Joint Optimization for Consistent Multiple Graph Matching

The problem of graph matching in general is NP-hard and approaches have been proposed for its sub optimal solution, most focusing on finding the one-to-one node mapping between two graphs. A more general and challenging problem arises when one aims to find consistent mappings across a number of graphs more than two. Conventional graph pair matching methods often result in mapping inconsistency since the mapping between two graphs can either be determined by pair mapping or by an additional anchor graph. To address this issue, a novel formulation is derived which is maximized via alternating optimization. Our method enjoys several advantages: 1) the mappings are jointly optimized rather than sequentially performed by applying pair matching, allowing the global affinity information across graphs can be propagated and explored, 2) the number of concerned variables to optimize is in linear with the number of graphs, being superior to local pair matching resulting in O(n^2) variables, 3) the mapping consistency constraints are analytically satisfied during optimization, and 4) off-the-shelf graph pair matching solvers can be reused under the proposed framework in an `out-of-the-box' fashion. Competitive results on both the synthesized data and the real data are reported, by varying the level of deformation, outliers and edge densities.