Alternating Direction Graph Matching

TL;DR

This paper presents a flexible, scalable graph matching method that handles arbitrary constraints using an alternating direction approach, outperforming existing methods on benchmarks.

Contribution

It introduces a novel decomposition-based framework for graph matching that accommodates arbitrary order constraints and potential functions.

Findings

Outperforms existing pairwise graph matching methods on benchmarks.

Achieves competitive results in higher-order graph matching.

Demonstrates scalability and modularity of the proposed framework.

Abstract

In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a decomposition of the matching constraints. Graph matching is then reformulated as a non-convex non-separable optimization problem that can be split into smaller and much-easier-to-solve subproblems, by means of the alternating direction method of multipliers. The proposed framework is modular, scalable, and can be instantiated into different variants. Two instantiations are studied exploring pairwise and higher-order constraints. Experimental results on widely adopted benchmarks involving synthetic and real examples demonstrate that the proposed solutions outperform existing pairwise graph matching methods, and competitive with the state of the art in higher-order settings.