Kinematic Reeb Graph Extraction Based on Heat Diffusion

This paper presents a new approach of Reeb graph extraction adapted to 3D dynamic triangular Meshes. Particularly, we propose a new continuous scalar function, used for Reeb graph construction. This function is based on the heat diffusion properties. The restriction of the heat kernel to temporal domain makes the scalar function intrinsic and stable against perturbations. Due to the presence of neighborhood information in the heat kernel associated to each vertex, the proposed Reeb Graph extraction can be extremely useful as local shape descriptor for non-rigid shape retrieval. Experiments show that the proposed structural analysis technique achieves high accuracy and stability under topology changes and various perturbations through time.