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

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.