Simple points, topological numbers and geodesic neighborhoods in cubic grids
Pattern Recognition Letters
Building skeleton models via 3-D medial surface/axis thinning algorithms
CVGIP: Graphical Models and Image Processing
A Boolean characterization of three-dimensional simple points
Pattern Recognition Letters
A fast parallel algorithm for thinning digital patterns
Communications of the ACM
A novel cubic-order algorithm for approximating principal direction vectors
ACM Transactions on Graphics (TOG)
Skeleton extraction by mesh contraction
ACM SIGGRAPH 2008 papers
Skeleton-Based Recognition of Chinese Calligraphic Character Image
PCM '08 Proceedings of the 9th Pacific Rim Conference on Multimedia: Advances in Multimedia Information Processing
Medial Representations: Mathematics, Algorithms and Applications
Medial Representations: Mathematics, Algorithms and Applications
Surface sketching with a voxel-based skeleton
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
3D Feature Line Detection Based on Vertex Labeling and 2D Skeletonization
SMI '10 Proceedings of the 2010 Shape Modeling International Conference
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Complex models can be simply described by notions such as skeletons. These robust shape descriptors faithfully characterize the geometry and the topology of an object. Several methods have been developed yet to obtain the skeleton from regular object representations (e.g. 2D images or 3D volumes) but only a few attempt to extract the skeleton from unstructured 3D mesh patches. In this article, we extract a skeleton by topological thinning from vertex sets lying on arbitrary triangulated surface meshes in 3D. The key idea comes down to eroding a 2D set located on a discrete 2-manifold. The main difficulty is to transpose the notion of neighborhood from the classical thinning algorithms where the adjacency is constant (e.g. 26-adjacency in digital volumes, 8-adjacency in 2D images) to the mesh domain where the neighborhood is variable due to the adjacency of each vertex. Thus we propose a thinning operator dedicated to irregular meshes in order to extract the skeleton of a vertex set. To estimate the robustness of our technique, several tests and an application to the feature line detection are presented as a case-study.