Image retrieval using Nash equilibrium and Kalai-Smorodinsky solution

: pp. 646–657
Received: May 23, 2021
Accepted: June 07, 2021
LIMSAD, FSAC, Hassan II University of Casablanca, Casablanca, Morocco
LMA, FSTM, Hassan II University of Casablanca, Mohammedia, Morocco
LERMA, EMI, Mohammed V University Rabat, Morocco

In this paper, we propose a new formulation of Nash games for solving a general multi-objectives optimization problems.  The objective of this approach is to split the optimization variables, allowing us to determine numerically the strategies between two players.  The first player minimizes his function cost using the variables of the first table P and the second player, using the second table Q.  The original contribution of this work concerns the construction of the two tables of allocations that lead to a Nash equilibrium on the Pareto front.  The second proposition of this paper is to find a Nash Equilibrium solution, which coincides with the Kalai--Smorodinsky solution.  Two algorithms that calculate P, Q and their associated Nash equilibrium, by using some extension of the normal boundary intersection approach, are tried out successfully.  Then, we propose a search engine to look for similar images of a given image based on multiple image representations using Color, Texture and Shape Features.

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Mathematical Modeling and Computing, Vol. 8, No. 4, pp. 646–657 (2021)