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A common approach to define convolutions on meshes is to interpret them as agraph and apply graph convolutional networks (GCNs). Such GCNs utilizeisotropic kernels and are therefore insensitive to the relative orientation ofvertices and thus to the geometry of the mesh as a whole. We propose GaugeEquivariant Mesh CNNs which generalize GCNs to apply anisotropic gaugeequivariant kernels. Since the resulting features carry orientationinformation, we introduce a geometric message passing scheme defined byparallel transporting features over mesh edges. Our experiments validate thesignificantly improved expressivity of the proposed model over conventionalGCNs and other methods.

Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs