Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs

• URL: http://arxiv.org/abs/2003.05425v3
• Date: Fri, 19 Nov 2021 12:00:16 GMT
• Title: Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs
• Authors: Pim de Haan, Maurice Weiler, Taco Cohen and Max Welling
• Abstract summary: A common approach to define convolutions on meshes is to interpret them as a graph and apply graph convolutional networks (GCNs) We propose Gauge Equivariant Mesh CNNs which generalize GCNs to apply anisotropic gauge equivariant kernels. Our experiments validate the significantly improved expressivity of the proposed model over conventional GCNs and other methods.
• Score: 81.12344211998635
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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