Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs [article]

Pim de Haan, Maurice Weiler, Taco Cohen, Max Welling
2021 arXiv   pre-print
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
more » ... e 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.
arXiv:2003.05425v3 fatcat:jv4txtctfrgmvjpkguvmttu4r4