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Second-order priors on the smoothness of 3D surfaces are a better model of typical scenes than first-order priors. However, stereo reconstruction using global inference algorithms, such as graph cuts, has not been able to incorporate second-order priors because the triple cliques needed to express them yield intractable (nonsubmodular) optimization problems. This paper shows that inference with triple cliques can be effectively performed. Our optimization strategy is a development of recent extensions to alpha-expansion, based on the ldquo QPBOrdquo algorithm. The strategy is to repeatedly merge proposal depth maps using a novel extension of QPBO. Proposal depth maps can come from any source, for example, frontoparallel planes as in alpha-expansion, or indeed any existing stereo algorithm, with arbitrary parameter settings.