From 0b8aa83b8f4d5540cc5fd25b307e412ff92923b9 Mon Sep 17 00:00:00 2001 From: Nuno Miguel Nobre Date: Thu, 22 Jun 2023 21:08:21 +0100 Subject: [PATCH 1/3] Improve the Triangulated Surface Mesh Segmentation user manual --- .../Surface_Mesh_Segmentation.txt | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/Surface_mesh_segmentation/doc/Surface_mesh_segmentation/Surface_Mesh_Segmentation.txt b/Surface_mesh_segmentation/doc/Surface_mesh_segmentation/Surface_Mesh_Segmentation.txt index c947aac7dd7..b618ef20ce0 100644 --- a/Surface_mesh_segmentation/doc/Surface_mesh_segmentation/Surface_Mesh_Segmentation.txt +++ b/Surface_mesh_segmentation/doc/Surface_mesh_segmentation/Surface_Mesh_Segmentation.txt @@ -102,12 +102,12 @@ The energy function minimized using alpha-expansion graph cut algorithm \cgalCit \f$ E(\bar{x}) = \sum\limits_{f \in F} e_1(f, x_f) + \lambda \sum\limits_{ \{f,g\} \in N} e_2(x_f, x_g) \f$ - \f$ e_1(f, x_f) = -log(max(P(f|x_f), \epsilon)) \f$ + \f$ e_1(f, x_f) = -\log(\max(P(f|x_f), \epsilon_1)) \f$ \f$ e_2(x_f, x_g) = \left \{ \begin{array}{rl} - -log(\theta(f,g)/\pi) &\mbox{ $x_f \ne x_g$} \\ + -\log(w\max(1 - |\theta(f,g)|/\pi, \epsilon_2)) &\mbox{ $x_f \ne x_g$} \\ 0 &\mbox{ $x_f = x_g$} \end{array} \right \} \f$ @@ -119,8 +119,8 @@ where: - \f$x_f\f$ denotes the cluster assigned to facet \f$f\f$, - \f$P(f|x_p)\f$ denotes the probability of assigning facet \f$f\f$ to cluster \f$x_p\f$, - \f$\theta(f,g)\f$ denotes the dihedral angle between neighboring facets \f$f\f$ and \f$g\f$: - concave angles and convex angles are weighted by 1 and 0.1 respectively, - - \f$\epsilon\f$ denotes the minimal probability threshold, + convex angles, \f$[-\pi, 0]\f$, and concave angles, \f$]0, \pi]\f$, are weighted by \f$w=0.08\f$ and \f$w=1\f$, respectively, + - \f$\epsilon_1, \epsilon_2\f$ denote minimal probability and angle thresholds, respectively, - \f$\lambda \in [0,1]\f$ denotes a smoothness parameter. @@ -128,7 +128,7 @@ where: Note both terms of the energy function, \f$ e_1 \f$ and \f$ e_2 \f$, are always non-negative. The first term of the energy function provides the contribution of the soft clustering probabilities. -The second term of the energy function is a geometric criterion that is larger when two adjacent facets sharing a sharp and concave edge are not in the same cluster. +The second term of the energy function is a geometric criterion that is larger the closer to \f$\pm\pi\f$, i.e. the flatter, the dihedral angle between two adjacent facets not in the same cluster is. The smoothness parameter makes this geometric criterion more or less prevalent. Assigning a high value to the smoothness parameter results in a small number of segments (since constructing a segment boundary would be expensive). From 56097acf827f2c354d3b449fd77de12ae1b316ad Mon Sep 17 00:00:00 2001 From: Nuno Miguel Nobre Date: Thu, 22 Jun 2023 21:14:30 +0100 Subject: [PATCH 2/3] Add Polyhedron_items_with_id_3 to PolyhedronItems_3 concept reference --- Polyhedron/doc/Polyhedron/Concepts/PolyhedronItems_3.h | 1 + 1 file changed, 1 insertion(+) diff --git a/Polyhedron/doc/Polyhedron/Concepts/PolyhedronItems_3.h b/Polyhedron/doc/Polyhedron/Concepts/PolyhedronItems_3.h index 62c23598c49..2b6150c70a1 100644 --- a/Polyhedron/doc/Polyhedron/Concepts/PolyhedronItems_3.h +++ b/Polyhedron/doc/Polyhedron/Concepts/PolyhedronItems_3.h @@ -15,6 +15,7 @@ polyhedral surface renames faces to facets. \cgalHasModel `CGAL::Polyhedron_items_3` \cgalHasModel `CGAL::Polyhedron_min_items_3` +\cgalHasModel `CGAL::Polyhedron_items_with_id_3` \sa `CGAL::Polyhedron_3` \sa `HalfedgeDSItems` From 993060cbdde7d9c08f4425ddafc9b0c7e6c649dc Mon Sep 17 00:00:00 2001 From: Nuno Nobre Date: Wed, 5 Jul 2023 14:55:02 +0100 Subject: [PATCH 3/3] Simplify description in the Triangulated Surface Mesh Segmentation user manual Co-authored-by: Sebastien Loriot --- .../doc/Surface_mesh_segmentation/Surface_Mesh_Segmentation.txt | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Surface_mesh_segmentation/doc/Surface_mesh_segmentation/Surface_Mesh_Segmentation.txt b/Surface_mesh_segmentation/doc/Surface_mesh_segmentation/Surface_Mesh_Segmentation.txt index b618ef20ce0..ca138cd3e89 100644 --- a/Surface_mesh_segmentation/doc/Surface_mesh_segmentation/Surface_Mesh_Segmentation.txt +++ b/Surface_mesh_segmentation/doc/Surface_mesh_segmentation/Surface_Mesh_Segmentation.txt @@ -128,7 +128,7 @@ where: Note both terms of the energy function, \f$ e_1 \f$ and \f$ e_2 \f$, are always non-negative. The first term of the energy function provides the contribution of the soft clustering probabilities. -The second term of the energy function is a geometric criterion that is larger the closer to \f$\pm\pi\f$, i.e. the flatter, the dihedral angle between two adjacent facets not in the same cluster is. +The second term of the energy function is a geometric criterion that is larger the closer to \f$\pm\pi\f$ the dihedral angle between two adjacent facets not in the same cluster is. The smoothness parameter makes this geometric criterion more or less prevalent. Assigning a high value to the smoothness parameter results in a small number of segments (since constructing a segment boundary would be expensive).