Rotation Equivariant Convolutions in Deformable Registration of Brain MRI

Deformable image registration plays a fundamental role in medical image analysis by enabling spatial alignment of anatomical structures across subjects. While recent deep learning-based approaches have significantly improved computational efficiency, many existing methods remain limited in capturing long-range anatomical correspondence and maintaining deformation consistency. In this work, we present a cycle inverse-consistent transformer-based framework for deformable brain MRI registration. The model integrates a Swin-UNet architecture with bidirectional consistency constraints, enabling the joint estimation of forward and backward deformation fields. This design allows the framework to capture both local anatomical details and global spatial relationships while improving deformation stability. We conduct a comprehensive evaluation of the proposed framework on a large multi-center dataset consisting of 2851 T1-weighted brain MRI scans aggregated from 13 public datasets. Experimental results demonstrate that the proposed framework achieves strong and balanced performance across multiple quantitative evaluation metrics while maintaining stable and physically plausible deformation fields. Detailed quantitative comparisons with baseline methods, including ANTs, ICNet, and VoxelMorph, are provided in the appendix. Experimental results demonstrate that CICTM achieves consistently strong performance across multiple evaluation criteria while maintaining stable and physically plausible deformation fields. These properties make the proposed framework suitable for large-scale neuroimaging datasets where both accuracy and deformation stability are critical.

Deep learning registration methods routinely stack two kinds of enhancement on a base network: architectural additions such as affine pre-alignment stages, and training-objective additions such as regularization losses. Papers tend to adopt both at once, so it is unclear which is doing the work. I ran a controlled ablation to separate them. Using the OASIS brain MRI dataset (394 training subjects, 20 test subjects), I trained four variants of the same registration pipeline: a baseline 3D U-Net with basic similarity losses, the same U-Net with a full regularization suite, an affine-plus-deformable architecture with basic losses, and the affine architecture with the full suite. I evaluated registration accuracy (MSE, NCC, SSIM), deformation quality (Jacobian determinant preservation, displacement statistics, an anatomical plausibility score), and computational cost. Regularization alone accounted for most of the gain: a 21.3% relative gain on the MSE-improvement metric (1.78% to 2.16%, P<.001) and a 21.8% relative gain in NCC improvement, while cutting maximum deformation from 53.1 to 0.51 units, a 99.0% reduction, at essentially no computational cost (-0.06% inference time). The combined model produced the largest accuracy gain, 25.8% (1.78% to 2.24%), and raised anatomical plausibility from 0.596 to 0.930, at a moderate +9.8% inference-time cost. Gradient correlation rose from 0.742 at baseline to 0.980 for the fully enhanced model. All enhanced variants reached sub-voxel accuracy under plausible deformation constraints. Regularization losses are the primary driver in this setting, delivering the accuracy gains and almost all of the deformation control for free at inference time, while the affine architecture adds a smaller complementary benefit at acceptable cost. The 99% reduction in unrealistic deformations addresses a known barrier to clinical deployment.

Medical image registration benefits significantly from deep learning, yet existing approaches often lack physical explainability and fine-grained deformation control. Motivated by Demons algorithms, we propose a novel DrivenMorph framework that bridges attention mechanisms with variational image registration by incorporating difference modeling as a physically inspired inductive bias. The resulting driving force, computed from local differences in the latent feature space, provides explicit semantic guidance throughout the registration process. It directly drives the registration process through a neural Demons layer that simulates force-displacement interactions to generate smooth and anatomically consistent deformation. Unlike previous methods, our approach not only integrates traditional registration principles with popular deep networks, providing an explainable and efficient solution for learning-based medical image registration, but also separates difference modeling from deformation, improving modularity and explainability. Extensive experiments on multiple 3D brain MRI datasets demonstrate superior performance over state of-the-art learning-based and optimization-based methods. Furthermore, visualizations and statistical analyses confirm that the learned driving force aligns closely with actual deformation patterns, supporting its explanatory value.