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

arXiv: https://arxiv.org/abs/2508.12445 · HTML: https://mlsanity.com/paper/2508.12445/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 38 references that are in the map.
- First posted on arXiv 17 Aug 2025.

## Builds on (most cited first, 5 of 5)

- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [ViT-V-Net: Vision Transformer for Unsupervised Volumetric Medical Image Registration](https://mlsanity.com/paper/2104.06468/) (2021)
- [XMorpher: Full Transformer for Deformable Medical Image Registration via Cross Attention](https://mlsanity.com/paper/2206.07349/) (2022)
- [WarpPINN: Cine-MR image registration with physics-informed neural networks](https://mlsanity.com/paper/2211.12549/) (2022)

## Built on by (most cited first, 2 of 2)

- [GENRE-CMR: Generalizable Deep Learning for Diverse Multi-Domain Cardiac MRI Reconstruction](https://mlsanity.com/paper/2508.20600/) (2025)
- [Flow Matching-enabled Test-Time Refinement for Unsupervised Cardiac MR Registration](https://mlsanity.com/paper/2603.01073/) (2026)

## Abstract (arXiv)

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^circ, 45^circ, 90^circ, 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 intra-patient 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. FractMorph-Light, a lightweight variant of our model with only 29.6M parameters, preserves high accuracy while halving model complexity. Furthermore, we demonstrate the generality of our approach with solid performance on a cerebral atlas-to-patient dataset. 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 is available at https://github.com/shayankebriti/FractMorph.