E(3)-Equivariant Mesh Neural Networks
This work addresses the need for efficient and effective 3D mesh processing in computer vision and graphics, though it is incremental as it extends existing graph neural network methods.
The paper tackles the problem of geometric deep learning on 3D meshes by developing an equivariant mesh neural network that outperforms more complex methods, achieving faster run-time and no expensive pre-processing.
Triangular meshes are widely used to represent three-dimensional objects. As a result, many recent works have address the need for geometric deep learning on 3D mesh. However, we observe that the complexities in many of these architectures does not translate to practical performance, and simple deep models for geometric graphs are competitive in practice. Motivated by this observation, we minimally extend the update equations of E(n)-Equivariant Graph Neural Networks (EGNNs) (Satorras et al., 2021) to incorporate mesh face information, and further improve it to account for long-range interactions through hierarchy. The resulting architecture, Equivariant Mesh Neural Network (EMNN), outperforms other, more complicated equivariant methods on mesh tasks, with a fast run-time and no expensive pre-processing. Our implementation is available at https://github.com/HySonLab/EquiMesh