(untitled) (Contemporary Mathematics, 2025)
Deformable Image Registration (DIR) is a fundamental problem in biomedical imaging that analyzes organ displacements and deformations by comparing images from different states. DIR becomes particularly challenging when analyzing images that display non-affine large deformations or noisy image data. In this study, two novel similarity measures for DIR based on the Radon Transform (RT) are introduced, which, together with a linear elastic regularizer, define the formulation of the proposed projection-based DIR models. We present a theoretical analysis of the proposed RT-DIR formulation, providing conditions for the existence and uniqueness of solutions in the continuous case. The proposed RT-DIR methods are implemented using a finite-element-based deformation system and a gradient-informed quasi-Newton optimization algorithm. We compare the performance of these methods against a traditional DIR approach that employs the Sum of Squared Differences (SSD) as the similarity measure. Experimental tests include synthetic random non-affine deformations with varying noise levels and a case of real lung deformation. We show that the RT-based models exhibit enhanced accuracy in capturing non-affine deformations, higher robustness to noise, and a significantly faster convergence rate compared to the SSD-based method. We further demonstrate the applicability of the RT-DIR method on human lung images.