A Framework Based on Compressed Manifold Modes for Robust Local Spectral Analysis

Abstract

Compressed Manifold Modes (CMM) were recently introduced as a solution to one of the drawbacks of spectral analysis on triangular meshes. The eigenfunctions of the Laplace-Beltrami operator on a mesh depend on the whole shape which makes them sensitive to local aspects. CMM are solutions of an extended problem that have a compact rather than global support and are thus suitable for a wider range of applications. In order to use CMM in real applications, an extensive test has been performed to better understand the limits of their computation (convergence and speed) according to the compactness parameter, the mesh resolution and the number of requested modes. The contribution of this paper is to propose a robust choice of parameters, the automated computation of an adequate number of modes (or eigenfunctions), stability with mutltiresolution and isometric meshes, and an example application with high potential for shape indexation.