  As two fundamental problems, graph cuts and graph matching have been
investigated over decades, resulting in vast literature in these two topics
respectively. However the way of jointly applying and solving graph cuts and
matching receives few attention. In this paper, we first formalize the problem
of simultaneously cutting a graph into two partitions i.e. graph cuts and
establishing their correspondence i.e. graph matching. Then we develop an
optimization algorithm by updating matching and cutting alternatively, provided
with theoretical analysis. The efficacy of our algorithm is verified on both
synthetic dataset and real-world images containing similar regions or
structures.
