Multilevel thresholding is an important approach for image segmentation which has drawn much attention during the past few years. The Tsallis entropy method is implemented for its effectiveness and simplicity. Although it is efficient and gives an excellent result in the case of bi-level thresholding, its evaluation becomes complexity when the number of thresholds increases. To overcome the problem, the metaheuristic algorithms are applied in this search area for searching the optimal thresholds. In this paper, a modified grasshopper optimization algorithm (GOA) is adopted to render multilevel Tsallis cross entropy more practical and reduce the complexity. The Levy flight algorithm is employed to modify the original GOA and balance the exploration and exploitation of the GOA. Experiments are conducted between five state-ofthe-art metaheuristic algorithms and the proposed one. In addition, the proposed approach is compared with thresholding techniques depending on between-class variance (Otsu) method and the Renyi entropy function. Both real life images and plant stomata images are used in the experiments to test the performance of the algorithms involved. Qualitative experimental results show that the proposed segmentation approach has a fewer iterations and a higher segmentation accuracy. INDEX TERMS Multi-threshold color image segmentation, Tsallis entropy method, grasshopper optimization algorithm, Levy flight.

Hybrid algorithms have attracted more and more attention in the field of optimization algorithms. In this paper, three hybrid algorithms are proposed to solve feature selection problems based on seagull optimization algorithm (SOA) and thermal exchange optimization (TEO). In the first algorithm, we take the roulette wheel to choose one of the two algorithms for located updating. Another method is to join the TEO algorithm for optimization after SOA algorithm iteration. The last method is to adopt TEO algorithm's heat exchange formula to improve the seagull attack mode of SOA algorithm, so as to improve the exploitation ability of SOA algorithm. The performance of proposed methods is evaluated on 20 standard benchmark datasets in the UCI repository and compared with three well-known hybrid optimization feature selection methods in the literature. The experimental results illustrate that the proposed algorithm has high efficiency in improving classification accuracy, ensuring the ability of hybrid SOA algorithm in feature selection and classification task information attribute selection, and reducing the CPU time.

The grayscale co-occurrence matrix (GLCM) can be adapted to segment the image according to the pixels, but the segmentation effect becomes worse as the number of threshold increases. To solve this problem, we propose an improved salp swarm algorithm (LSSA) to optimize GLCM, with the novel diagonal class entropy (DCE) as the fitness function of the GLCM algorithm. At the same time, in order to increase the optimization ability of traditional SSA algorithm, Levy flight (LF) strategy should be improved. Through experiments on the LSSA algorithm of the color natural images, the satellite images, and the Berkeley images, the segmentation quality of the segmented images is evaluated by peak signal-to-noise ratio, feature similarity, probability rand index, variation of information, global consistency error, and boundary displacement error. The experimental results show that the segmentation ability of the GLCM-LSSA algorithm is superior to other comparison algorithms and has a good segmentation ability.

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Multithreshold segmentation is an indispensable part of modern image processing. Color images contain more information than gray images, therefore RGB multi-thresholding segmentation techniques have been drawn much attention during recent years. Multiverse optimization (MVO) algorithm has a strong advantage in finding the optimal solution of three channels for RGB. In this paper, an MVO algorithm based on Lévy flight (LMVO) is proposed. Lévy flight is an efficient strategy which can not only increase the population diversity to prevent premature convergence but also improve the ability to jump out of the local optimum. Therefore, LMVO conduces to achieve a better balance between exploration and exploitation of MVO, so that it is faster and more robust than MVO and avoids premature convergence. Further LMVO algorithm is compared with the other eight famous meta-heuristics algorithms, by maximizing the objective function of Kapur's entropy method or of Otsu method to determine the optimal threshold. The maximum objective function, peak signal-to-noise ratio (PSNR), feature similarity index (FSIM), structural similarity index (SSIM), CPU calculation time, optimal threshold value, and Wilcoxon's rank-sum test are used to evaluate the quality of the segmented image. The experimental results show that this method has obvious advantages in terms of objective function value, image quality measurement, convergence performance, and robustness.