Skeleton Extraction of Vertex Sets Lying on Arbitrary Triangulated 3D Meshes

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.