal_x));
pcl::for_each_type<FieldList> (SetIfFieldExists<PointOutT, float> (output.points[i], "normal_y", normals_->points[i].normal_y));
pcl::for_each_type<FieldList> (SetIfFieldExists<PointOutT, float> (output.points[i], "normal_z", normals_->points[i].normal_z));
pcl::for_each_type<FieldList> (SetIfFieldExists<PointOutT, float> (output.points[i], "curvature", normals_->points[i].curvature));
}
}
// Set proper widths and heights for the clouds
output.height = 1;
output.width = static_cast<std::uint32_t> (output.size ());
deinitCompute ();
}
//////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointInT, typename PointOutT> void
pcl::MovingLeastSquares<PointInT, PointOutT>::computeMLSPointNormal (int index,
const std::vector<int> &nn_indices,
PointCloudOut &projected_points,
NormalCloud &projected_points_normals,
PointIndices &corresponding_input_indices,
MLSResult &mls_result) const
{
// Note: this method is const because it needs to be thread-safe
// (MovingLeastSquaresOMP calls it from multiple threads)
mls_result.computeMLSSurface<PointInT> (*input_, index, nn_indices, search_radius_, order_);
switch (upsample_method_)
{
case (NONE):
{
const MLSResult::MLSProjectionResults proj = mls_result.projectQueryPoint (projection_method_, nr_coeff_);
addProjectedPointNormal (index, proj.point, proj.normal, mls_result.curvature, projected_points, projected_points_normals, corresponding_input_indices);
break;
}
case (SAMPLE_LOCAL_PLANE):
{
// Uniformly sample a circle around the query point using the radius and step parameters
for (float u_disp = -static_cast<float> (upsampling_radius_); u_disp <= upsampling_radius_; u_disp += static_cast<float> (upsampling_step_))
for (float v_disp = -static_cast<float> (upsampling_radius_); v_disp <= upsampling_radius_; v_disp += static_cast<float> (upsampling_step_))
if (u_disp * u_disp + v_disp * v_disp < upsampling_radius_ * upsampling_radius_)
{
MLSResult::MLSProjectionResults proj = mls_result.projectPointSimpleToPolynomialSurface (u_disp, v_disp);
addProjectedPointNormal (index, proj.point, proj.normal, mls_result.curvature, projected_points, projected_points_normals, corresponding_input_indices);
}
break;
}
case (RANDOM_UNIFORM_DENSITY):
{
// Compute the local point density and add more samples if necessary
const int num_points_to_add = static_cast<int> (std::floor (desired_num_points_in_radius_ / 2.0 / static_cast<double> (nn_indices.size ())));
// Just add the query point, because the density is good
if (num_points_to_add <= 0)
{
// Just add the current point
const MLSResult::MLSProjectionResults proj = mls_result.projectQueryPoint (projection_method_, nr_coeff_);
addProjectedPointNormal (index, proj.point, proj.normal, mls_result.curvature, projected_points, projected_points_normals, corresponding_input_indices);
}
else
{
// Sample the local plane
for (int num_added = 0; num_added < num_points_to_add;)
{
const double u = (*rng_uniform_distribution_) (rng_);
const double v = (*rng_uniform_distribution_) (rng_);
// Check if inside circle; if not, try another coin flip
if (u * u + v * v > search_radius_ * search_radius_ / 4)
continue;
MLSResult::MLSProjectionResults proj;
if (order_ > 1 && mls_result.num_neighbors >= 5 * nr_coeff_)
proj = mls_result.projectPointSimpleToPolynomialSurface (u, v);
else
proj = mls_result.projectPointToMLSPlane (u, v);
addProjectedPointNormal (index, proj.point, proj.normal, mls_result.curvature, projected_points, projected_points_normals, corresponding_input_indices);
num_added++;
}
}
break;
}
default:
break;
}
}
template <typename PointInT, typename PointOutT> void
pcl::MovingLeastSquares<PointInT, PointOutT>::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
{
PointOutT aux;
aux.x = static_cast<float> (point[0]);
aux.y = static_cast<float> (point[1]);
aux.z = static_cast<float> (point[2]);
// Copy additional point information if available
copyMissingFields (input_->points[index], aux);
projected_points.push_back (aux);
corresponding_input_indices.indices.push_back (index);
if (compute_normals_)
{
pcl::Normal aux_normal;
aux_normal.normal_x = static_cast<float> (normal[0]);
aux_normal.normal_y = static_cast<float> (normal[1]);
aux_normal.normal_z = static_cast<float> (normal[2]);
aux_normal.curvature = curvature;
projected_points_normals.push_back (aux_normal);
}
}
//////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointInT, typename PointOutT> void
pcl::MovingLeastSquares<PointInT, PointOutT>::performProcessing (PointCloudOut &output)
{
// Compute the number of coefficients
nr_coeff_ = (order_ + 1) * (order_ + 2) / 2;
#ifdef _OPENMP
// (Maximum) number of threads
const unsigned int threads = threads_ == 0 ? 1 : threads_;
// Create temporaries for each thread in order to avoid synchronization
typename PointCloudOut::CloudVectorType projected_points (threads);
typename NormalCloud::CloudVectorType projected_points_normals (threads);
std::vector<PointIndices> corresponding_input_indices (threads);
#endif
// For all points
#ifdef _OPENMP
#pragma omp parallel for schedule (dynamic,1000) num_threads (threads)
#endif
for (int cp = 0; cp < static_cast<int> (indices_->size ()); ++cp)
{
// Allocate enough space to hold the results of nearest neighbor searches
// \note resize is irrelevant for a radiusSearch ().
std::vector<int> nn_indices;
std::vector<float> nn_sqr_dists;
// Get the initial estimates of point positions and their neighborhoods
if (searchForNeighbors ((*indices_)[cp], nn_indices, nn_sqr_dists))
{
// Check the number of nearest neighbors for normal estimation (and later for polynomial fit as well)
if (nn_indices.size () >= 3)
{
// This thread's ID (range 0 to threads-1)
#ifdef _OPENMP
const int tn = omp_get_thread_num ();
// Size of projected points before computeMLSPointNormal () adds points
std::size_t pp_size = projected_points[tn].size ();
#else
PointCloudOut projected_points;
NormalCloud projected_points_normals;
#endif
// Get a plane approximating the local surface's tangent and project point onto it
const int index = (*indices_)[cp];
std::size_t mls_result_index = 0;
if (cache_mls_results_)
mls_result_index = index; // otherwise we give it a dummy location.
#ifdef _OPENMP
computeMLSPointNormal (index, nn_indices, projected_points[tn], projected_points_normals[tn], corresponding_input_indices[tn], mls_results_[mls_result_index]);
// Copy all information from the input cloud to the output points (not doing any interpolation)
for (std::size_t pp = pp_size; pp < projected_points[tn].size (); ++pp)
copyMissingFields (input_->points[(*indices_)[cp]], projected_points[tn][pp]);
#else
computeMLSPointNormal (index, nn_indices, projected_points, projected_points_normals, *corresponding_input_indices_, mls_results_[mls_result_index]);
// Append projected points to output
output.insert (output.end (), projected_points.begin (), projected_points.end ());
if (compute_normals_)
normals_->insert (normals_->end (), projected_points_normals.begin (), projected_points_normals.end ());
#endif
}
}
}
#ifdef _OPENMP
// Combine all threads' results into the output vectors
for (unsigned int tn = 0; tn < threads; ++tn)
{
output.insert (output.end (), projected_points[tn].begin (), projected_points[tn].end ());
corresponding_input_indices_->indices.insert (corresponding_input_indices_->indices.end (),
corresponding_input_indices[tn].indices.begin (), corresponding_input_indices[tn].indices.end ());
if (compute_normals_)
normals_->insert (normals_->end (), projected_points_normals[tn].begin (), projected_points_normals[tn].end ());
}
#endif
// Perform the distinct-cloud or voxel-grid upsampling
performUpsampling (output);
}
//////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointInT, typename PointOutT> void
pcl::MovingLeastSquares<PointInT, PointOutT>::performUpsampling (PointCloudOut &output)
{
if (upsample_method_ == DISTINCT_CLOUD)
{
corresponding_input_indices_.reset (new PointIndices);
for (std::size_t dp_i = 0; dp_i < distinct_cloud_->size (); ++dp_i) // dp_i = distinct_point_i
{
// Distinct cloud may have nan points, skip them
if (!std::isfinite (distinct_cloud_->points[dp_i].x))
continue;
// Get 3D position of point
//Eigen::Vector3f pos = distinct_cloud_->points[dp_i].getVector3fMap ();
std::vector<int> nn_indices;
std::vector<float> nn_dists;
tree_->nearestKSearch (distinct_cloud_->points[dp_i], 1, nn_indices, nn_dists);
int input_index = nn_indices.front ();
// If the closest point did not have a valid MLS fitting result
// OR if it is too far away from the sampled point
if (mls_results_[input_index].valid == false)
continue;
Eigen::Vector3d add_point = distinct_cloud_->points[dp_i].getVector3fMap ().template cast<double> ();
MLSResult::MLSProjectionResults proj = mls_results_[input_index].projectPoint (add_point, projection_method_, 5 * nr_coeff_);
addProjectedPointNormal (input_index, proj.point, proj.normal, mls_results_[input_index].curvature, output, *normals_, *corresponding_input_indices_);
}
}
// For the voxel grid upsampling method, generate the voxel grid and dilate it
// Then, project the newly obtained points to the MLS surface
if (upsample_method_ == VOXEL_GRID_DILATION)
{
corresponding_input_indices_.reset (new PointIndices);
MLSVoxelGrid voxel_grid (input_, indices_, voxel_size_);
for (int iteration = 0; iteration < dilation_iteration_num_; ++iteration)
voxel_grid.dilate ();
for (typename MLSVoxelGrid::HashMap::iterator m_it = voxel_grid.voxel_grid_.begin (); m_it != voxel_grid.voxel_grid_.end (); ++m_it)
{
// Get 3D position of point
Eigen::Vector3f pos;
voxel_grid.getPosition (m_it->first, pos);
PointInT p;
p.x = pos[0];
p.y = pos[1];
p.z = pos[2];
std::vector<int> nn_indices;
std::vector<float> nn_dists;
tree_->nearestKSearch (p, 1, nn_indices, nn_dists);
int input_index = nn_indices.front ();
// If the closest point did not have a valid MLS fitting result
// OR if it is too far away from the sampled point
if (mls_results_[input_index].valid == false)
continue;
Eigen::Vector3d add_point = p.getVector3fMap ().template cast<double> ();
MLSResult::MLSProjectionResults proj = mls_results_[input_index].projectPoint (add_point, projection_method_, 5 * nr_coeff_);
addProjectedPointNormal (input_index, proj.point, proj.normal, mls_results_[input_index].curvature, output, *normals_, *corresponding_input_indices_);
}
}
}
//////////////////////////////////////////////////////////////////////////////////////////////
pcl::MLSResult::MLSResult (const Eigen::Vector3d &a_query_point,
const Eigen::Vector3d &a_mean,
const Eigen::Vector3d &a_plane_normal,
const Eigen::Vector3d &a_u,
const Eigen::Vector3d &a_v,
const Eigen::VectorXd &a_c_vec,
const int a_num_neighbors,
const float a_curvature,
const int a_order) :
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),
curvature (a_curvature), order (a_order), valid (true)
{}
void
pcl::MLSResult::getMLSCoordinates (const Eigen::Vector3d &pt, double &u, double &v, double &w) const
{
Eigen::Vector3d delta = pt - mean;
u = delta.dot (u_axis);
v = delta.dot (v_axis);
w = delta.dot (plane_normal);
}
void
pcl::MLSResult::getMLSCoordinates (const Eigen::Vector3d &pt, double &u, double &v) const
{
Eigen::Vector3d delta = pt - mean;
u = delta.dot (u_axis);
v = delta.dot (v_axis);
}
double
pcl::MLSResult::getPolynomialValue (const double u, const double v) const
{
// Compute the polynomial's terms at the current point
// Example for second order: z = a + b*y + c*y^2 + d*x + e*x*y + f*x^2
int j = 0;
double u_pow = 1;
double result = 0;
for (int ui = 0; ui <= order; ++ui)
{
double v_pow = 1;
for (int vi = 0; vi <= order - ui; ++vi)
{
result += c_vec[j++] * u_pow * v_pow;
v_pow *= v;
}
u_pow *= u;
}
return (result);
}
pcl::MLSResult::PolynomialPartialDerivative
pcl::MLSResult::getPolynomialPartialDerivative (const double u, const double v) const
{
// Compute the displacement along the normal using the fitted polynomial
// and compute the partial derivatives needed for estimating the normal
PolynomialPartialDerivative d{};
Eigen::VectorXd u_pow (order + 2), v_pow (order + 2);
int j = 0;
d.z = d.z_u = d.z_v = d.z_uu = d.z_vv = d.z_uv = 0;
u_pow (0) = v_pow (0) = 1;
for (int ui = 0; ui <= order; ++ui)
{
for (int vi = 0; vi <= order - ui; ++vi)
{
// Compute displacement along normal
d.z += u_pow (ui) * v_pow (vi) * c_vec[j];
// Compute partial derivatives
if (ui >= 1)
d.z_u += c_vec[j] * ui * u_pow (ui - 1) * v_pow (vi);
if (vi >= 1)
d.z_v += c_vec[j] * vi * u_pow (ui) * v_pow (vi - 1);
if (ui >= 1 && vi >= 1)
d.z_uv += c_vec[j] * ui * u_pow (ui - 1) * vi * v_pow (vi - 1);
if (ui >= 2)
d.z_uu += c_vec[j] * ui * (ui - 1) * u_pow (ui - 2) * v_pow (vi);
if (vi >= 2)
d.z_vv += c_vec[j] * vi * (vi - 1) * u_pow (ui) * v_pow (vi - 2);
if (ui == 0)
v_pow (vi + 1) = v_pow (vi) * v;
++j;
}
u_pow (ui + 1) = u_pow (ui) * u;
}
return (d);
}
Eigen::Vector2f
pcl::MLSResult::calculatePrincipleCurvatures (const double u, const double v) const
{
Eigen::Vector2f k (1e-5, 1e-5);
// Note: this use the Monge Patch to derive the Gaussian curvature and Mean Curvature found here http://mathworld.wolfram.com/MongePatch.html
// Then:
// k1 = H + sqrt(H^2 - K)
// k1 = H - sqrt(H^2 - K)
if (order > 1 && c_vec.size () >= (order + 1) * (order + 2) / 2 && std::isfinite (c_vec[0]))
{
const PolynomialPartialDerivative d = getPolynomialPartialDerivative (u, v);
const double Z = 1 + d.z_u * d.z_u + d.z_v * d.z_v;
const double Zlen = std::sqrt (Z);
const double K = (d.z_uu * d.z_vv - d.z_uv * d.z_uv) / (Z * Z);
const 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);
const double disc2 = H * H - K;
assert (disc2 >= 0.0);
const double disc = std::sqrt (disc2);
k[0] = H + disc;
k[1] = H - disc;
if (std::abs (k[0]) > std::abs (k[1])) std::swap (k[0], k[1]);
}
else
{
PCL_ERROR ("No Polynomial fit data, unable to calculate the principle curvatures!\n");
}
return (k);
}
pcl::MLSResult::MLSProjectionResults
pcl::MLSResult::projectPointOrthogonalToPolynomialSurface (const double u, const double v, const double w) const
{
double gu = u;
double gv = v;
double gw = 0;
MLSProjectionResults result;
result.normal = plane_normal;
if (order > 1 && c_vec.size () >= (order + 1) * (order + 2) / 2 && std::isfinite (c_vec[0]))
{
PolynomialPartialDerivative d = getPolynomialPartialDerivative (gu, gv);
gw = d.z;
double err_total;
const double dist1 = std::abs (gw - w);
double dist2;
do
{
double e1 = (gu - u) + d.z_u * gw - d.z_u * w;
double e2 = (gv - v) + d.z_v * gw - d.z_v * w;
const double F1u = 1 + d.z_uu * gw + d.z_u * d.z_u - d.z_uu * w;
const double F1v = d.z_uv * gw + d.z_u * d.z_v - d.z_uv * w;
const double F2u = d.z_uv * gw + d.z_v * d.z_u - d.z_uv * w;
const double F2v = 1 + d.z_vv * gw + d.z_v * d.z_v - d.z_vv * w;
Eigen::MatrixXd J (2, 2);
J (0, 0) = F1u;
J (0, 1) = F1v;
J (1, 0) = F2u;
J (1, 1) = F2v;
Eigen::Vector2d err (e1, e2);
Eigen::Vector2d update = J.inverse () * err;
gu -= update (0);
gv -= update (1);
d = getPolynomialPartialDerivative (gu, gv);
gw = d.z;
dist2 = std::sqrt ((gu - u) * (gu - u) + (gv - v) * (gv - v) + (gw - w) * (gw - w));
err_total = std::sqrt (e1 * e1 + e2 * e2);
} while (err_total > 1e-8 && dist2 < dist1);
if (dist2 > dist1) // the optimization was diverging reset the coordinates for simple projection
{
gu = u;
gv = v;
d = getPolynomialPartialDerivative (u, v);
gw = d.z;
}
result.u = gu;
result.v = gv;
result.normal -= (d.z_u * u_axis + d.z_v * v_axis);
result.normal.normalize ();
}
result.point = mean + gu * u_axis + gv * v_axis + gw * plane_normal;
return (result);
}
pcl::MLSResult::MLSProjectionResults
pcl::MLSResult::projectPointToMLSPlane (const double u, const double v) const
{
MLSProjectionResults result;
result.u = u;
result.v = v;
result.normal = plane_normal;
result.point = mean + u * u_axis + v * v_axis;
return (result);
}
pcl::MLSResult::MLSProjectionResults
pcl::MLSResult::projectPointSimpleToPolynomialSurface (const double u, const double v) const
{
MLSProjectionResults result;
double w = 0;
result.u = u;
result.v = v;
result.normal = plane_normal;
if (order > 1 && c_vec.size () >= (order + 1) * (order + 2) / 2 && std::isfinite (c_vec[0]))
{
const PolynomialPartialDerivative d = getPolynomialPartialDerivative (u, v);
w = d.z;
result.normal -= (d.z_u * u_axis + d.z_v * v_axis);
result.normal.normalize ();
}
result.point = mean + u * u_axis + v * v_axis + w * plane_normal;
return (result);
}
pcl::MLSResult::MLSProjectionResults
pcl::MLSResult::projectPoint (const Eigen::Vector3d &pt, ProjectionMethod method, int required_neighbors) const
{
double u, v, w;
getMLSCoordinates (pt, u, v, w);
MLSResult::MLSProjectionResults proj;
if (order > 1 && num_neighbors >= required_neighbors && std::isfinite (c_vec[0]) && method != NONE)
{
if (method == ORTHOGONAL)
proj = projectPointOrthogonalToPolynomialSurface (u, v, w);
else // SIMPLE
proj = projectPointSimpleToPolynomialSurface (u, v);
}
else
{
proj = projectPointToMLSPlane (u, v);
}
return (proj);
}
pcl::MLSResult::MLSProjectionResults
pcl::MLSResult::projectQueryPoint (ProjectionMethod method, int required_neighbors) const
{
MLSResult::MLSProjectionResults proj;
if (order > 1 && num_neighbors >= required_neighbors && std::isfinite (c_vec[0]) && method != NONE)
{
if (method == ORTHOGONAL)
{
double u, v, w;
getMLSCoordinates (query_point, u, v, w);
proj = projectPointOrthogonalToPolynomialSurface (u, v, w);
}
else // SIMPLE
{
// Projection onto MLS surface along Darboux normal to the height at (0,0)
proj.point = mean + (c_vec[0] * plane_normal);
// Compute tangent vectors using the partial derivates evaluated at (0,0) which is c_vec[order_+1] and c_vec[1]
proj.normal = plane_normal - c_vec[order + 1] * u_axis - c_vec[1] * v_axis;
proj.normal.normalize ();
}
}
else
{
proj.normal = plane_normal;
proj.point = mean;
}
return (proj);
}
template <typename PointT> void
pcl::MLSResult::computeMLSSurface (const pcl::PointCloud<PointT> &cloud,
int index,
const std::vector<int> &nn_indices,
double search_radius,
int polynomial_order,
std::function<double(const double)> weight_func)
{
// Compute the plane coefficients
EIGEN_ALIGN16 Eigen::Matrix3d covariance_matrix;
Eigen::Vector4d xyz_centroid;
// Estimate the XYZ centroid
pcl::compute3DCentroid (cloud, nn_indices, xyz_centroid);
// Compute the 3x3 covariance matrix
pcl::computeCovarianceMatrix (cloud, nn_indices, xyz_centroid, covariance_matrix);
EIGEN_ALIGN16 Eigen::Vector3d::Scalar eigen_value;
EIGEN_ALIGN16 Eigen::Vector3d eigen_vector;
Eigen::Vector4d model_coefficients (0, 0, 0, 0);
pcl::eigen33 (covariance_matrix, eigen_value, eigen_vector);
model_coefficients.head<3> ().matrix () = eigen_vector;
model_coefficients[3] = -1 * model_coefficients.dot (xyz_centroid);
query_point = cloud.points[index].getVector3fMap ().template cast<double> ();
if (!std::isfinite(eigen_vector[0]) || !std::isfinite(eigen_vector[1]) || !std::isfinite(eigen_vector[2]))
{
// Invalid plane coefficients, this may happen if the input cloud is non-dense (it contains invalid points).
// Keep the input point and stop here.
valid = false;
mean = query_point;
return;
}
// Projected query point
valid = true;
const double distance = query_point.dot (model_coefficients.head<3> ()) + model_coefficients[3];
mean = query_point - distance * model_coefficients.head<3> ();
curvature = covariance_matrix.trace ();
// Compute the curvature surface change
if (curvature != 0)
curvature = std::abs (eigen_value / curvature);
// Get a copy of the plane normal easy access
plane_normal = model_coefficients.head<3> ();
// Local coordinate system (Darboux frame)
v_axis = plane_normal.unitOrthogonal ();
u_axis = plane_normal.cross (v_axis);
// Perform polynomial fit to update point and normal
////////////////////////////////////////////////////
num_neighbors = static_cast<int> (nn_indices.size ());
order = polynomial_order;
if (order > 1)
{
const int nr_coeff = (order + 1) * (order + 2) / 2;
if (num_neighbors >= nr_coeff)
{
if (!weight_func)
weight_func = [=] (const double sq_dist) { return this->computeMLSWeight (sq_dist, search_radius * search_radius); };
// Allocate matrices and vectors to hold the data used for the polynomial fit
Eigen::VectorXd weight_vec (num_neighbors);
Eigen::MatrixXd P (nr_coeff, num_neighbors);
Eigen::VectorXd f_vec (num_neighbors);
Eigen::MatrixXd P_weight_Pt (nr_coeff, nr_coeff);
// Update neighborhood, since point was projected, and computing relative
// positions. Note updating only distances for the weights for speed
std::vector<Eigen::Vector3d, Eigen::aligned_allocator<Eigen::Vector3d> > de_meaned (num_neighbors);
for (std::size_t ni = 0; ni < static_cast<std::size_t>(num_neighbors); ++ni)
{
de_meaned[ni][0] = cloud.points[nn_indices[ni]].x - mean[0];
de_meaned[ni][1] = cloud.points[nn_indices[ni]].y - mean[1];
de_meaned[ni][2] = cloud.points[nn_indices[ni]].z - mean[2];
weight_vec (ni) = weight_func (de_meaned[ni].dot (de_meaned[ni]));
}
// Go through neighbors, transform them in the local coordinate system,
// save height and the evaluation of the polynome's terms
for (std::size_t ni = 0; ni < static_cast<std::size_t>(num_neighbors); ++ni)
{
// Transforming coordinates
const double u_coord = de_meaned[ni].dot(u_axis);
const double v_coord = de_meaned[ni].dot(v_axis);
f_vec (ni) = de_meaned[ni].dot (plane_normal);
// Compute the polynomial's terms at the current point
int j = 0;
double u_pow = 1;
for (int ui = 0; ui <= order; ++ui)
{
double v_pow = 1;
for (int vi = 0; vi <= order - ui; ++vi)
{
P (j++, ni) = u_pow * v_pow;
v_pow *= v_coord;
}
u_pow *= u_coord;
}
}
// Computing coefficients
const Eigen::MatrixXd P_weight = P * weight_vec.asDiagonal(); // size will be (nr_coeff_, nn_indices.size ());
P_weight_Pt = P_weight * P.transpose ();
c_vec = P_weight * f_vec;
P_weight_Pt.llt ().solveInPlace (c_vec);
}
}
}
//////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointInT, typename PointOutT>
pcl::MovingLeastSquares<PointInT, PointOutT>::MLSVoxelGrid::MLSVoxelGrid (PointCloudInConstPtr& cloud,
IndicesPtr &indices,
float voxel_size) :
voxel_grid_ (), data_size_ (), voxel_size_ (voxel_size)
{
pcl::getMinMax3D (*cloud, *indices, bounding_min_, bounding_max_);
Eigen::Vector4f bounding_box_size = bounding_max_ - bounding_min_;
const double max_size = (std::max) ((std::max)(bounding_box_size.x (), bounding_box_size.y ()), bounding_box_size.z ());
// Put initial cloud in voxel grid
data_size_ = static_cast<std::uint64_t> (1.5 * max_size / voxel_size_);
for (std::size_t i = 0; i < indices->size (); ++i)
if (std::isfinite (cloud->points[(*indices)[i]].x))
{
Eigen::Vector3i pos;
getCellIndex (cloud->points[(*indices)[i]].getVector3fMap (), pos);
std::uint64_t index_1d;
getIndexIn1D (pos, index_1d);
Leaf leaf;
voxel_grid_[index_1d] = leaf;
}
}
//////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointInT, typename PointOutT> void
pcl::MovingLeastSquares<PointInT, PointOutT>::MLSVoxelGrid::dilate ()
{
HashMap new_voxel_grid = voxel_grid_;
for (typename MLSVoxelGrid::HashMap::iterator m_it = voxel_grid_.begin (); m_it != voxel_grid_.end (); ++m_it)
{
Eigen::Vector3i index;
getIndexIn3D (m_it->first, index);
// Now dilate all of its voxels
for (int x = -1; x <= 1; ++x)
for (int y = -1; y <= 1; ++y)
for (int z = -1; z <= 1; ++z)
if (x != 0 || y != 0 || z != 0)
{
Eigen::Vector3i new_index;
new_index = index + Eigen::Vector3i (x, y, z);
std::uint64_t index_1d;
getIndexIn1D (new_index, index_1d);
Leaf leaf;
new_voxel_grid[index_1d] = leaf;
}
}
voxel_grid_ = new_voxel_grid;
}
/////////////////////////////////////////////////////////////////////////////////////////////
template <typename PointInT, typename PointOutT> void
pcl::MovingLeastSquares<PointInT, PointOutT>::copyMissingFields (const PointInT &point_in,
PointOutT &point_out) const
{
PointOutT temp = point_out;
copyPoint (point_in, point_out);
point_out.x = temp.x;
point_out.y = temp.y;
point_out.z = temp.z;
}
#define PCL_INSTANTIATE_MovingLeastSquares(T,OutT) template class PCL_EXPORTS pcl::MovingLeastSquares<T,OutT>;
#define PCL_INSTANTIATE_MovingLeastSquaresOMP(T,OutT) template class PCL_EXPORTS pcl::MovingLeastSquaresOMP<T,OutT>;
#endif // PCL_SURFACE_IMPL_MLS_H_
pcl::MLSResult::num_neighbors
int num_neighbors
The number of neighbors used to create the mls surface.
Definition: mls.h:221
pcl::MLSResult::projectPointOrthogonalToPolynomialSurface
MLSProjectionResults projectPointOrthogonalToPolynomialSurface(const double u, const double v, const double w) const
Project a point orthogonal to the polynomial surface.
Definition: mls.hpp:563
pcl::MLSResult::projectPointToMLSPlane
MLSProjectionResults projectPointToMLSPlane(const double u, const double v) const
Project a point onto the MLS plane.
Definition: mls.hpp:628
pcl::_Normal::curvature
float curvature
Definition: point_types.hpp:784
pcl::MovingLeastSquares::computeMLSPointNormal
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:170
pcl::K
Definition: norms.h:54
pcl::Normal
A point structure representing normal coordinates and the surface curvature estimate.
Definition: point_types.hpp:795
pcl::PointCloud::end
iterator end()
Definition: point_cloud.h:430
pcl::IndicesPtr
shared_ptr< Indices > IndicesPtr
Definition: pcl_base.h:61
pcl::PointCloud::height
std::uint32_t height
The point cloud height (if organized as an image-structure).
Definition: point_cloud.h:402
pcl::geometry::distance
float distance(const PointT &p1, const PointT &p2)
Definition: geometry.h:60
pcl::MovingLeastSquares::MLSVoxelGrid::getCellIndex
void getCellIndex(const Eigen::Vector3f &p, Eigen::Vector3i &index) const
Definition: mls.h:632
pcl::PointCloud::points
std::vector< PointT, Eigen::aligned_allocator< PointT > > points
The point data.
Definition: point_cloud.h:397
pcl::MovingLeastSquares::addProjectedPointNormal
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:248
pcl::MLSResult::PolynomialPartialDerivative::z_uu
double z_uu
The partial derivative d^2z/du^2.
Definition: mls.h:75
pcl::MovingLeastSquares::MLSVoxelGrid
A minimalistic implementation of a voxel grid, necessary for the point cloud upsampling.
Definition: mls.h:602
geometry.h
pcl::MLSResult::MLSResult
MLSResult()
Definition: mls.h:93
pcl::MLSResult::MLSProjectionResults::u
double u
The u-coordinate of the projected point in local MLS frame.
Definition: mls.h:85
pcl::MovingLeastSquares::MLSVoxelGrid::MLSVoxelGrid
MLSVoxelGrid(PointCloudInConstPtr &cloud, IndicesPtr &indices, float voxel_size)
Definition: mls.hpp:832
pcl::MLSResult::curvature
float curvature
The curvature at the query point.
Definition: mls.h:222
pcl::MovingLeastSquares::PointCloudInConstPtr
typename PointCloudIn::ConstPtr PointCloudInConstPtr
Definition: mls.h:275
pcl::MovingLeastSquares::copyMissingFields
void copyMissingFields(const PointInT &point_in, PointOutT &point_out) const
Definition: mls.hpp:887
pcl::MLSResult::MLSProjectionResults::point
Eigen::Vector3d point
The projected point.
Definition: mls.h:87
pcl::MLSResult::MLSProjectionResults::normal
Eigen::Vector3d normal
The projected point's normal.
Definition: mls.h:88
pcl::MovingLeastSquares::MLSVoxelGrid::bounding_max_
Eigen::Vector4f bounding_max_
Definition: mls.h:649
pcl::PointCloud< PointOutT >
pcl::eigen33
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:291
pcl::MLSResult::PolynomialPartialDerivative::z_vv
double z_vv
The partial derivative d^2z/dv^2.
Definition: mls.h:76
pcl::MLSResult::PolynomialPartialDerivative::z_v
double z_v
The partial derivative dz/dv.
Definition: mls.h:74
pcl::MovingLeastSquares::MLSVoxelGrid::dilate
void dilate()
Definition: mls.hpp:858
pcl::MovingLeastSquares::performUpsampling
void performUpsampling(PointCloudOut &output)
Perform upsampling for the distinct-cloud and voxel-grid methods.
Definition: mls.hpp:364
pcl::PointCloud< PointOutT >::CloudVectorType
std::vector< PointCloud< PointOutT >, Eigen::aligned_allocator< PointCloud< PointOutT > > > CloudVectorType
Definition: point_cloud.h:414
pcl::MLSResult::computeMLSSurface
void computeMLSSurface(const pcl::PointCloud< PointT > &cloud, int index, const std::vector< int > &nn_indices, double search_radius, int polynomial_order=2, std::function< double(const double)> weight_func={})
Smooth a given point and its neighborghood using Moving Least Squares.
Definition: mls.hpp:716
pcl::MovingLeastSquares::MLSVoxelGrid::getPosition
void getPosition(const std::uint64_t &index_1d, Eigen::Vector3f &point) const
Definition: mls.h:639
pcl::PointCloud::width
std::uint32_t width
The point cloud width (if organized as an image-structure).
Definition: point_cloud.h:400
pcl::copyPoint
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
pcl::MovingLeastSquares::MLSVoxelGrid::getIndexIn1D
void getIndexIn1D(const Eigen::Vector3i &index, std::uint64_t &index_1d) const
Definition: mls.h:615
pcl::MLSResult::calculatePrincipleCurvatures
Eigen::Vector2f calculatePrincipleCurvatures(const double u, const double v) const
Calculate the principle curvatures using the polynomial surface.
Definition: mls.hpp:531
pcl::SetIfFieldExists
A helper functor that can set a specific value in a field if the field exists.
Definition: point_traits.h:283
pcl::MLSResult::getPolynomialPartialDerivative
PolynomialPartialDerivative getPolynomialPartialDerivative(const double u, const double v) const
Calculate the polynomial's first and second partial derivatives.
Definition: mls.hpp:486
pcl::MLSResult::MLSProjectionResults::v
double v
The u-coordinate of the projected point in local MLS frame.
Definition: mls.h:86
pcl::MLSResult::ProjectionMethod
ProjectionMethod
Definition: mls.h:62
pcl::computeCovarianceMatrix
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.
pcl::MLSResult
Data structure used to store the results of the MLS fitting.
Definition: mls.h:60
pcl::MovingLeastSquares::process
void process(PointCloudOut &output) override
Base method for surface reconstruction for all points given in <setInputCloud (), setIndices ()>
Definition: mls.hpp:57
pcl::MLSResult::PolynomialPartialDerivative
Data structure used to store the MLS polynomial partial derivatives.
Definition: mls.h:70
pcl::MLSResult::PolynomialPartialDerivative::z_u
double z_u
The partial derivative dz/du.
Definition: mls.h:73
pcl::search::KdTree
search::KdTree is a wrapper class which inherits the pcl::KdTree class for performing search function...
Definition: kdtree.h:61
pcl::MLSResult::PolynomialPartialDerivative::z_uv
double z_uv
The partial derivative d^2z/dudv.
Definition: mls.h:77
pcl::MLSResult::MLSProjectionResults
Data structure used to store the MLS projection results.
Definition: mls.h:81
pcl::PointIndices::indices
std::vector< int > indices
Definition: PointIndices.h:19
pcl::PointIndices
Definition: PointIndices.h:12
pcl::PointCloud::header
pcl::PCLHeader header
The point cloud header.
Definition: point_cloud.h:394
pcl::MovingLeastSquares::MLSVoxelGrid::voxel_size_
float voxel_size_
Definition: mls.h:651
pcl::search::OrganizedNeighbor
OrganizedNeighbor is a class for optimized nearest neigbhor search in organized point clouds.
Definition: organized.h:62
pcl::PointCloud::size
std::size_t size() const
Definition: point_cloud.h:435
pcl::PointCloud::insert
iterator insert(iterator position, const PointT &pt)
Insert a new point in the cloud, given an iterator.
Definition: point_cloud.h:495
pcl::getMinMax3D
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
pcl::MovingLeastSquares::MLSVoxelGrid::data_size_
std::uint64_t data_size_
Definition: mls.h:650
pcl::MLSResult::projectQueryPoint
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:685
pcl::MovingLeastSquares::KdTreePtr
typename KdTree::Ptr KdTreePtr
Definition: mls.h:265
pcl::MovingLeastSquares::MLSVoxelGrid::bounding_min_
Eigen::Vector4f bounding_min_
Definition: mls.h:649
pcl::MovingLeastSquares::MLSVoxelGrid::HashMap
std::map< std::uint64_t, Leaf > HashMap
Definition: mls.h:647
pcl::MovingLeastSquares::performProcessing
void performProcessing(PointCloudOut &output) override
Abstract surface reconstruction method.
Definition: mls.hpp:280
pcl::MLSResult::projectPointSimpleToPolynomialSurface
MLSProjectionResults projectPointSimpleToPolynomialSurface(const double u, const double v) const
Project a point along the MLS plane normal to the polynomial surface.
Definition: mls.hpp:640
pcl::PointCloud::begin
iterator begin()
Definition: point_cloud.h:429
pcl::MovingLeastSquares::MLSVoxelGrid::voxel_grid_
HashMap voxel_grid_
Definition: mls.h:648
pcl::MLSResult::PolynomialPartialDerivative::z
double z
The z component of the polynomial evaluated at z(u, v).
Definition: mls.h:72
pcl::compute3DCentroid
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
pcl::MLSResult::projectPoint
MLSProjectionResults projectPoint(const Eigen::Vector3d &pt, ProjectionMethod method, int required_neighbors=0) const
Project a point using the specified method.
Definition: mls.hpp:663
pcl::MLSResult::getPolynomialValue
double getPolynomialValue(const double u, const double v) const
Calculate the polynomial.
Definition: mls.hpp:464
pcl::MovingLeastSquares::MLSVoxelGrid::Leaf
Definition: mls.h:605
pcl::MLSResult::getMLSCoordinates
void getMLSCoordinates(const Eigen::Vector3d &pt, double &u, double &v, double &w) const
Given a point calculate it's 3D location in the MLS frame.
Definition: mls.hpp:447
pcl::PointCloud::push_back
void push_back(const PointT &pt)
Insert a new point in the cloud, at the end of the container.
Definition: point_cloud.h:467
centroid.h
pcl::traits::fieldList
Definition: point_traits.h:179
pcl::uint64_t
std::uint64_t uint64_t
Definition: pcl_macros.h:98