Alternating Direction Graph Matching
This addresses graph matching for computer vision and pattern recognition, offering a scalable solution with incremental improvements over prior methods.
The paper tackles graph matching with arbitrary constraints by reformulating it as a non-convex optimization problem solved via alternating direction method of multipliers, resulting in a modular framework that outperforms existing pairwise methods and is competitive in higher-order settings.
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.