Keywords: DWI, Group action, Homogeneous spaces G-CNN, Image Segmentation
TL;DR: We propose a novel separable SE(3) group convolutional neural network for Diffusion MRI data, implemented in a direct and light-weight way.
Abstract: We present a Group Convolutional Network for Segmentation of Diffusion Weighted Imaging data (DWI). The network incorporates group actions that are natural for this type of data, in the form of $SE(3)$ equivariant convolutions, i.e., roto-translation equivariant convolutions. The equivariance property provides an important inductive bias and may alleviate the need for data augmentation strategies. Instead of performing group equivariant convolutions via spectral (Fourier-based) approaches, as is common for $SE(3)$ equivariance, we implement direct and light-weight regular group convolutions. We study the effect of equivariance and weight sharing over $SE(3)$ on performances of the networks on DWI scans from the Human Connectome project. We show how that full $SE(3)$ equivariance improves segmentations, while limiting the number of learnable parameters.