Multilevel thresholding has got more attention in recent years with various successful applications. However, the implementation becomes more and more complex and time-consuming when the number of thresholds is high, and color images which contain more information are even worse. Therefore, this paper proposes an alternative hybrid algorithm for color image segmentation, the advantages of which lie in extracting the best features from the high performance of two algorithms and overcoming the limitations of each algorithm to some extent. Two techniques, Otsu's method, and Kapur's entropy, are used as fitness function to determine the segmentation threshold values. Harris hawks optimization (HHO) is a novel and general-purpose algorithm, and the hybridization of HHO is fulfilled by adding another powerful algorithm-differential evolution (DE), which is known as HHO-DE. More specifically, the whole population is divided into two equal subpopulations which will be assigned to HHO and DE algorithms, respectively. Then both algorithms operate in parallel to update the positions of each subpopulation during the iterative process. In order to fully demonstrate the superior performance of HHO-DE, the proposed method is compared with the seven state-of-the-art algorithms by an array of experiments on ten benchmark images. Meanwhile, five measures, including the average fitness values, standard deviation (STD), peak signal to noise ratio (PSNR), structure similarity index (SSIM), and feature similarity index (FSIM), are used to evaluate the performance of each algorithm. In addition, Wilcoxon's rank sum test for statistical analysis and the comparison with the super-pixel method are also conducted to verify the superiority of HHO-DE. The experimental results reveal that the proposed method significantly outperforms other algorithms. Hence, the HHO-DE algorithm is a remarkable and promising tool for multilevel thresholding color image segmentation.

Multilevel thresholding is a very active research field in image segmentation, and has been successfully used in various applications. However, the computational time will increase exponentially as the number of thresholds increases, and for color images which contain more information this is even worse. To overcome the drawback while maintaining segmentation accuracy, a modified version of dragonfly algorithm (DA) with opposition-based learning (OBLDA) for color image segmentation is proposed in this paper. The opposition-based learning (OBL) strategy simultaneously considers the current solution and the opposite solution, which are symmetrical in the search space. With the introduction of OBL, the proposed algorithm has a faster convergence speed and more balanced exploration–exploitation compared with the original DA. In order to clearly demonstrate the outstanding performance of the OBLDA, the proposed method is compared with seven state-of-the-art meta-heuristic algorithms, through experiments on 10 test images. The optimal threshold values are calculated by the maximization of between-class variance and Kapur’s entropy. Meanwhile, some indicators, including peak signal to noise ratio (PSNR), feature similarity index (FSIM), structure similarity index (SSIM), the average fitness values, standard deviation (STD), and computation time are used as evaluation criteria in the experiments. The promising results reveal that proposed method has the advantages of high accuracy and remarkable stability. Wilcoxon’s rank sum test and Friedman test are also performed to verify the superiority of OBLDA in a statistical way. Furthermore, various satellite images are also included for robustness testing. In conclusion, the OBLDA algorithm is a feasible and effective method for multilevel thresholding color image segmentation.

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