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We introduce a new technique that can reduce any higher-order Markov random field with binary labels into a first-order one that has the same minima as the original. Moreover, we combine the reduction with the fusion-move and QPBO algorithms to optimize higher-order multi-label problems. While many vision problems today are formulated as energy minimization problems, they have mostly been limited to using first-order energies, which consist of unary and pairwise clique potentials, with a fewdoi:10.1109/cvpr.2009.5206689 dblp:conf/cvpr/Ishikawa09 fatcat:rng4csnxkjhnpomrlio2vrryga