Rotation Equivariant Convolutions in Deformable Registration of Brain MRI

2026-04-09

AI Summary

This work addresses the limitation of conventional convolutional neural networks in lacking rotational equivariance, which hinders their ability to effectively model the rotational symmetries of anatomical structures in brain MRI and thereby constrains the accuracy and robustness of deformable registration. To overcome this, the study introduces rotational equivariant convolutions into brain MRI registration for the first time, explicitly incorporating geometric priors by replacing the standard encoder with an equivariant counterpart. Experimental results across multiple public datasets demonstrate that the proposed approach consistently achieves superior registration accuracy under both standard and rotated inputs, while simultaneously reducing model parameter count. Moreover, it exhibits enhanced data efficiency and generalization capability, particularly in scenarios with limited training data.

Abstract

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.

Problem

• rotation equivariance
• image registration
• brain MRI
• convolutional neural networks
• anatomical symmetry

Innovation

• rotation equivariance
• deformable registration
• brain MRI
• geometric priors
• sample efficiency