Topology-Preserving Registration: A Solution via Graph Cuts

In this work we propose a topology-preserving registration method based on a discrete Markov random field of deformations and a block-matching procedure. For that purpose, the fidelity of a given deformation to the data is established by a block-matching strategy, the smoothness of the transformation is favored by an appropriate prior on the field and topology preservation is guaranteed by imposing some hard-constraints on the local configurations of the field. The resulting deformation is defined as the maximum a posteriori of the field and it is estimated via graph cuts. Results on medical images show the efficiency of using graph cuts based fusion moves for the optimization of the field even though its potentials are neither sparse nor separable and the reduced fused problem turns to be non-submodular.