Image segmentation is a very significant process in image analysis. Much effort based on thresholding has been made on this field as it is simple and intuitive, commonly used thresholding approaches are to optimize a criterion such as between-class variance or entropy for seeking appropriate threshold values. However, a mass of computational cost is needed and efficiency is broken down as an exhaustive search is utilized for finding the optimal thresholds, which results in application of evolutionary algorithm and swarm intelligence to obtain the optimal thresholds. This paper considers image thresholding as a constrained optimization problem and optimal thresholds for 1-level or multi-level thresholding in an image are acquired by maximizing the fuzzy entropy via a newly proposed bat algorithm. The optimal thresholding is achieved through the convergence of bat algorithm. The proposed method has been tested on some natural and infrared images. The results are compared with the fuzzy entropy based methods that are optimized by artificial bee colony algorithm (ABC), genetic algorithm (GA), particle swarm optimization (PSO) and ant colony optimization (ACO); moreover, they are also compared with thresholding methods based on criteria of between-class variance and Kapur's entropy optimized by bat algorithm. It is demonstrated that the proposed method is robust, adaptive, encouraging on the score of CPU time and exhibits the better performance than other methods involved in the paper in terms of objective function values. 
Fuzzy entropy based optimal thresholding using bat algorithm