# Leveraging SO(3)-steerable convolutions for pose-robust semantic segmentation in 3D medical data

## TL;DR

This paper introduces a new family of 3D segmentation networks using SO(3)-steerable convolutions based on spherical harmonics, enhancing robustness to unseen poses and improving efficiency in medical imaging tasks.

## Contribution

It presents a novel segmentation network architecture employing SO(3)-steerable convolutions that do not require rotation augmentation, improving robustness and efficiency in 3D medical image segmentation.

## Key findings

- Enhanced robustness to unseen data poses.
- Reduced need for data augmentation during training.
- Improved segmentation accuracy and parameter efficiency.

## Abstract

Convolutional neural networks (CNNs) allow for parameter sharing and translational equivariance by using convolutional kernels in their linear layers. By restricting these kernels to be SO(3)-steerable, CNNs can further improve parameter sharing. These rotationally-equivariant convolutional layers have several advantages over standard convolutional layers, including increased robustness to unseen poses, smaller network size, and improved sample efficiency. Despite this, most segmentation networks used in medical image analysis continue to rely on standard convolutional kernels. In this paper, we present a new family of segmentation networks that use equivariant voxel convolutions based on spherical harmonics. These networks are robust to data poses not seen during training, and do not require rotation-based data augmentation during training. In addition, we demonstrate improved segmentation performance in MRI brain tumor and healthy brain structure segmentation tasks, with enhanced robustness to reduced amounts of training data and improved parameter efficiency. Code to reproduce our results, and to implement the equivariant segmentation networks for other tasks is available at http://github.com/SCAN-NRAD/e3nn_Unet