Nonlinear medical image registration based on Wasserstein distance and functions of bounded deformation

Abstract Nonlinear image registration is a fundamental and challenging task in the field of medical image analysis, aimed at finding a displacement field and densely aligning all the pixels of interest within a fixed coordinate system. However, traditional similarity measures in image registration models are primarily based on local similarities of image intensities or intensity-related features, and hence insufficient for comparing global similarity of the image intensities. Wasserstein distance is well-known for its characteristic of quantifying global similarity between distributions in optimal transport theory. Inspired by this, we introduce a novel deformable registration model called the BDOT model. Formulated within a variational framework, the BDOT model incorporates the second-order Wasserstein distance as a novel similarity measurement. Under the joint action of two data terms within the model, the registered image and the fixed image demonstrate a high degree of similarity, encompassing both overall intensity distributions and local structural details. We prove the existence of solutions to the BDOT model and derive an efficient algorithm. Numerical experiments show the effectiveness of the BDOT model and its superiority to other variational models. Moreover, the displacement field obtained by the BDOT model is more natural and plausible, enhancing the real ism and applicability of image registration.