Incorporating sliding and local rigidity constraints in neural-based image registration

Image registration is widely used in various applications to estimate the deformations of moving structures in image pairs acquired at different times. Spatial regularization strategies often take a one-size-fits-all approach by imposing uniform deformation constraints across the entire image domain. This fails to account for the spatially heterogeneous mechanical properties of the registered structures, a limitation that is especially critical in poorly contrasted regions, where the deformations estimation relies almost entirely on regularization. We propose a physics-informed framework for neural-based image registration, in which the neural network is trained under locally adaptive constraints derived from solid mechanics. The procedure enforces rigid displacements, shearing motions, or pseudo-elastic deformations depending on the local structure type. By embedding physical laws directly into the training objective, the network learns to internalize these constraints and generalizes them at inference time with no other information than that contained in the new registered images. We validate our approach on synthetic and real 3D abdominal medical images, demonstrating that the mechanics-informed trained network transfers these constraints to unseen patients within the same cohort, favoring rigidity in hard tissues and capturing sliding motion at tissue interfaces, yielding deformations more consistent with the assumed mechanical behavior of each structure, at a small and quantified cost in intensity-based alignment. The code is publicly available for 3D images at https://github.com/Kheil-Z/biomechanical_DLIR .