Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs
This addresses a limitation in mesh processing for computer graphics or geometry applications, though it appears incremental as it builds on existing GCNs.
The paper tackled the problem of isotropic kernels in graph convolutional networks (GCNs) on meshes, which ignore orientation and geometry, by proposing Gauge Equivariant Mesh CNNs with anisotropic kernels and geometric message passing, resulting in significantly improved expressivity over conventional GCNs and other methods.
A common approach to define convolutions on meshes is to interpret them as a graph and apply graph convolutional networks (GCNs). Such GCNs utilize isotropic kernels and are therefore insensitive to the relative orientation of vertices and thus to the geometry of the mesh as a whole. We propose Gauge Equivariant Mesh CNNs which generalize GCNs to apply anisotropic gauge equivariant kernels. Since the resulting features carry orientation information, we introduce a geometric message passing scheme defined by parallel transporting features over mesh edges. Our experiments validate the significantly improved expressivity of the proposed model over conventional GCNs and other methods.