\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - Triangulated Surface Mesh Segmentation

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Modules | Functions
Triangulated Surface Mesh Segmentation Reference

##

Ilker O. Yaz and Sébastien Loriot
This package provides a method to generate a segmentation of a triangulated surface mesh. The algorithm first computes the Shape Diameter Function (SDF) for all facets and applies a graph-cut based algorithm over these values. Low level functions are provided to replace any intermediate step by a custom one.

Introduced in: CGAL 4.4
Depends on: 3D Fast Intersection and Distance Computation
BibTeX: cgal:y-smsimpl-16a
License: GPL
Windows Demo: Operations on Polyhedra
Common Demo Dlls: dlls

## Classified Reference Pages

## Concepts

- `SegmentationGeomTraits`

## Main Functions

- `CGAL::sdf_values()`
- `CGAL::sdf_values_postprocessing()`
- `CGAL::segmentation_from_sdf_values()`
- `CGAL::segmentation_via_sdf_values()`

## Modules
| Concepts

## Functions
template<class Polyhedron , class SDFPropertyMap , class PointPropertyMap = typename boost::property_map<Polyhedron, boost::vertex_point_t>::type, class GeomTraits = typename Kernel_traits<typename boost::property_traits<PointPropertyMap>::value_type>::Kernel>
std::pair< double, double > | CGAL::sdf_values (const Polyhedron &polyhedron, SDFPropertyMap sdf_values_map, double cone_angle=2.0/3.0 *CGAL_PI, std::size_t number_of_rays=25, bool postprocess=true, PointPropertyMap ppmap=PointPropertyMap(), GeomTraits traits=GeomTraits())
| Function computing the Shape Diameter Function over a surface mesh. More...
template<class Polyhedron , class SDFPropertyMap >
std::pair< double, double > | CGAL::sdf_values_postprocessing (const Polyhedron &polyhedron, SDFPropertyMap sdf_values_map)
| Function post-processing raw SDF values computed per facet. More...
template<class Polyhedron , class SDFPropertyMap , class SegmentPropertyMap , class PointPropertyMap = typename boost::property_map<Polyhedron, boost::vertex_point_t>::type, class GeomTraits = typename Kernel_traits<typename boost::property_traits<PointPropertyMap>::value_type>::Kernel>
std::size_t | CGAL::segmentation_from_sdf_values (const Polyhedron &polyhedron, SDFPropertyMap sdf_values_map, SegmentPropertyMap segment_ids, std::size_t number_of_clusters=5, double smoothing_lambda=0.26, bool output_cluster_ids=false, PointPropertyMap ppmap=PointPropertyMap(), GeomTraits traits=GeomTraits())
| Function computing the segmentation of a surface mesh given an SDF value per facet. More...
template<class Polyhedron , class SegmentPropertyMap , class PointPropertyMap = typename boost::property_map<Polyhedron, boost::vertex_point_t>::type, class GeomTraits = typename Kernel_traits<typename boost::property_traits<PointPropertyMap>::value_type>::Kernel>
std::size_t | CGAL::segmentation_via_sdf_values (const Polyhedron &polyhedron, SegmentPropertyMap segment_ids, double cone_angle=2.0/3.0 *CGAL_PI, std::size_t number_of_rays=25, std::size_t number_of_clusters=5, double smoothing_lambda=0.26, bool output_cluster_ids=false, PointPropertyMap ppmap=PointPropertyMap(), GeomTraits traits=GeomTraits())
| Function computing the segmentation of a surface mesh. More...

## Function Documentation

template<class Polyhedron , class SDFPropertyMap , class PointPropertyMap = typename boost::property_map<Polyhedron, boost::vertex_point_t>::type, class GeomTraits = typename Kernel_traits<typename boost::property_traits<PointPropertyMap>::value_type>::Kernel>

std::pair<double, double> CGAL::sdf_values | ( | const Polyhedron & | polyhedron,
|  | SDFPropertyMap | sdf_values_map,
|  | double | cone_angle = `2.0 / 3.0 * CGAL_PI`,
|  | std::size_t | number_of_rays = `25`,
|  | bool | postprocess = `true`,
|  | PointPropertyMap | ppmap = `PointPropertyMap()`,
|  | GeomTraits | traits = `GeomTraits()`
| ) |  |

Function computing the Shape Diameter Function over a surface mesh.

This function implements the Shape Diameter Function (SDF) as described in [4]. It is possible to compute raw SDF values (without post-processing). In such a case, -1 is used to indicate when no SDF value could be computed for a facet.

Precondition
  polyhedron.is_pure_triangle()

Template Parameters

  Polyhedron | a model of `FaceListGraph`
  SDFPropertyMap | a `ReadWritePropertyMap` with `boost::graph_traits<Polyhedron>::face_descriptor` as key and `double` as value type
  GeomTraits | a model of `SegmentationGeomTraits`
  PointPropertyMap | a `ReadablePropertyMap` with `boost::graph_traits<Polyhedron>::vertex_descriptor` as key and `GeomTraits::Point_3` as value type.

Parameters

  | polyhedron | surface mesh on which SDF values are computed
  [out] | sdf_values_map | the SDF value of each facet
  | cone_angle | opening angle in radians for the cone of each facet
  | number_of_rays | number of rays picked in the cone of each facet. In our experiments, we observe that increasing the number of rays beyond the default has little effect on the quality of the segmentation result
  | postprocess | if `true`, `CGAL::sdf_values_postprocessing()` is called on raw SDF value computed.
  | traits | traits class
  | ppmap | point property map. An overload is provided with `get(boost::vertex_point,polyhedron)` as default.

Returns
  minimum and maximum raw SDF values if postprocess is `true`, otherwise minimum and maximum SDF values (before linear normalization)

`#include <CGAL/mesh_segmentation.h>`

Examples:
  Surface_mesh_segmentation/sdf_values_example.cpp, Surface_mesh_segmentation/segmentation_from_sdf_values_example.cpp, Surface_mesh_segmentation/segmentation_from_sdf_values_SM_example.cpp, and Surface_mesh_segmentation/segmentation_with_facet_ids_example.cpp.

template<class Polyhedron , class SDFPropertyMap >

std::pair<double, double> CGAL::sdf_values_postprocessing | ( | const Polyhedron & | polyhedron,
|  | SDFPropertyMap | sdf_values_map
| ) |  |

Function post-processing raw SDF values computed per facet.

Post-processing steps applied :

- Facets with -1 SDF values are assigned the average SDF value of their edge-adjacent neighbors. If there is still a facet having -1 SDF value, the minimum valid SDF value assigned to it. Note that this step is not inherited from the paper. The main reason for not assigning 0 to facets with no SDF values (i.e. -1) is that it can obstruct log-normalization process which takes place at the beginning of `CGAL::segmentation_from_sdf_values()`.
- SDF values are smoothed with bilateral filtering.
- SDF values are linearly normalized between [0,1].

See the section Post-processing of Raw SDF Values for more details.

Precondition
  polyhedron.is_pure_triangle()
  Raw values should be greater or equal to 0. -1 indicates when no value could be computed

Template Parameters

  Polyhedron | a model of `FaceListGraph`
  SDFPropertyMap | a `ReadWritePropertyMap` with `boost::graph_traits<Polyhedron>::face_descriptor` as key and `double` as value type

Parameters

  | polyhedron | surface mesh on which SDF values are computed
  [in,out] | sdf_values_map | the SDF value of each facet

Returns
  minimum and maximum SDF values before linear normalization

`#include <CGAL/mesh_segmentation.h>`

template<class Polyhedron , class SDFPropertyMap , class SegmentPropertyMap , class PointPropertyMap = typename boost::property_map<Polyhedron, boost::vertex_point_t>::type, class GeomTraits = typename Kernel_traits<typename boost::property_traits<PointPropertyMap>::value_type>::Kernel>

std::size_t CGAL::segmentation_from_sdf_values | ( | const Polyhedron & | polyhedron,
|  | SDFPropertyMap | sdf_values_map,
|  | SegmentPropertyMap | segment_ids,
|  | std::size_t | number_of_clusters = `5`,
|  | double | smoothing_lambda = `0.26`,
|  | bool | output_cluster_ids = `false`,
|  | PointPropertyMap | ppmap = `PointPropertyMap()`,
|  | GeomTraits | traits = `GeomTraits()`
| ) |  |

Function computing the segmentation of a surface mesh given an SDF value per facet.

This function fills a property map which associates a segment-id (in [0, number of segments -1]) or a cluster-id (in [0, `number_of_clusters` -1]) to each facet. A segment is a set of connected facets which are placed under the same cluster (see Figure 60.5).

Note
  Log-normalization is applied on `sdf_values_map` before segmentation. As described in the original paper [4], this normalization is done to preserve thin parts of the mesh by increasing the distance between smaller SDF values and reducing it between larger ones.
  There is no direct relation between the parameter `number_of_clusters` and the final number of segments after segmentation. However, setting a large number of clusters will result in a detailed segmentation of the mesh with a large number of segments.

Precondition
  polyhedron.is_pure_triangle()
  number_of_clusters > 0

Template Parameters

  Polyhedron | a model of `FaceListGraph`
  SDFPropertyMap | a `ReadablePropertyMap` with `boost::graph_traits<Polyhedron>::face_descriptor` as key and `double` as value type
  SegmentPropertyMap | a `ReadWritePropertyMap` with `boost::graph_traits<Polyhedron>::face_descriptor` as key and `std::size_t` as value type
  GeomTraits | a model of `SegmentationGeomTraits`
  PointPropertyMap | a `ReadablePropertyMap` with `boost::graph_traits<Polyhedron>::vertex_descriptor` as key and `GeomTraits::Point_3` as value type.

Parameters

  | polyhedron | surface mesh corresponding to the SDF values
  | sdf_values_map | the SDF value of each facet between [0-1]
  [out] | segment_ids | the segment or cluster id of each facet
  | number_of_clusters | number of clusters for the soft clustering
  | smoothing_lambda | factor which indicates the importance of the surface features for the energy minimization. It is recommended to choose a value in the interval [0,1]. See the section Hard clustering for more details.
  | output_cluster_ids | if `false` fill `segment_ids` with segment-ids, and with cluster-ids otherwise (see Figure 60.5)
  | traits | traits class
  | ppmap | point property map. An overload is provided with `get(boost::vertex_point,polyhedron)` as default.

Returns
  number of segments if `output_cluster_ids` is set to `false` and `number_of_clusters` otherwise

`#include <CGAL/mesh_segmentation.h>`

Examples:
  Surface_mesh_segmentation/segmentation_from_sdf_values_example.cpp, Surface_mesh_segmentation/segmentation_from_sdf_values_SM_example.cpp, and Surface_mesh_segmentation/segmentation_with_facet_ids_example.cpp.

template<class Polyhedron , class SegmentPropertyMap , class PointPropertyMap = typename boost::property_map<Polyhedron, boost::vertex_point_t>::type, class GeomTraits = typename Kernel_traits<typename boost::property_traits<PointPropertyMap>::value_type>::Kernel>

std::size_t CGAL::segmentation_via_sdf_values | ( | const Polyhedron & | polyhedron,
|  | SegmentPropertyMap | segment_ids,
|  | double | cone_angle = `2.0 / 3.0 * CGAL_PI`,
|  | std::size_t | number_of_rays = `25`,
|  | std::size_t | number_of_clusters = `5`,
|  | double | smoothing_lambda = `0.26`,
|  | bool | output_cluster_ids = `false`,
|  | PointPropertyMap | ppmap = `PointPropertyMap()`,
|  | GeomTraits | traits = `GeomTraits()`
| ) |  |

Function computing the segmentation of a surface mesh.

This function is equivalent to calling the functions `CGAL::sdf_values()` and `CGAL::segmentation_from_sdf_values()` with the same parameters.

Note
  There is no direct relation between the parameter `number_of_clusters` and the final number of segments after segmentation. However, setting a large number of clusters will result in a detailed segmentation of the mesh with a large number of segments.
  For computing segmentations of the mesh with different parameters (i.e. number of levels, and smoothing lambda), it is more efficient to first compute the SDF values using `CGAL::sdf_values()` and use them in different calls to `CGAL::segmentation_from_sdf_values()`.

Precondition
  polyhedron.is_pure_triangle()
  number_of_clusters > 0

Template Parameters

  Polyhedron | a model of `FaceListGraph`
  SegmentPropertyMap | a `ReadWritePropertyMap` with `boost::graph_traits<Polyhedron>::face_descriptor` as key and `std::size_t` as value type
  GeomTraits | a model of `SegmentationGeomTraits`
  PointPropertyMap | a `ReadablePropertyMap` with `boost::graph_traits<Polyhedron>::vertex_descriptor` as key and `GeomTraits::Point_3` as value type.

Parameters

  | polyhedron | surface mesh on which SDF values are computed
  [out] | segment_ids | the segment or cluster id of each facet
  | cone_angle | opening angle in radians for the cone of each facet
  | number_of_rays | number of rays picked in the cone of each facet. In our experiments, we observe that increasing the number of rays beyond the default has a little effect on the quality of the segmentation result
  | number_of_clusters | number of clusters for the soft clustering
  | smoothing_lambda | factor which indicates the importance of the surface features for the energy minimization. It is recommended to choose a value in the interval [0,1]. See the section Hard clustering for more details.
  | output_cluster_ids | if `false` fill `segment_ids` with segment-ids, and with cluster-ids otherwise (see Figure 60.5)
  | traits | traits class
  | ppmap | point property map. An overload is provided with `get(boost::vertex_point,polyhedron)` as default.

Returns
  number of segments if `output_cluster_ids` is set to `false` and `number_of_clusters` otherwise

`#include <CGAL/mesh_segmentation.h>`

Examples:
  Surface_mesh_segmentation/segmentation_via_sdf_values_example.cpp.