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Image segmentation, the process of partitioning an image into meaningful regions, is a fundamental step in image processing, crucial for applications like computer vision, medical imaging, and object recognition. Image segmentation is an essential step of image processing that directly affects its success. Among the methods used for image segmentation, histogram-based thresholding is prevalent. Two well-known approaches to histogram-based thresholding are Otsu's and Kapur's methods in gray images that maximize the between-class variance and the entropy measure, respectively. Both techniques were introduced for bi-level thresholding. However, these techniques can be expanded to multilevel image thresholding. For this to occur, a large number of iterations are required to account for exact threshold values. To this end, various optimization techniques have been used to overcome this drawback. Recently, a new optimization algorithm called Battle Royal Optimizer (BRO) has been published, which is shown to solve various optimization tasks effectively. In this study, BRO has been applied to yield optimum threshold values in multilevel image thresholding. Here is also demonstrated the effectiveness of BRO for image segmentation on various images from the standard publicly accessible Berkeley segmentation dataset. We compare the performance of BRO to other state-of-the-art optimization-based methods and show that it outperforms them in terms of fitness value, Peak Signal-to-Noise Ratio, Structural Similarity Index Method, Feature Similarity Index Method (FSIM), Color FSIM (FSIMc), and Standard Deviation. These results underscore the potential of BRO as a promising solution for image segmentation tasks, particularly through its effective implementation of multilevel thresholding. [ABSTRACT FROM AUTHOR]

• An efficient method for image thresholding is proposed. • The Harris hawk optimizer is used for image segmentation. • The Harris hawk optimizer is tested over a multidimensional real problem. • The quality of the segmentation results is higher than other algorithms. • The performance of the algorithm is tested on digital mammograms. Segmentation is a crucial phase in image processing because it simplifies the representation of an image and facilitates its analysis. The multilevel thresholding method is more efficient for segmenting digital mammograms compared to the classic bi-level thresholding since it uses a higher number of intensities to represent different regions in the image. In the literature, there are different techniques for multilevel segmentation; however, most of these approaches do not obtain good segmented images. In addition, they are computationally expensive. Recently, statistical criteria such as Otsu, Kapur, and cross-entropy have been utilized in combination with evolutionary and swarm-based strategies to investigate the optimal threshold values for multilevel segmentation. In this paper, an efficient methodology for multilevel segmentation is proposed using the Harris Hawks Optimization (HHO) algorithm and the minimum cross-entropy as a fitness function. To substantiate the results and effectiveness of the HHO-based method, it has been tested over a benchmark set of reference images, with the Berkeley segmentation database, and with medical images of digital mammography. The proposed HHO-based solver is verified based on other comparable optimizers and two machine learning algorithms K -means and the Fuzzy IterAg. The comparisons were performed based on three groups. This first one is to provide evidence of the optimization capabilities of the HHO using the Wilcoxon test, and the second is to verify segmented image quality using the PSNR, SSIM, and FSIM metrics. Then, the third way is to verify the segmented image comparing it with the ground-truth through the metrics PRI, GCE, and VoI. The experimental results, which are validated by statistical analysis, show that the introduced method produces efficient and reliable results in terms of quality, consistency, and accuracy in comparison with the other methods. This HHO-based method presents an improvement over other segmentation approaches that are currently used in the literature. [ABSTRACT FROM AUTHOR]