3D diffeomorphic image registration with Cauchy–Riemann constraint and lower bounded deformation divergence

In order to eliminate mesh folding in 3D image registration problem, we propose a 3D diffeomorphic image registration model with Cauchy–Riemann constraint and lower bounded deformation divergence. This model preserves the local shape and ensures no mesh folding. The existence of solution for the proposed model is proved. Furthermore, an alternating directional projection 3D image registration algorithm is presented to solve the proposed model. Moreover, numerical tests show that the proposed algorithm is competitive compared with the other four algorithms.