# Advancing Deformable Medical Image Registration with Multi-axis Cross-covariance Attention

arXiv: https://arxiv.org/abs/2412.18545 · HTML: https://mlsanity.com/paper/2412.18545/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 42 references that are in the map.
- First posted on arXiv 24 Dec 2024.

## Builds on (most cited first, 25 of 25)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [XCiT: Cross-Covariance Image Transformers](https://mlsanity.com/paper/2106.09681/) (2021)
- [MAXIM: Multi-Axis MLP for Image Processing](https://mlsanity.com/paper/2201.02973/) (2022)
- [LocalViT: Analyzing Locality in Vision Transformers](https://mlsanity.com/paper/2104.05707/) (2021)
- [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)
- [Deep Learning in Medical Image Registration: A Survey](https://mlsanity.com/paper/1903.02026/) (2019)
- [Fast Symmetric Diffeomorphic Image Registration with Convolutional Neural Networks](https://mlsanity.com/paper/2003.09514/) (2020)
- [Hire-MLP: Vision MLP via Hierarchical Rearrangement](https://mlsanity.com/paper/2108.13341/) (2021)
- [Improved Transformer for High-Resolution GANs](https://mlsanity.com/paper/2106.07631/) (2021)
- [A survey on deep learning in medical image registration: new technologies, uncertainty, evaluation metrics, and beyond](https://mlsanity.com/paper/2307.15615/) (2023)
- [Sparse MLP for Image Recognition: Is Self-Attention Really Necessary?](https://mlsanity.com/paper/2109.05422/) (2021)
- [The Brain Tumor Sequence Registration (BraTS-Reg) Challenge: Establishing Correspondence Between Pre-Operative and Follow-up MRI Scans of Diffuse Glioma Patients](https://mlsanity.com/paper/2112.06979/) (2021)
- [ModeT: Learning Deformable Image Registration via Motion Decomposition Transformer](https://mlsanity.com/paper/2306.05688/) (2023)
- [Non-iterative Coarse-to-fine Registration based on Single-pass Deep Cumulative Learning](https://mlsanity.com/paper/2206.12596/) (2022)
- [Enhancing Medical Image Registration via Appearance Adjustment Networks](https://mlsanity.com/paper/2103.05213/) (2021)
- [Brain Tumor Sequence Registration with Non-iterative Coarse-to-fine Networks and Dual Deep Supervision](https://mlsanity.com/paper/2211.07876/) (2022)
- [Symmetric Transformer-based Network for Unsupervised Image Registration](https://mlsanity.com/paper/2204.13575/) (2022)
- [Full-resolution MLPs Empower Medical Dense Prediction](https://mlsanity.com/paper/2311.16707/) (2023)

## Built on by (most cited first, 1 of 1)

- [Attention-Driven Framework for Non-Rigid Medical Image Registration](https://mlsanity.com/paper/2602.07088/) (2026)

## Abstract (arXiv)

Deformable image registration is a fundamental requirement for medical image analysis. Recently, transformers have been widely used in deep learning-based registration methods for their ability to capture long-range dependency via self-attention (SA). However, the high computation and memory loads of SA (growing quadratically with the spatial resolution) hinder transformers from processing subtle textural information in high-resolution image features, e.g., at the full and half image resolutions. This limits deformable registration as the high-resolution textural information is crucial for finding precise pixel-wise correspondence between subtle anatomical structures. Cross-covariance Attention (XCA), as a "transposed" version of SA that operates across feature channels, has complexity growing linearly with the spatial resolution, providing the feasibility of capturing long-range dependency among high-resolution image features. However, existing XCA-based transformers merely capture coarse global long-range dependency, which are unsuitable for deformable image registration relying primarily on fine-grained local correspondence. In this study, we propose to improve existing deep learning-based registration methods by embedding a new XCA mechanism. To this end, we design an XCA-based transformer block optimized for deformable medical image registration, named Multi-Axis XCA (MAXCA). Our MAXCA serves as a general network block that can be embedded into various registration network architectures. It can capture both global and local long-range dependency among high-resolution image features by applying regional and dilated XCA in parallel via a multi-axis design. Extensive experiments on two well-benchmarked inter-/intra-patient registration tasks with seven public medical datasets demonstrate that our MAXCA block enables state-of-the-art registration performance.