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Szeliski et al. published an influential study in 2006 on energy minimizationmethods for Markov Random Fields (MRF). This study provided valuable insightsin choosing the best optimization technique for certain classes of problems.While these insights remain generally useful today, the phenomenal success ofrandom field models means that the kinds of inference problems that have to besolved changed significantly. Specifically, the models today often includehigher order interactions, flexible connectivity structures, largela\-bel-spaces of different cardinalities, or learned energy tables. To reflectthese changes, we provide a modernized and enlarged study. We present anempirical comparison of 32 state-of-the-art optimization techniques on a corpusof 2,453 energy minimization instances from diverse applications in computervision. To ensure reproducibility, we evaluate all methods in the OpenGM 2framework and report extensive results regarding runtime and solution quality.Key insights from our study agree with the results of Szeliski et al. for thetypes of models they studied. However, on new and challenging types of modelsour findings disagree and suggest that polyhedral methods and integerprogramming solvers are competitive in terms of runtime and solution qualityover a large range of model types.

A Comparative Study of Modern Inference Techniques for Structured Discrete Energy Minimization Problems