Matching as a Non-Cooperative Game

Abstract

With this paper we offer a game-theoretic perspective for the all-pervasive matching problem in computer vision. Specifically, we formulate the matching problem as a (population) non-cooperative game where the potential associations between the items to be matched correspond to (pure) strategies, while payoffs reflect the degree of compatibility between competing hypotheses. Within this formulation, the solutions of the matching problem correspond to evolutionary stable states (ESS's), a robust population-based generalization of the notion of a Nash equilibrium. In order to find ESS's of our matching game, we propose using a novel, fast evolutionary game dynamics motivated by Darwinian selection processes, which let the pure strategies play against each other until an equilibrium is reached. A distinguishing feature of the proposed framework is that it allows one to naturally deal with general many-to-many matching problems even in the presence of asymmetric compatibilities. The potential of the proposed approach is demonstrated via two sets of image matching experiments, both of which show that our results outperform those obtained using well-known domain-specific algorithms.