A novel diffeomorphic model for image registration and its algorithm

In this work, we investigate image registration by mapping one image to another in a variational framework and focus on both model robustness and solver efficiency. We first propose a new variational model with a special regularizer, based on the quasi-conformal theory, which can guarantee that the registration map is diffeomorphic. It is well known that when the deformation is large, many variational models including the popular diffusion model cannot ensure diffeomorphism. One common observation is that the fidelity error appears small while the obtained transform is incorrect by way of mesh folding. However, direct reformulation from the Beltrami framework does not lead to effective models; our new regularizer is constructed based on this framework and added to the diffusion model to get a new model, which can achieve diffeomorphism. However, the idea is applicable to a wide class of models. We then propose an iterative method to solve the resulting nonlinear optimization problem and prove the convergence of the method. Numerical experiments can demonstrate that the new model can not only get a diffeomorphic registration even when the deformation is large, but also possess the accuracy in comparing with the currently best models.