Joint Cuts and Matching of Partitions in One Graph
This addresses a novel integration of graph cuts and matching for applications like image analysis, though it appears incremental as it combines existing techniques.
The paper tackles the problem of simultaneously partitioning a graph into two parts and establishing correspondence between those partitions, developing an alternating optimization algorithm with theoretical analysis. The algorithm's efficacy is verified on synthetic datasets and real-world images containing similar regions or structures.
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.