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In this paper, we consider the approximate weighted graph matching problemand introduce stable and informative first and second order compatibility termssuitable for inclusion into the popular integer quadratic program formulation.Our approach relies on a rigorous analysis of stability of spectral signaturesbased on the graph Laplacian. In the case of the first order term, we derive anobjective function that measures both the stability and informativeness of agiven spectral signature. By optimizing this objective, we design new spectralnode signatures tuned to a specific graph to be matched. We also introduce thepairwise heat kernel distance as a stable second order compatibility term; wejustify its plausibility by showing that in a certain limiting case itconverges to the classical adjacency matrix-based second order compatibilityfunction. We have tested our approach on a set of synthetic graphs, thewidely-used CMU house sequence, and a set of real images. These experimentsshow the superior performance of our first and second order compatibility termsas compared with the commonly used ones.

Stable and Informative Spectral Signatures for Graph Matching