Learning Spectral Dictionary for Local Representation of Mesh

For meshes, sharing the topology of a template is a common and practical setting in face-, hand-, and body-related applications. Meshes are irregular since each vertex's neighbors are unordered and their orientations are inconsistent with other vertices. Previous methods use isotropic filters or predefined local coordinate systems or learning weighting matrices for each vertex of the template to overcome the irregularity. Learning weighting matrices for each vertex to soft-permute the vertex's neighbors into an implicit canonical order is an effective way to capture the local structure of each vertex. However, learning weighting matrices for each vertex increases the parameter size linearly with the number of vertices and large amounts of parameters are required for high-resolution 3D shapes. In this paper, we learn spectral dictionary (i.e., bases) for the weighting matrices such that the parameter size is independent of the resolution of 3D shapes. The coefficients of the weighting matrix bases for each vertex are learned from the spectral features of the template's vertex and its neighbors in a weight-sharing manner. Comprehensive experiments demonstrate that our model produces state-of-the-art results with a much smaller model size.