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cgal/Surface_mesh_segmentation/include/CGAL/Surface_mesh_segmentation.h

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#ifndef CGAL_SURFACE_MESH_SEGMENTATION_H
#define CGAL_SURFACE_MESH_SEGMENTATION_H
/* NEED TO BE DONE */
/* About implementation:
/* 1) Generic implementation which supports multiple number type (FT) not OK for now */
/* 2) I am not using BGL, as far as I checked there is a progress on BGL redesign
(https://cgal.geometryfactory.com/CGAL/Members/wiki/Features/BGL) which introduces some features
for face-based traversal / manipulation by FaceGraphs */
/* 3) Deciding on which parameters will be taken from user */
/* 4) Make it more readable: calculate_sdf_value_of_facet function.
/* About paper (and correctness / efficiency etc.):
/* 1) Weighting ray distances with inverse of their angles: not sure how to weight exactly */
/* 2) Anisotropic smoothing: have no idea what it is exactly, should read some material (google search is not enough) */
/* 3) Deciding how to generate rays in cone: for now using "polar angle" and "generate in square then accept-reject" techniques */
#include <iostream>
#include <fstream>
#include <cmath>
#include <vector>
#include <algorithm>
//#include "Expectation_maximization.h"
#include <CGAL/AABB_tree.h>
#include <CGAL/AABB_traits.h>
#include <CGAL/AABB_polyhedron_triangle_primitive.h>
#define PI 3.14159265359
#define LOG_5 1.60943791
#define NORMALIZATION_ALPHA 4.0
namespace CGAL
{
template <class Polyhedron>
class Surface_mesh_segmentation
{
//type definitions
public:
typedef typename Polyhedron::Traits Kernel;
typedef typename Polyhedron::Facet Facet;
typedef typename Kernel::Vector_3 Vector;
typedef typename Kernel::Point_3 Point;
typedef typename Kernel::FT FT;
//Should we access types (inner classes etc.) via traits ? may be something like this:
//typedef typename boost::graph_traits<Polyhedron>::facet_iterator facet_iterator; ???
typedef typename Polyhedron::Facet_iterator Facet_iterator;
typedef typename Polyhedron::Facet_handle Facet_handle;
protected:
typedef typename Kernel::Ray_3 Ray;
typedef typename CGAL::AABB_polyhedron_triangle_primitive<Kernel, Polyhedron>
Primitive;
typedef typename CGAL::AABB_tree<CGAL::AABB_traits<Kernel, Primitive>>
Tree;
typedef typename Tree::Object_and_primitive_id
Object_and_primitive_id;
typedef std::map<Facet_handle, FT> Face_value_map;
typedef std::map<Facet_handle, int> Face_center_map;
template <typename ValueTypeName>
struct compare_pairs {
bool operator()(ValueTypeName& v1, ValueTypeName& v2) {
return v1.second < v2.second;
}
};
//member variables
public:
Polyhedron* mesh;
Face_value_map sdf_values;
Face_center_map centers;
int number_of_centers;
protected:
std::ofstream log_file;
//member functions
public:
Surface_mesh_segmentation(Polyhedron* mesh) : mesh(mesh),
log_file("log_file.txt"), number_of_centers(5) {
calculate_sdf_values();
//write_sdf_values("sdf_values_2.txt");
//read_sdf_values("sdf_values.txt");
//apply_GMM_fitting();
}
//protected:
void calculate_sdf_values() {
Tree tree(mesh->facets_begin(), mesh->facets_end());
for(Facet_iterator facet_it = mesh->facets_begin();
facet_it != mesh->facets_end(); ++facet_it) {
CGAL_precondition(facet_it->is_triangle()); //Mesh should contain triangles.
Point v1 = facet_it->halfedge()->vertex()->point();
Point v2 = facet_it->halfedge()->next()->vertex()->point();
Point v3 = facet_it->halfedge()->next()->next()->vertex()->point();
Point center = CGAL::centroid(v1, v2, v3);
Vector normal = CGAL::unit_normal(v1, v2,
v3) * -1.0; //Assuming triangles are CCW oriented.
FT sdf = calculate_sdf_value_of_facet(facet_it, center, normal, tree,
(1.0/3.0) * PI, 7);
sdf_values.insert(std::pair<Facet_handle, FT>(facet_it, sdf));
}
normalize_sdf_values();
smooth_sdf_values();
}
FT calculate_sdf_value_of_facet(const Facet_handle& facet, const Point& center,
const Vector& normal_const, const Tree& tree, double half_cone_angle,
int ray_count_sqrt) const {
Kernel::Plane_3 plane(center, normal_const);
Vector v1 = plane.base1();
Vector v2 = plane.base2();
v1 = v1 / CGAL::sqrt(v1.squared_length());
v2 = v2 / CGAL::sqrt(v2.squared_length());
//Vector v1 = on_plane - center;
//v1 = v1 / sqrt(v1.squared_length());
//Vector v2 = CGAL::cross_product(normal, v1);
int ray_count = ray_count_sqrt * ray_count_sqrt;
std::vector<FT> ray_distances, ray_weights;
ray_distances.reserve(ray_count);
ray_weights.reserve(ray_count);
double angle_st_dev = half_cone_angle / 2; //Not sure what to use here.
double normal_distance = 1.0 / tan(half_cone_angle);
Vector normal = normal_const * normal_distance;
double mid_point = (ray_count_sqrt-1) / 2.0;
for(int i = 0; i < ray_count_sqrt; ++i)
for(int j = 0; j < ray_count_sqrt; ++j) {
double picking_1 = i / (double) (ray_count_sqrt-1);
double picking_2 = j / (double) (ray_count_sqrt-1);
double R = picking_1;
double Q = 2 * picking_2 * PI;
Vector random_vector = (v1 * (R * cos(Q))) + (v2 * (R * sin(Q)));
double dist_to_center = R;
//double w1 = (i - mid_point)/(mid_point);
//double w2 = (j - mid_point)/(mid_point);
//double dist_to_center = sqrt(w1*w1 + w2*w2);
//if(dist_to_center > 1.0) { continue; }
//Vector random_vector = (v1 * w1) + (v2 * w2);
//random_vector = random_vector * tan(half_cone_angle);
Ray ray(center, normal + random_vector);
FT min_distance;
bool is_found;
cast_and_return_minimum(ray, tree, facet, is_found, min_distance);
if(!is_found) {
continue;
}
double angle = atan(dist_to_center / normal_distance);
FT weight = FT(exp(-0.5 * (pow(angle / angle_st_dev, 2))));
ray_weights.push_back(weight);
ray_distances.push_back(min_distance);
}
return calculate_sdf_value_from_rays(ray_distances, ray_weights);
}
FT calculate_sdf_value_from_rays( std::vector<FT>& ray_distances,
std::vector<FT>& ray_weights) const {
FT total_weights = FT(0.0), total_distance = FT(0.0);
FT median_sdf = FT(0.0), st_dev = FT(0.0);
int accepted_ray_count = ray_distances.size();
if(accepted_ray_count == 0) {
return FT(0.0);
} else if(accepted_ray_count == 1) {
return ray_distances[0];
} else {
int half_ray_count = accepted_ray_count / 2;
std::nth_element(ray_distances.begin(), ray_distances.begin() + half_ray_count,
ray_distances.end());
if( accepted_ray_count % 2 == 0) {
FT median_1 = ray_distances[half_ray_count];
FT median_2 = *std::max_element(ray_distances.begin(),
ray_distances.begin() + half_ray_count);
median_sdf = (median_1 + median_2) / 2;
} else {
median_sdf = ray_distances[half_ray_count];
}
}
for(std::vector<FT>::iterator dist_it = ray_distances.begin();
dist_it != ray_distances.end(); ++dist_it) {
FT dif = (*dist_it) - median_sdf;
st_dev += dif * dif;
}
st_dev = CGAL::sqrt(st_dev / (ray_distances.size()));
std::vector<FT>::iterator w_it = ray_weights.begin();
for(std::vector<FT>::iterator dist_it = ray_distances.begin();
dist_it != ray_distances.end(); ++dist_it, ++w_it) {
if(fabs((*dist_it) - median_sdf) > st_dev) {
continue;
}
total_distance += (*dist_it) * (*w_it);
total_weights += (*w_it);
}
return total_distance / total_weights;
}
void cast_and_return_minimum(const Ray& ray, const Tree& tree,
const Facet_handle& facet,
bool& is_found, FT& min_distance) const {
std::list<Object_and_primitive_id> intersections;
tree.all_intersections(ray, std::back_inserter(intersections));
Vector min_i_ray;
Tree::Primitive_id min_id;
is_found = false;
for(std::list<Object_and_primitive_id>::iterator op_it = intersections.begin();
op_it != intersections.end() ; ++op_it) {
CGAL::Object object = op_it->first;
Tree::Primitive_id id = op_it->second;
Point i_point;
if(id == facet) {
continue; //Since center is located on related facet, we should skip it if there is an intersection with it.
}
if(!CGAL::assign(i_point, object)) {
continue; //What to do here (in case of intersection object is a segment), I am not sure ???
}
Vector i_ray = (ray.source() - i_point);
FT new_distance = CGAL::sqrt(i_ray.squared_length());
if(!is_found || new_distance < min_distance) {
min_distance = new_distance;
min_id = id;
min_i_ray = i_ray;
is_found = true;
}
}
if(!is_found) {
return;
}
Point min_v1 = min_id->halfedge()->vertex()->point();
Point min_v2 = min_id->halfedge()->next()->vertex()->point();
Point min_v3 = min_id->halfedge()->next()->next()->vertex()->point();
Vector min_normal = CGAL::normal(min_v1, min_v2, min_v3) * -1.0;
if(CGAL::angle(CGAL::ORIGIN + min_i_ray, Point(CGAL::ORIGIN),
CGAL::ORIGIN + min_normal) != CGAL::ACUTE) {
is_found = false;
}
}
void normalize_sdf_values() {
FT max_value = std::max_element(sdf_values.begin(), sdf_values.end(),
compare_pairs<Face_value_map::value_type>())->second;
FT min_value = std::min_element(sdf_values.begin(), sdf_values.end(),
compare_pairs<Face_value_map::value_type>())->second;
FT max_min_dif = max_value - min_value;
for(Face_value_map::iterator pair_it = sdf_values.begin();
pair_it != sdf_values.end(); ++pair_it) {
FT linear_normalized = (pair_it->second - min_value) / max_min_dif;
double log_normalized = log(CGAL::to_double(linear_normalized) *
NORMALIZATION_ALPHA + 1) / LOG_5; // how to log a generic Number_type(FT)?.
pair_it->second = FT(log_normalized);
}
}
void smooth_sdf_values() {
Face_value_map smoothed_sdf_values;
for(Face_value_map::iterator pair_it = sdf_values.begin();
pair_it != sdf_values.end(); ++pair_it) {
Facet_handle f = pair_it->first;
Facet::Halfedge_around_facet_circulator facet_circulator = f->facet_begin();
FT total_neighbor_sdf = FT(0.0);
do {
total_neighbor_sdf += sdf_values[facet_circulator->opposite()->facet()];
} while( ++facet_circulator != f->facet_begin());
total_neighbor_sdf /= 3;
smoothed_sdf_values[f] = (sdf_values[f] + total_neighbor_sdf) / 2;
}
sdf_values = smoothed_sdf_values;
}
//void apply_GMM_fitting()
//{
// std::vector<double> sdf_vector;
// for(Facet_iterator facet_it = mesh->facets_begin(); facet_it != mesh->facets_end(); ++facet_it)
// {
// sdf_vector.push_back(sdf_values[facet_it]);
// }
// Expectation_maximization fitter(number_of_centers, sdf_vector);
// std::vector<int> center_memberships;
// fitter.fill_with_center_ids(center_memberships);
// std::vector<int>::iterator center_it = center_memberships.begin();
// for(Facet_iterator facet_it = mesh->facets_begin(); facet_it != mesh->facets_end(); ++facet_it, ++center_it)
// {
// centers.insert(std::pair<Facet_handle, int>(facet_it, (*center_it)));
// }
//}
void write_sdf_values(const char* file_name) {
std::ofstream output(file_name);
for(Facet_iterator facet_it = mesh->facets_begin();
facet_it != mesh->facets_end(); ++facet_it) {
output << sdf_values[facet_it] << std::endl;
}
output.close();
}
void read_sdf_values(const char* file_name) {
std::ifstream input(file_name);
for(Facet_iterator facet_it = mesh->facets_begin();
facet_it != mesh->facets_end(); ++facet_it) {
FT sdf_value;
input >> sdf_value;
sdf_values.insert(std::pair<Facet_handle, FT>(facet_it, sdf_value));
}
}
};
} //namespace CGAL
#undef LOG_5
#undef PI
#undef NORMALIZATION_ALPHA
#endif //CGAL_SURFACE_MESH_SEGMENTATION_H
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