MAP-Inference for Highly-Connected Graphs with DC-Programming

The design of inference algorithms for discrete-valued Markov Random Fields constitutes an ongoing research topic in computer vision. Large state-spaces, none-submodular energy-functions, and highly-connected structures of the underlying graph render this problem particularly difficult. Established techniques that work well for sparsely connected grid-graphs used for image labeling, degrade for non-sparse models used for object recognition. In this context, we present a new class of mathematically sound algorithms that can be flexibly applied to this problem class with a guarantee to converge to a critical point of the objective function. The resulting iterative algorithms can be interpreted as simple message passing algorithms that converge by construction, in contrast to other message passing algorithms. Numerical experiments demonstrate its performance in comparison with established techniques.