# Vector Field Attention for Deformable Image Registration

arXiv: https://arxiv.org/abs/2407.10209 · HTML: https://mlsanity.com/paper/2407.10209/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 57 references that are in the map.
- First posted on arXiv 14 Jul 2024.

## Builds on (most cited first, 30 of 31)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume](https://mlsanity.com/paper/1709.02371/) (2017)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Vision Transformer with Deformable Attention](https://mlsanity.com/paper/2201.00520/) (2022)
- [AANet: Adaptive Aggregation Network for Efficient Stereo Matching](https://mlsanity.com/paper/2004.09548/) (2020)
- [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019)
- [Large Deformation Diffeomorphic Image Registration with Laplacian Pyramid Networks](https://mlsanity.com/paper/2006.16148/) (2020)
- [Learn2Reg: comprehensive multi-task medical image registration challenge, dataset and evaluation in the era of deep learning](https://mlsanity.com/paper/2112.04489/) (2021)
- [MaskFlownet: Asymmetric Feature Matching with Learnable Occlusion Mask](https://mlsanity.com/paper/2003.10955/) (2020)
- [Quicksilver: Fast Predictive Image Registration - a Deep Learning Approach](https://mlsanity.com/paper/1703.10908/) (2017)
- [ViT-V-Net: Vision Transformer for Unsupervised Volumetric Medical Image Registration](https://mlsanity.com/paper/2104.06468/) (2021)
- [End-to-End Unsupervised Deformable Image Registration with a Convolutional Neural Network](https://mlsanity.com/paper/1704.06065/) (2017)
- [A survey on deep learning in medical image registration: new technologies, uncertainty, evaluation metrics, and beyond](https://mlsanity.com/paper/2307.15615/) (2023)
- [Dual-Stream Pyramid Registration Network](https://mlsanity.com/paper/1909.11966/) (2019)
- [3D Whole Brain Segmentation using Spatially Localized Atlas Network Tiles](https://mlsanity.com/paper/1903.12152/) (2019)
- [XMorpher: Full Transformer for Deformable Medical Image Registration via Cross Attention](https://mlsanity.com/paper/2206.07349/) (2022)
- [Anatomical Priors in Convolutional Networks for Unsupervised Biomedical Segmentation](https://mlsanity.com/paper/1903.03148/) (2019)
- [Closing the Gap between Deep and Conventional Image Registration using Probabilistic Dense Displacement Networks](https://mlsanity.com/paper/1907.10931/) (2019)
- [Fast 3D registration with accurate optimisation and little learning for Learn2Reg 2021](https://mlsanity.com/paper/2112.03053/) (2021)
- [U-Net vs Transformer: Is U-Net Outdated in Medical Image Registration?](https://mlsanity.com/paper/2208.04939/) (2022)
- [Evaluating the Impact of Intensity Normalization on MR Image Synthesis](https://mlsanity.com/paper/1812.04652/) (2018)
- [On Finite Difference Jacobian Computation in Deformable Image Registration](https://mlsanity.com/paper/2212.06060/) (2022)
- [ModeT: Learning Deformable Image Registration via Motion Decomposition Transformer](https://mlsanity.com/paper/2306.05688/) (2023)
- [Joint Progressive and Coarse-to-fine Registration of Brain MRI via Deformation Field Integration and Non-Rigid Feature Fusion](https://mlsanity.com/paper/2109.12384/) (2021)
- [Coordinate Translator for Learning Deformable Medical Image Registration](https://mlsanity.com/paper/2203.03626/) (2022)
- [Voxelmorph++ Going beyond the cranial vault with keypoint supervision and multi-channel instance optimisation](https://mlsanity.com/paper/2203.00046/) (2022)
- [Deformable Cross-Attention Transformer for Medical Image Registration](https://mlsanity.com/paper/2303.06179/) (2023)
- [Deformer: Towards Displacement Field Learning for Unsupervised Medical Image Registration](https://mlsanity.com/paper/2207.03180/) (2022)

## Built on by (most cited first, 10 of 10)

- [Beyond the LUMIR challenge: The pathway to foundational registration models](https://mlsanity.com/paper/2505.24160/) (2025)
- [Unsupervised learning of spatially varying regularization for diffeomorphic image registration](https://mlsanity.com/paper/2412.17982/) (2024)
- [A Scalable Distributed Framework for Multimodal GigaVoxel Image Registration](https://mlsanity.com/paper/2509.25044/) (2025)
- [Biomechanical Constraints Assimilation in Deep-Learning Image Registration: Application to sliding and locally rigid deformations](https://mlsanity.com/paper/2504.05444/) (2025)
- [Surrogate Supervision for Robust and Generalizable Deformable Image Registration](https://mlsanity.com/paper/2509.09869/) (2025)
- [Zero-shot Multi-Contrast Brain MRI Registration by Intensity Randomizing T1-weighted MRI (LUMIR25)](https://mlsanity.com/paper/2602.06292/) (2026)
- [An FPGA Implementation of Displacement Vector Search for Intra Pattern Copy in JPEG XS](https://mlsanity.com/paper/2603.10671/) (2026)
- [Adapting Frozen Mono-modal Backbones for Multi-modal Registration via Contrast-Agnostic Instance Optimization](https://mlsanity.com/paper/2603.26393/) (2026)
- [The Right Prior for the Right Deformation: Rethinking Continuous Deformable Image Registration](https://mlsanity.com/paper/2608.16146/) (2026)
- [Is Deformable Image Registration Ready for Brain Metastasis Reirradiation Dose Accumulation? A Longitudinal MRI Benchmark of Registration Accuracy](https://mlsanity.com/paper/2608.28705/) (2026)

## Abstract (arXiv)

Deformable image registration establishes non-linear spatial correspondences between fixed and moving images. Deep learning-based deformable registration methods have been widely studied in recent years due to their speed advantage over traditional algorithms as well as their better accuracy. Most existing deep learning-based methods require neural networks to encode location information in their feature maps and predict displacement or deformation fields though convolutional or fully connected layers from these high-dimensional feature maps. In this work, we present Vector Field Attention (VFA), a novel framework that enhances the efficiency of the existing network design by enabling direct retrieval of location correspondences. VFA uses neural networks to extract multi-resolution feature maps from the fixed and moving images and then retrieves pixel-level correspondences based on feature similarity. The retrieval is achieved with a novel attention module without the need of learnable parameters. VFA is trained end-to-end in either a supervised or unsupervised manner. We evaluated VFA for intra- and inter-modality registration and for unsupervised and semi-supervised registration using public datasets, and we also evaluated it on the Learn2Reg challenge. Experimental results demonstrate the superior performance of VFA compared to existing methods. The source code of VFA is publicly available at https://github.com/yihao6/vfa/.