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Formulations of the Image Decomposition Problem as a Multicut Problem (MP)w.r.t. a superpixel graph have received considerable attention. In contrast,instances of the MP w.r.t. a pixel grid graph have received little attention,firstly, because the MP is NP-hard and instances w.r.t. a pixel grid graph arehard to solve in practice, and, secondly, due to the lack of long-range termsin the objective function of the MP. We propose a generalization of the MP withlong-range terms (LMP). We design and implement two efficient algorithms(primal feasible heuristics) for the MP and LMP which allow us to studyinstances of both problems w.r.t. the pixel grid graphs of the images in theBSDS-500 benchmark. The decompositions we obtain do not differ significantlyfrom the state of the art, suggesting that the LMP is a competitive formulationof the Image Decomposition Problem. To demonstrate the generality of the LMP,we apply it also to the Mesh Decomposition Problem posed by the Princetonbenchmark, obtaining state-of-the-art decompositions.

Efficient Decomposition of Image and Mesh Graphs by Lifted Multicuts