Efficient MRF Deformation Model for Non-Rigid Image Matching

We propose a novel MRF-based model for deformable image matching. Given two images, the task is to estimate a mapping from one image to the other maximizing the quality of the match. We consider mappings defined by a discrete deformation field constrained to preserve 2D continuity. We pose the task as finding MAP configurations of a pairwise MRF. We propose a more compact MRF representation of the problem which leads to a weaker, though computationally more tractable, linear programming relaxation -the approximation technique we choose to apply. The number of dual LP variables grows linearly with the search window side, rather than quadratically as in previous approaches. To solve the relaxed problem (suboptimally), we apply TRW-S (Sequential Tree-Reweighted Message passing) algorithm [13, 5]. Using our representation and the chosen optimization scheme, we are able to match much wider deformations than was considered previously in global optimization framework. We further elaborate on continuity and data terms to achieve more appropriate description of smooth deformations. The performance of our technique is demonstrated on both synthetic and real-world experiments.