Appropriate Order of Regularization in 3D/2D Image Registration: International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2025)

This paper pertains to the order of regularization in variational 3D/2D image registration. Such registration problems often occur in image-guided interventions, e.g. in ardiology, neurology, or orthopedics. In order to align 3D pre-operative data with 2D data acquired during the intervention, a 3D deformation is calculated. A common approach is to minimize an energy that consists of a data fitting and a regularization term. While the first is evaluated on a 2D set, the regularization acts on a 3D domain. Thus, the regularizer has to ensure that the information given on the 2D set is transferred to the 3D domain. Therefore, the regularization should be chosen such that the resulting 3D deformation is sufficiently smooth, e.g. continuously differentiable. This work addresses the question which regularization order is required to guarantee continuously differentiable deformations.