Laplace-Beltrami Eigenfunctions for Deformation Invariant Shape Representation

Abstract

A deformation invariant representation of surfaces, the GPS embedding, is introduced using the eigenvalues and eigenfunctions of the Laplace-Beltrami differential operator. Notably, since the definition of the GPS embedding completely avoids the use of geodesic distances, and is based on objects of global character, the obtained representation is robust to local topology changes. The GPS embedding captures enough information to handle various shape processing tasks as shape classification, segmentation, and correspondence. To demonstrate the practical relevance of the GPS embedding, we introduce a deformation invariant shape descriptor called G2-distributions, and demonstrate their discriminative power, invariance under natural deformations, and robustness.