Graphical Models and Deformable Diffeomorphic Population Registration Using Global and Local Metrics

In this paper we propose a novel framework to unite a population to an optimal (unknown) pose through their mutual deformation. The registration criterion comprises three terms, the first imposes compactness on appearance of the registered population at the pixel level, the second tries to minimize the individual distances between all possible pairs of images, while the last is a regularization one imposing smoothness on the deformation fields. The problem is reformulated as a graphical model that consists of hidden (deformation fields) and observed variables (intensities). A novel deformation grid-based scheme is proposed that guarantees the diffeomorphism of the deformation and is computationally favorably compared to standard deformation methods. Towards addressing important deformations we propose a compositional approach where the deformations are recovered through the sub-optimal solutions of successive discrete MRFs by using efficient linear programming. Promising experimental results using real 2D data demonstrate the potentials of our approach.