Moving Frame Net: SE(3)-Equivariant Network for Volumes
This work addresses the need for efficient SE(3)-equivariant networks in medical imaging, though it is incremental as it builds on prior moving frames methods.
The paper tackled the problem of building rotation and translation equivariant neural networks for 3D volumes by reducing the computational cost of moving frames from repeated per-layer calculations to a single input-stage computation, resulting in a model that outperforms benchmarks in medical volume classification on most MedMNIST3D datasets.
Equivariance of neural networks to transformations helps to improve their performance and reduce generalization error in computer vision 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.