A Unifying Computational Framework for Histogram-based 3D Shape Descriptors

In this paper, we propose a novel framework for 3D histogram based shape descriptors based on modeling the probability density functions of geometrical quantities, shape functions which measure 3D surface properties, as mixtures of Gaussians. We make use of the special geometry of triangular meshes in 3D, provide efficient means to approximate the moments of shape functions per triangle, and as a consequence cope with mesh triangles of arbitrary sizes and shapes. This boils down to choosing a set of surface points more representative than the triangle centers and to modeling the local surface geometry in an implicit way. Our framework produces a number of 3D shape descriptors that prove to be quite discriminative in a retrieval application. We test and compare our descriptors to other histogram based methods on two 3D model databases, Princeton Shape Benchmark and Sculpteur, fundamentally different in semantic content and mesh quality. The results are superior to well known histogram based 3D shape descriptors proposed in the literature.