Laplacian spectral distances and kernels on 3D shapes

Abstract

This paper presents an alternative means of deriving and discretizing spectral distances and kernels on a 3D shape by filtering its Laplacian spectrum. Through the selection of a filter map, we design new spectral kernels and distances, whose smoothness and encoding of both local and global properties depend on the convergence of the filtered Laplacian eigenvalues to zero. Approximating the discrete spectral distances through the Taylor approximation of the filter map, the proposed computation is independent of the evaluation of the Laplacian spectrum, bypasses the computational and storage limits of previous work, which requires the selection of a specific subset of eigenpairs, and guarantees a higher approximation accuracy and a lower computational cost.