A Novel Diffeomorphic Model for Image Registration and Its Algorithm

Abstract

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.

Constrained Linear Curvature Image Registration Model and Its Numerical Algorithm

“…In this part, we use three experiments to show that our new model (CLC) has good performance by comparing it with diffeomorphic demons (DDemons) [43], linear curvature model (LC) [28], mean curvature model (MC) [8], hyperelastic regularizer (Hyper) [20], and Zhang-Chen model (ZC) [42]. In order to illustrate the capabilities of our model, we select two pairs of artificial images.…”

“…e image difference after registration from (d) the LC model [28] (ε � 2.41%), (e) Hyper model [20] (ε � 1.01%), and (f ) DDemons model [43] (ε � 16.74%). e transformed template image T(x + u(x)) from (g) the ZC model [42] and (h) MC model [8]. e image difference after registration from (i) the ZC model [42] (ε � 1.22%) and (j) MC model [8] (ε � 2.15%).…”

“…e transformed template image T(x + u(x)) from (g) the ZC model [42] and (h) MC model [8]. e image difference after registration from (i) the ZC model [42] (ε � 1.22%) and (j) MC model [8] (ε � 2.15%).…”

“…Table 7: Quantitative measurements using the DDemons model [43], ZC model [42], Hyper model [20], and MC model [8] for processing Example 2 shown in Figures 3(a) and 3(b). [20], and (c) DDemons model [43].…”

“…To solve this problem, Haber and Modersitzki proposed a new registration model by adding additional explicit volume inequality constraints [32]; however, this constrained method usually leads to solving a large-scale highly nonlinear inequality constrained optimization problem. Other methods to ensure the regularity of the displacement field can be found in the literature [20,[38][39][40][41][42][43]. However, some of them require more computation time due to the complexity of the regularizer.…”