Moving Frame Net: SE(3)-Equivariant Network for Volumes

Mateus Sangalli, Samy Blusseau, Santiago Velasco-Forero, Jesus Angulo

Keywords: Lie groups, Group equivariance, 3D image classification, Moving frames

TL;DR: The method of moving frames is applied to construct a SE(3)-equivariance neural network on 3D volumes using a moving frame computed from the input.

Abstract:

Equivariance of neural networks to transformations helps to improve their performance and reduce generalization error in computer visions tasks, as they apply to datasets presenting symmetries (e.g. scalings, rotations, translations).
The method of moving frames is classical for deriving operators invariant to the action of a Lie group in a manifold.
Recently, a rotation and translation equivariant neural network for image data was proposed based on the moving frames approach. In this paper we significantly improve that approach by reducing the computation of moving frames to only one, at the input stage, instead of repeated computations at each layer. The equivariance of the resulting architecture is proved theoretically and we build a rotation and translation equivariant neural network to process volumes, i.e. signals on the 3D space.
Our trained model overperforms the benchmarks in the medical volume classification of most of the tested datasets from MedMNIST3D.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2211.03420/code)