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

arXiv: https://arxiv.org/abs/2303.00351 · HTML: https://mlsanity.com/paper/2303.00351/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 19 references that are in the map.
- First posted on arXiv 1 Mar 2023.

## Builds on (most cited first, 12 of 12)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [The Medical Segmentation Decathlon](https://mlsanity.com/paper/2106.05735/) (2021)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Learning with invariances in random features and kernel models](https://mlsanity.com/paper/2102.13219/) (2021)
- [Rotation-Equivariant Deep Learning for Diffusion MRI](https://mlsanity.com/paper/2102.06942/) (2021)
- [Sample Efficient Semantic Segmentation using Rotation Equivariant Convolutional Networks](https://mlsanity.com/paper/1807.00583/) (2018)
- [Beyond CNNs: Exploiting Further Inherent Symmetries in Medical Images for Segmentation](https://mlsanity.com/paper/2005.03924/) (2020)

## Built on by (most cited first, 2 of 2)

- [Equivariant symmetry-aware head pose estimation for fetal MRI](https://mlsanity.com/paper/2512.04890/) (2025)
- [Rotation Equivariant Convolutions in Deformable Registration of Brain MRI](https://mlsanity.com/paper/2604.08034/) (2026)

## Abstract (arXiv)

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