Multi-modal diffeomorphic registration using mutual information: Application to the registration of CT and MR pulmonary images

In this paper, we present a new algorithm to register multimodal images using mutual information in a fully diffeomorphic framework. Our driving motivation is to define a one-to-one mapping in CT/MR 3D pulmonary images acquired from patients with empyema. Due to the large amount of respiratory motion and the presence of strong pathologies, preserving the invertibility of the deformations can be challenging using non-diffeomorphic registration, but would be ensured using a diffeomorphic registration approach. Our main contribution is to propose a computationally tractable technique to estimate the gradients of mutual information in this context. This task can be particularly time consuming since the gradients of mutual information are computed voxel-wise but depend on the information contained in the whole images. Our strategy is then integrated into the Log-Domain Diffeomorphic Demons formalism, making it the first method simultaneously using exponential maps to encode the deformations and mutual information to compare the images. We finally test the whole algorithm on seven CT/MR image volumes of the chest. Results show that the estimated deformations are similar to those obtained using free-form deformations, with the additional property to always estimate invertible deformations.