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METHODS article

Front. Artif. Intell.
Sec. Medicine and Public Health
Volume 8 - 2025 | doi: 10.3389/frai.2025.1369717

SE(3) Group Convolutional Neural Networks and a Study on Group Convolutions and Equivariance for DWI Segmentation

Provisionally accepted
Renfei Liu Renfei Liu 1*Francois Lauze Francois Lauze 1Erik J Bekkers Erik J Bekkers 2Sune Darkner Sune Darkner 1Kenny Erleben Kenny Erleben 1
  • 1 University of Copenhagen, Copenhagen, Denmark
  • 2 University of Amsterdam, Amsterdam, Netherlands

The final, formatted version of the article will be published soon.

    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.

    Keywords: Geometric deep learning, Group action, Homogeneous spaces GCNN, image segmentation, Diffusion Weighted Imaging

    Received: 12 Jan 2024; Accepted: 15 Jan 2025.

    Copyright: © 2025 Liu, Lauze, Bekkers, Darkner and Erleben. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Renfei Liu, University of Copenhagen, Copenhagen, Denmark

    Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.