Optimal mapping of graph homomorphism onto self organising Hopfield network

In a recent paper by us, a novel programming strategy was proposed to obtain homomorphic graph matching using the Hopfield network. Subsequently a self-organisation scheme was also proposed to adaptively learn the constraint parameter which is required to generate the desired homomorphic mapping for every pair of model and scene data. In this paper, an augmented weighted model attributed relational graph (WARG) representation scheme is proposed. The representation scheme incorporates a distinct weighting factor and tolerance parameter for every model attribute. To estimate the parameters in a simplified form of the model WARG representation, learning schemes are presented. A heuristic learning scheme is employed to estimate suitable values for threshold parameters. The computation of weighting factors is formulated as an optimisation problem and solved using the quadratic programming algorithm. The formulation implicitly evaluates ambiguity, robustness and discriminatory power of the relational attributes chosen for graph matching and assigns weighting factors appropriately to the chosen attributes. Experimental results are presented to demonstrate that the parameter learning schemes are essential when the models have intra-model ambiguity and the optimal set of parameters always generates a better mapping.