Joint Cuts and Matching of Partitions in One Graph

TL;DR

This paper introduces a novel approach that jointly performs graph cuts and graph matching, optimizing both tasks simultaneously to improve partitioning and correspondence in graphs, with demonstrated effectiveness on synthetic and real data.

Contribution

It formalizes the combined problem of graph cuts and matching and proposes an alternating optimization algorithm with theoretical analysis.

Findings

Effective on synthetic datasets

Successful on real-world images with similar regions

Provides a new framework for joint graph partitioning and matching

Abstract

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.