Multiscale Representation of 3D Surfaces via Stochastic Mesh Laplacian

Multiscale representation of a 3D surface mesh is a useful tool to understand a mesh both locally and globally. One method is to analyse eigenvalues and eigenvectors of some matrix which represents a discrete operator (e.g. the Laplacian) taking into account the topological and/or geometric structure of the input mesh. However, eigendecomposition is computationally expensive, making this method intractable for meshes containing more than a few thousand vertices. To overcome this problem, we present a novel method for multiscale mesh representation which avoids solving an eigenproblem, based on the proposed stochastic mesh Laplacian. We present the complete algorithm and the theoretical analysis of the stochastic mesh Laplacian. In the experiments, we compare our method with several state-of-the-art approaches to demonstrate its advantages over popular frameworks such as spectral mesh processing, heat diffusion and wavelets. The utility of the method is demonstrated via applications in mesh saliency and interest point detection.