Multicuts enable to conveniently represent discrete graphical models for unsupervised and supervised image segmentation, based on local energy functions that exhibit symmetries. The basic Potts model and natural extensions thereof to higher-order models provide a prominent class of representatives, that cover a broad range of segmentation problems relevant to image analysis and computer vision. We show how to take into account such higher-order terms systematically in view of computational inference, and present results of a comprehensive and competitive numerical evaluation of a variety of dedicated cutting-plane algorithms. Our results reveal ways to evaluate a significant subset of models globally optimal, without compromising runtime. Polynomially solvable relaxations are studied as well, along with advanced rounding schemes for post-processing.
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