Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs

TL;DR

This paper introduces Gauge Equivariant Mesh CNNs that utilize anisotropic, gauge-equivariant kernels and a geometric message passing scheme to better capture the orientation and geometry of meshes, improving expressivity.

Contribution

It presents a novel gauge equivariant convolutional framework for meshes that incorporates anisotropic kernels and orientation-aware message passing.

Findings

Significantly improved expressivity over traditional GCNs.

Effective capture of mesh orientation and geometry.

Validated through experimental results.

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.