AN ENERGY FUNCTION AND CONTINUOUS EDIT PROCESS FOR GRAPH MATCHING

The contributions of this article are twofold. First, we develop a new nonquadratic energy function for graph matching. The starting point i s a recently reported mixture model that gauges relational consistency using a series of exponential functions of the Hamming distances betw een graph neighborhoods. We compute the effective neighborhood potenti als associated with the mixture model by identifying the single probab ility function of zero Kullback divergence. This new energy function i s simply a weighted sum of graph Hamming distances. The second contrib ution is to locate matches by graduated assignment. Rather than solvin g the mean-field saddle-point equations, which are intractable for our nonquadratic energy function, we apply the soft-assign ansatz to the derivatives of our energy function. Here we introduce a novel departur e from the standard graduated assignment formulation of graph matching by allowing the connection strengths of the data graph to update them selves. The aim is to provide a means by which the structure of the da ta graph can be updated so as to rectify structural errors. The method is evaluated experimentally and is shown to outperform its quadratic counterpart.