Sparse approximation of 3D shapes via spectral graph wavelets

Abstract

This paper investigates the compressive representation of 3D meshes and articulates a novel sparse approximation method for 3D shapes based on spectral graph wavelets. The originality of this paper is centering on the first attempt of exploiting spectral graph wavelets in the sparse representation for 3D shape geometry. Conventional spectral mesh compression employs the eigenfunctions of mesh Laplacian as shape bases. The Laplacian eigenbases, generalizing the Fourier bases from Euclidean domain to manifold, exhibit global support and are neither efficient nor precise in representing local geometry. To ameliorate, we advocate an innovative approach to 3D mesh compression using spectral graph wavelets as dictionary to encode mesh geometry. In contrast to Laplacian eigenbases, the spectral graph wavelets are locally defined at individual vertices and can better capture local shape information in a more accurate way. Nonetheless, the multiscale spectral graph wavelets form a redundant dictionary as shape bases, therefore we formulate the compression of 3D shape as a sparse approximation problem that can be readily handled by powerful algorithms such as orthogonal matching pursuit. Various experiments demonstrate that our method is superior to the existing spectral mesh compression methods.