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@ -22,7 +22,7 @@ The final segmentation is then obtained via a graph-cut algorithm that considers
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together with the result of the soft clustering.
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We refer to a comprehensive survey on mesh segmentation \cgalCite{Shamir2008SegmentationSurvey} for different segmentation techniques.
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This package offers the computation of the SDF values and the mesh segmentation result as independant functions.
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This package offers the computation of the SDF values and the mesh segmentation result as independent functions.
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This allows an alternative implementation of the SDF to be directly plugged into the segmentation algorithm,
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and also to reuse the SDF values several times with different parameters for the segmentation algorithm.
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@ -47,16 +47,16 @@ Influence of pose changes over SDF values and the segmentation.
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\subsubsection Surface_mesh_segmentationRawSDF Computation of Raw SDF Values
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For a given input mesh, the raw SDF values are computed by processing each facet one by one. For a given facet,
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several rays are sampled in a cone constructed using the centroid of the facet as apex and inward-normal of the facet as axis.
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Each ray in casted into a segment, its endpoints being the apex of the cone and the first mesh facet intersection point.
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Each ray in cast into a segment, its endpoints being the apex of the cone and the first mesh facet intersection point.
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If a ray forms an obtuse angle with the inward-normal of the first intersected facet, it is not accepted.
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Using the lenghts of the accepted casted rays, which intuitively correspond to a local volume sampling,
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Using the lengths of the accepted cast rays, which intuitively correspond to a local volume sampling,
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the raw SDF value is calculated by first applying an outlier removal procedure and then taking average of the lengths.
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Note that only facets having no accepted rays get no raw SDF values
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(the package also accepts input meshes with holes, in such a case rays that can not be casted to a segment are also not accepted).
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(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).
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The raw SDF values can be computed using the function `compute_sdf_values()`, setting `postprocess` to `false`.
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\subsubsection Surface_mesh_segmentationPostprocessing Postprocessing of Raw SDF Values
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\subsubsection Surface_mesh_segmentationPostprocessing Post-processing of Raw SDF Values
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After having calculated the raw SDF value for each facet, the SDF values used in the segmentation algorithm are
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the result of several post-processing steps:
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@ -218,7 +218,7 @@ Number of triangles | `%Simple_cartesian<double>` | `%Exact_predicates_inexact_
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100,332 | 48.7 | 88.1
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</center>
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<!-- This is only to keep the results, the flag is not documentated
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<!-- This is only to keep the results, the flag is not documented
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<center>
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Number of triangles | `%Simple_cartesian<double>` | `%Exact_predicates_inexact_constructions_kernel` (`EPICK`) | `EPICK` with `Fast_sdf_calculation_mode = false`
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---------------------| -------------------------: | --------------------------------------------------------: | -----------------------------------------------:
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@ -265,7 +265,7 @@ A comparison with biased and uniform sampling of points can be seen in \cgalFigu
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\section Surface_mesh_segmentationImplementationhistory Implementation History
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The initial implementation of this package is the result of the work of Ilker O. Yaz during the 2012 season
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of the Google Summer of Code. He has been mentored by Sebastien Loriot who also contributed to the documentation
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of the Google Summer of Code. He has been mentored by Sébastien Loriot who also contributed to the documentation
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and the API definition.
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*/
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