Vectorial Fractional-Order Regularizer-Based Diffeomorphic Image Registration Model and its Numerical Algorithm

Abstract A diffeomorphic image registration model with a vectorial fractional-order regularizer is introduced to handle displacement fields with varying smoothness and to avoid mesh folding. Furthermore, we combine the damped Newton method with the Armijo line search and apply a multilevel strategy to solve the discretized version of the new model. Furthermore, both the existence of solutions to the model and the convergence of the algorithm have been established. Numerical experiments on synthetic and real images confirm the superiority of the proposed model and the effectiveness of the algorithm.