Higher-Order Clique Reduction in Binary Graph Cut

e 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 Q B algorithms to optimize higher-order multi-label problems. hile 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 few exceptions that consider triples, his is because of the lack of efficient algorithms to optimize energies with higher-order interactions. ur algorithm challenges this restriction that limits the representational power of the models, so that higher-order energies can be used to capture the rich statistics of natural scenes. o demonstrate the algorithm, we minimize a third-order energy, which allows clique potentials with up to four pixels, in an image restoration problem. he problem uses the Fields of Experts model, a learned spatial prior of natural images that has been used to test two belief propagation algorithms capable of optimizing higher-order energies. he results show that the algorithm exceeds the B algorithms in both optimization performance and speed.