Graph matching and registration

Deformable image registration is a fundamental problem in biomedical image analysis and several approaches have been proposed to tackle it. In this chapter, we cover approaches that use Markov Random Field (MRF) theory to model the deformable registration problem and discrete optimization techniques to solve it. We first detail how one can formulate the deformable registration problem as a minimal cost graph problem, where the nodes of the graph correspond to model discrete deformation elements, the edges of the graph encode regularization constraints and the labels correspond to displacements. The cases of geometric registration, iconic registration, and hybrid registration are covered. Then, we provide details about how one can solve the optimization problem that is associated with the constructed graph. Lastly, we present an example application of discrete graph-based registration to the problem of intra-subject registration of pulmonary Computed Tomography scans.