songsenand
/
cgal
mirror of https://github.com/CGAL/cgal
1
0
Fork 0
Code Issues Packages Projects Releases Wiki Activity

Improve the Triangulated Surface Mesh Segmentation user manual

This commit is contained in:
Nuno Miguel Nobre 2023-06-22 21:08:21 +01:00
parent 9cc17545b4
commit 0b8aa83b8f
1 changed files with 5 additions and 5 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

10
Surface_mesh_segmentation/doc/Surface_mesh_segmentation/Surface_Mesh_Segmentation.txt
View File

@ -102,12 +102,12 @@ The energy function minimized using alpha-expansion graph cut algorithm \cgalCit
<td> <td>
\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(\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) = \f$ e_2(x_f, x_g) =
\left \{ \left \{
\begin{array}{rl} \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{ $x_f = x_g$} 0 &\mbox{ $x_f = x_g$}
\end{array} \end{array}
\right \} \f$ \right \} \f$
@ -119,8 +119,8 @@ where:
- \f$x_f\f$ denotes the cluster assigned to facet \f$f\f$, - \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$P(f|x_p)\f$ 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$g\f$: - \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, 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$\epsilon\f$ denotes the minimal probability threshold, - \f$\epsilon_1, \epsilon_2\f$ denote minimal probability and angle thresholds, respectively,
- \f$\lambda \in [0,1]\f$ denotes a smoothness parameter. - \f$\lambda \in [0,1]\f$ denotes a smoothness parameter.
</td> </td>
</tr> </tr>
@ -128,7 +128,7 @@ where:
Note both terms of the energy function, \f$ e_1 \f$ and \f$ e_2 \f$, are always non-negative. Note both terms of the energy function, \f$ e_1 \f$ and \f$ e_2 \f$, are always non-negative.
The first term of the energy function provides the contribution of the soft clustering probabilities. The first term of the energy function provides the contribution of the soft clustering probabilities.
The second term of the energy function is a geometric criterion that is larger when two adjacent facets sharing a sharp and concave edge are not in the same cluster. The second term of the energy function is a geometric criterion that is larger the closer to \f$\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. 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). Assigning a high value to the smoothness parameter results in a small number of segments (since constructing a segment boundary would be expensive).