# Rotation Equivariant Convolutions in Deformable Registration of Brain MRI

arXiv: https://arxiv.org/abs/2604.08034 · HTML: https://mlsanity.com/paper/2604.08034/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 13 references that are in the map.
- First posted on arXiv 9 Apr 2026.

## Builds on (most cited first, 7 of 7)

- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [SE(3)-Equivariant and Noise-Invariant 3D Rigid Motion Tracking in Brain MRI](https://mlsanity.com/paper/2312.13534/) (2023)
- [Leveraging SO(3)-steerable convolutions for pose-robust semantic segmentation in 3D medical data](https://mlsanity.com/paper/2303.00351/) (2023)
- [RoTIR: Rotation-Equivariant Network and Transformers for Fish Scale Image Registration](https://mlsanity.com/paper/2401.11270/) (2024)

## Abstract (arXiv)

Image registration is a fundamental task that aligns anatomical structures between images. While CNNs perform well, they lack rotation equivariance - a rotated input does not produce a correspondingly rotated output. This hinders performance by failing to exploit the rotational symmetries inherent in anatomical structures, particularly in brain MRI. In this work, we integrate rotation-equivariant convolutions into deformable brain MRI registration networks. We evaluate this approach by replacing standard encoders with equivariant ones in three baseline architectures, testing on multiple public brain MRI datasets. Our experiments demonstrate that equivariant encoders have three key advantages: 1) They achieve higher registration accuracy while reducing network parameters, confirming the benefit of this anatomical inductive bias. 2) They outperform baselines on rotated input pairs, demonstrating robustness to orientation variations common in clinical practice. 3) They show improved performance with less training data, indicating greater sample efficiency. Our results demonstrate that incorporating geometric priors is a critical step toward building more robust, accurate, and efficient registration models.