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As two fundamental problems, graph cuts and graph matching have beeninvestigated over decades, resulting in vast literature in these two topicsrespectively. However the way of jointly applying and solving graph cuts andmatching receives few attention. In this paper, we first formalize the problemof simultaneously cutting a graph into two partitions i.e. graph cuts andestablishing their correspondence i.e. graph matching. Then we develop anoptimization algorithm by updating matching and cutting alternatively, providedwith theoretical analysis. The efficacy of our algorithm is verified on bothsynthetic dataset and real-world images containing similar regions orstructures.

Joint Cuts and Matching of Partitions in One Graph