Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric\n graphs

2020/03/11 by Pim de Haan, Maurice Weiler, de Haan, Pim +5 · 6 citations
Computer Science · Engineering · #3D Shape Modeling and Analysis #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Generative Adversarial Networks and Image Synthesis #Human Pose and Action Recognition #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Video Surveillance and Tracking Methods

paper · pdf · doi:10.48550/arxiv.2003.05425

openalex publication_date 2020/03/11 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Geometric Deep Learning: Going beyond Euclidean data
• Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds
• Parallel Transport Convolution: A New Tool for Convolutional Neural Networks on Manifolds
• PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space
• Detecting Functionality-Specific Vulnerabilities via Retrieving Individual Functionality-Equivalent APIs in Open-Source Repositories
• General E(2)-Equivariant Steerable CNNs

Cited by

• Intrinsic and Triangulation-Agnostic Attention: A Simple and Powerful Approach for Learning on Meshes
• Gauge-Equivariant Graph Networks via Self-Interference Cancellation
• PoissonNet: A Local-Global Approach for Learning on Surfaces
• Probabilistic Numeric Convolutional Neural Networks
• A Wigner-Eckart Theorem for Group Equivariant Convolution Kernels
• Wall Shear Stress Estimation in Abdominal Aortic Aneurysms: Towards Generalisable Neural Surrogate Models

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