Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs

A common approach to define convolutions on meshes is to interpret them as a\ngraph and apply graph convolutional networks (GCNs). Such GCNs utilize\nisotropic kernels and are therefore insensitive to the relative orientation of\nvertices and thus to the geometry of the mesh as a whole. We propose Gauge\nEquivariant Mesh CNNs which generalize GCNs to apply anisotropic gauge\nequivariant kernels. Since the resulting features carry orientation\ninformation, we introduce a geometric message passing scheme defined by\nparallel transporting features over mesh edges. Our experiments validate the\nsignificantly improved expressivity of the proposed model over conventional\nGCNs and other methods.\n