3D mesh Reeb graph computation using commute-time and diffusion distances

Rachid El Khoury (1, 2) , Jean-Philippe Vandeborre (1, 2) , Mohamed Daoudi (2, 1)

1 LIFL - FOX MIIRE
2 Institut TELECOM/TELECOM Lille1

3D-model analysis plays an important role in numerous applications. In this paper, we present an approach for Reeb graph extraction using a novel mapping function. Our mapping function computes a real value for each vertex which provides interesting insights to describe topology structure of the 3D-model. We perform discrete contour for each vertex according to our mapping function. Topology changes can be detected by discrete contours analysis to construct the Reeb graph. Our mapping function has some important properties. It is invariant to rigid and non rigid transformations, it is insensitive to noise, it is robust to small topology changes, and it does not depend on parameters. From the extracted graph, these properties show the significant parts of a 3D-model. We retain the evaluation criteria to the properties of the mapping function, and compared them to those used in the state of the art. In the end, we present extracted Reeb graph on various models with different positions.

Mots clés: Reeb graph; topological skeleton; feature points; mapping function; diffusion geometry; Laplace- Beltrami

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]

Rachid El Khoury, Jean-Philippe Vandeborre, Mohamed Daoudi. 3D mesh Reeb graph computation using commute-time and diffusion distances. 3D Image Processing (3DIP) and Applications, Jan 2012, Burlingame, California, USA, United States. pp.8090-16. ⟨hal-00666106⟩