FractMorph: A Fractional Fourier-Based Multi-Domain Transformer for Deformable Image Registration

Deformable image registration (DIR) is a crucial and challenging technique for aligning anatomical structures in medical images and is widely applied in diverse clinical applications. However, existing approaches often struggle to capture fine-grained local deformations and large-scale global deformations simultaneously within a unified framework. We present FractMorph, a novel 3D dual-parallel transformer-based architecture that enhances cross-image feature matching through multi-domain fractional Fourier transform (FrFT) branches. Each Fractional Cross-Attention (FCA) block applies parallel FrFTs at fractional angles of 0{\deg}, 45{\deg}, 90{\deg}, along with a log-magnitude branch, to effectively extract local, semi-global, and global features at the same time. These features are fused via cross-attention between the fixed and moving image streams. A lightweight U-Net style network then predicts a dense deformation field from the transformer-enriched features. On the ACDC cardiac MRI dataset, FractMorph achieves state-of-the-art performance with an overall Dice Similarity Coefficient (DSC) of 86.45%, an average per-structure DSC of 75.15%, and a 95th-percentile Hausdorff distance (HD95) of 1.54 mm on our data split. We also introduce FractMorph-Light, a lightweight variant of our model with only 29.6M parameters, which maintains the superior accuracy of the main model while using approximately half the memory. Our results demonstrate that multi-domain spectral-spatial attention in transformers can robustly and efficiently model complex non-rigid deformations in medical images using a single end-to-end network, without the need for scenario-specific tuning or hierarchical multi-scale networks. The source code of our implementation is available at https://github.com/shayankebriti/FractMorph.