6. Microscopic Image Segmentation Based on Based Branch and Bound and Game Theory

In this work a new family of image segmentation algorithms is proposed. This paper is a generalization of the model proposed, called: Power Watershed segmentation framework. Indeed, we extended it for cases: \(2< q < \inf \) and \(p \rightarrow \inf \). To do so, we explore the segmentation a new formulation of the segmentation problem based on game theory is proposed optimization energy function as a game theory problem. In this new formulation, The minimization can be, then, optimization process is seen as a search of the Nash equilibrium of a non-cooperative strategic game. Indeed, the computation of Nash equilibrium in finite game is equivalent to a non linear optimization problem afterward. As the optimization problem thus formulated the computation of the Nash equilibrium is an NP-hard problem, then, we propose the use of the Branch and Bound method is used to solve it to find it in reasonable time. In this study moreover, the uniqueness of the Nash equilibrium is demonstrated using a potential game-theoretic approach. Then we propose a new family of segmentation approach with \(2< q < \inf \)and \(p \rightarrow \inf \), named Game-based PW. The obtained results of the proposed approach, show are better than those given by the original Power Watershed \(q = 2\).