Rotation Equivariant Convolutions in Deformable Registration of Brain MRI

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.