A framework for histogram-induced 3D descriptors

We present a novel framework to describe 3D shapes, based on modeling the probability density of their shape functions. These functions are conceived to reflect the 3D geometrical properties of the shape surfaces. The densities are modeled as mixtures of Gaussians, each component being the distribution induced by a mesh triangle. A fast algorithm is developed exploiting both the special geometry of 3D triangles with numerical approximations as well as a transform technique. We test and compare the proposed descriptors to other histogram-based methods on two different 3D model databases. It is shown that 3D shape descriptors outperform all of its competitors except one in retrieval applications. Furthermore our methodology provides a fertile ground to introduce and test new descriptors.