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This paper presents a new MRF optimization algorithm, which is derived from Linear Programming and manages to go beyond current state-of-the-art techniques (such as those based on graph-cuts or belief propagation). It does so by relying on a much tighter class of LP-relaxations, called cycle-relaxations. With the help of this class of relaxations, our algorithm tries to deal with a difficulty lying at the heart of MRF optimization: the existence of inconsistent cycles. To this end, it uses an operation called cycle-repairing. The goal of that operation is to fix any inconsistent cycles that may appear during optimization, instead of simply ignoring them as usually done up to now. The more the repaired cycles, the tighter the underlying LP relaxation becomes. As a result of this procedure, our algorithm is capable of providing almost optimal solutions even for very general MRFs with arbitrary potentials. Experimental results verify its effectiveness on difficult MRF problems, as well as its better performance compared to the state of the art.

Beyond Loose LP-Relaxations: Optimizing MRFs by Repairing Cycles