masi entropy
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Masi entropy is a popular criterion employed for identifying appropriate threshold values in image thresholding. However, with an increasing number of thresholds, the efficiency of Masi entropy-based multi-level thresholding algorithms becomes problematic. To overcome this, we propose a novel differential evolution (DE) algorithm as an effective population-based metaheuristic for Masi entropy-based multi-level image thresholding. Our ME-GDEAR algorithm benefits from a grouping strategy to enhance the efficacy of the algorithm for which a clustering algorithm is used to partition the current population. Then, an updating strategy is introduced to include the obtained clusters in the current population. We further improve the algorithm using attraction (towards the best individual) and repulsion (from random individuals) strategies. Extensive experiments on a set of benchmark images convincingly show ME-GDEAR to give excellent image thresholding performance, outperforming other metaheuristics in 37 out of 48 cases based on cost function evaluation, 26 of 48 cases based on feature similarity index, and 20 of 32 cases based on Dice similarity. The obtained results demonstrate that population-based metaheuristics can be successfully applied to entropy-based image thresholding and that strengthening both exploitation and exploration strategies, as performed in ME-GDEAR, is crucial for designing such an algorithm.

A novel multilevel threshold segmentation method for color satellite images based on Masi entropy is proposed in this paper. Lévy multiverse optimization algorithm (LMVO) has a strong advantage over the traditional multiverse optimization algorithm (MVO) in finding the optimal solution for the segmentation in the three channels of an RGB image. As the work advancement introduces a Lévy multiverse optimization algorithm which uses tournament selection instead of roulette wheel selection, and updates some formulas in the algorithm with mutation factor. Then, the proposal is called TLMVO, and another advantage is that the population diversity of the algorithm in the latest iterations is maintained. The Masi entropy is used as an application and combined with the improved TLMVO algorithm for satellite color image segmentation. Masi entropy combines the additivity of Renyi entropy and the non-extensibility of Tsallis entropy. By increasing the number of thesholds, the quality of segmenttion becomes better, then the dimensionality of the problem also increases. Fitness function value, average CPU running time, Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM) and Feature Similarity Index (FSIM) were used to evaluate the segmentation results. Further statistical evaluation was given by Wilcoxon's rank sum test and Friedman test. The experimental results show that the TLMVO algorithm has wide adaptability to high-dimensional optimization problems, and has obvious advantages in objective function value, image quality detection, convergence performance and robustness.