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

user manual changes after 3rd review round

This commit is contained in:
Sébastien Loriot 2013-11-05 16:40:33 +01:00
parent 5a2386f7ca
commit f160e9cbe0
1 changed files with 8 additions and 7 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

15
Surface_mesh_segmentation/doc/Surface_mesh_segmentation/Surface_Mesh_Segmentation.txt
View File

@ -41,15 +41,16 @@ Influence of pose changes over SDF values and the segmentation.
\subsubsection Surface_mesh_segmentationRawSDF Computation of Raw SDF Values
For a given input mesh, the raw SDF values are computed by processing each facet one by one. For a given facet,
several rays are sampled in a cone constructed using the centroid of the facet as apex and inward-normal of the facet as axis.
Each ray is cast into a segment, its endpoints being the apex of the cone and the first mesh facet intersection point.
If a ray forms an obtuse angle with the inward-normal of the first intersected facet, it is not accepted.
Using the lengths of the accepted cast rays, which intuitively correspond to a local volume sampling,
the raw SDF value is calculated by first applying an outlier removal procedure and then taking average of the lengths.
Note that only facets having no accepted rays get no raw SDF values
(the package also accepts input meshes with holes, in such a case rays that can not be cast to a segment are also not accepted).
Each ray is truncated into a segment, its endpoints being the apex of the cone and the first mesh facet intersection point.
Using the lengths of these truncated rays, which intuitively correspond to a local volume sampling,
the raw SDF value is calculated by first applying an outlier removal procedure and then taking the average of the lengths.
The raw SDF values can be computed using the function `compute_sdf_values()`, setting `postprocess` to `false`.
\note This package also accepts input meshes with holes. In such a case rays that can not be truncated to a segment
or rays that form an obtuse angle with the inward-normal of the first intersected facet are not accepted.
Only facets having no accepted rays get no raw SDF values
\subsubsection Surface_mesh_segmentationPostprocessing Post-processing of Raw SDF Values
After having calculated the raw SDF value for each facet, the SDF values used in the segmentation algorithm are
the result of several post-processing steps:
@ -60,7 +61,7 @@ The main reason for not assigning 0 to facets with no SDF values is that it can
- A bilateral smoothing \cgalCite{Tomasi1998Bilateral} is applied.
This smoothing technique removes the noise while trying to keep fast changes on SDF values unchanged since they are natural candidates for segment boundaries.
The bilateral smoothing has three parameters that are set by default as follows:
The bilateral smoothing has three parameters that are set as follows:
-\f$ w = \lfloor\sqrt{ |F| / 2000}\rfloor + 1 \f$, the window size (i.e. maximum level for breadth-first neighbor selection), where \f$ F \f$ denotes the set of facets
-\f$ \sigma_s = w / 2 \f$, the spatial parameter
-\f$ \sigma_{r_i} = \sqrt{1/|w_i| \sum_{f_j \in w_i}(SDF(f_j) - SDF(f_i))^2} \f$, the range parameter set for each facet \f$ f_i \f$; \f$ w_i \f$ denotes the set of neighboring facets of \f$ f_i \f$ collected using \f$ w \f$ in the facet neighbor breadth-first search