# SE(3) group convolutional neural networks and a study on group convolutions and equivariance for DWI segmentation

## TL;DR

This paper introduces a new neural network for medical imaging that uses advanced mathematical symmetries to improve performance and reduce the need for extra data.

## Contribution

The paper introduces an SE(3) Group Convolutional Neural Network for diffusion-weighted imaging segmentation with direct convolutions.

## Key findings

- Using SE(3) group actions improves segmentation performance with fewer parameters.
- Direct convolutions are more efficient than Fourier-based approaches.
- Group actions provide an inductive bias that reduces reliance on data augmentation.

## Abstract

We present an SE(3) Group Convolutional Neural Network along with a series of networks with different group actions for segmentation of Diffusion Weighted Imaging data. These networks gradually incorporate group actions that are natural for this type of data, in the form of convolutions that provide equivariant transformations of the data. This knowledge provides a potentially important inductive bias and may alleviate the need for data augmentation strategies. We study the effects of these actions on the performances of the networks by training and validating them using the diffusion data from the Human Connectome project. Unlike previous works that use Fourier-based convolutions, we implement direct convolutions, which are more lightweight. We show how incorporating more actions - using the SE(3) group actions - generally improves the performances of our segmentation while limiting the number of parameters that must be learned.