Game Theory and Its Applications in Imaging and Vision

It is very common to see many terms in a variational model from Imaging and Vision, each aiming to optimize some desirable measure. This is naturally so because we desire several objectives in an objective functional. Among these is data fidelity which in itself is not unique and often one hopes to have both L1 and L2 norms to be small for instance, or even two differing fidelities: one for geometric fitting and the other for statistical closeness. Regularity is another demanding quantity to be settled on. Apart from combination models where one wants both minimizations to be achieved (e.g., total generalized variation or infimal convolution) in some balanced way through an internal parameter, quite often, we demand both gradient and curvature based terms to be minimized; such demand can be conflicted. A conflict is resolved by a suitable choice of parameters which can be a daunting task. Overall, it is fair to state that many variational models for Imaging and Vision try to make multiple decisions through one complicated functional. Game theory deals with situations involving multiple decision makers, each making its optimal strategies. When assigning a decision (objective) by a variational model to a player by associating it with a game framework, many complicated functionals from Imaging and Vision modeling may be simplified and studied by game theory. The decoupling effect resulting from game theory reformulation is often evident when dealing with the choice of competing parameters. However, the existence of solutions and equivalence to the original formulations are emerging issues to be tackled. This chapter first presents a brief review of how game theory works and then focuses on a few typical Imaging and Vision problems, where game theory has been found useful for solving joint problems effectively.