Efficient MRF deformation model for non-rigid image matching

We propose a novel MRF-based model for deformable image matching (also known as registration). The deformation is described by a field of discrete variables, representing displacements of (blocks of) pixels. Discontinuities in the deformation are prohibited by imposing hard pairwise constraints in the model. Exact maximum a posteriori inference is intractable and we apply a linear programming relaxation technique.We show that, when reformulated in the form of two coupled fields of x- and y-displacements, the problem leads to a simpler relaxation to which we apply the sequential tree-reweighted message passing (TRW-S) algorithm [Wainwright-03, Kolmogorov-05]. This enables image registration with large displacements at a single scale. We employ fast message updates for a special type of interaction as was proposed [Felzenszwalb and Huttenlocher-04] for the max-product belief propagation (BP) and introduce a few independent speedups. In contrast to BP, the TRW-S allows us to compute per-instance approximation ratios and thus to evaluate the quality of the optimization. The performance of our technique is demonstrated on both synthetic and real-world experiments.