Consistent multi-modal non-rigid registration based on a variational approach

In this paper, a novel variational approach for multi-modal image registration based on consistent non-rigid transforms is proposed. The forward and backward transforms are computed in a variational framework simultaneously. A consistency energy is added into the variational registration framework and an iterative method assures that the forward and backward transforms are close approximate inverses of each other. This new scheme can provide more constraints on the forward and backward transforms and make them smoother. This reduces the chance of being stuck into a local minimum. We can incorporate the consistent transforms together with several kinds of information based similarity metrics such as mutual information and correlation ratio into the registration framework. An implicit finite difference scheme is used to solve the Euler–Lagrange equation numerically. Our proposed method is evaluated by using simulated multi-modal magnetic resonance images (MRI) and real medical images. The results of our proposed consistent registration and those using only forward or backward registration are compared. Improvements at the edge area can be easily seen from the registration results.