DiffOp-net: A Differential Operator-based Fully Convolutional Network for Unsupervised Deformable Image Registration

Existing unsupervised deformable image registration methods usually rely on metrics applied to the gradients of predicted displacement or velocity fields as a regularization term to ensure transformation smoothness, which potentially limits registration accuracy. In this study, we propose a novel approach to enhance unsupervised deformable image registration by introducing a new differential operator into the registration framework. This operator, acting on the velocity field and mapping it to a dual space, ensures the smoothness of the velocity field during optimization, facilitating accurate deformable registration. In addition, to tackle the challenge of capturing large deformations inside image pairs, we introduce a Cross-Coordinate Attention module (CCA) and embed it into a proposed Fully Convolutional Networks (FCNs)-based multi-resolution registration architecture. Evaluation experiments are conducted on two magnetic resonance imaging (MRI) datasets. Compared to various state-of-the-art registration approaches, including a traditional algorithm and three representative unsupervised learning-based methods, our method achieves superior accuracies, maintaining desirable diffeomorphic properties, and exhibiting promising registration speed.