Game theoretic hypergraph matching for multi-source image correspondences

In this paper, we develop a game theoretic hypergraph matching framework which enables refining feature correspondences of multi-source images. For images obtained from different sources, we commence by characterizing game strategies in terms of coarse correspondences based on feature similarities. In this scenario, mismatches tend to occur because one feature descriptor may exhibit certain ambiguity in characterizing feature similarities for multi-source images. To address this shortcoming, we develop payoffs for independent game players in terms of higher order strategy similarities, and identify strategies which extinguish in an evolutionary game for achieving maximum average payoff. To render a convenient computational framework, we establish an association uniform hypergraph, referred to as the game hypergraph, with each vertex representing a strategy and each uniform hyperedge characterizing a payoff for independent players. We then exploit the Baum-Eagon scheme for computing the maximum average game payoff for Nash equilibrium within the association hypergraph. Our method is invariant to scene scale variation because of the higher order structures characterized by the strategy similarities. Furthermore, our method is computationally more efficient than existing hypergraph matching methods because of coarse correspondences. Experimental results show the effectiveness of our method for refining multi-source feature correspondences.