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.

翻译：现有无监督可变形图像配准方法通常依赖应用于预测位移场或速度场梯度的度量作为正则化项，以确保变换平滑性，这可能会限制配准精度。本研究提出一种新方法，通过将新型微分算子引入配准框架来增强无监督可变形图像配准。该算子作用于速度场并将其映射到对偶空间，确保了优化过程中速度场的平滑性，从而促进精确的可变形配准。此外，为应对图像对内部大形变捕获的挑战，我们引入跨坐标注意力模块（CCA）并将其嵌入到基于全卷积网络（FCNs）的多分辨率配准架构中。在两个磁共振成像（MRI）数据集上进行了评估实验。与多种最先进的配准方法（包括一种传统算法和三种代表性无监督学习方法）相比，我们的方法实现了更优的精度，同时保持了理想微分同胚特性，并展现出具有竞争力的配准速度。