(Retracted) Hybrid whale optimization algorithm-Levy flight approach for multilevel thresholding image segmentation

Abstract

Determining the optimal threshold for multilevel image segmentation is a stimulating task. Image segmentation has many applications, such as content-based image retrieval, medical imaging, object detection, object recognition, machine vision, etc. In multilevel thresholding, multiple thresholds are used to segment complex images, and the images are segmented into multiple levels to extract meaningful information for further image analysis. Where threshold number is small, p-tile, Otsu, moment preserving, and entropy thresholding methods attain good accuracy. These classical thresholding methods are time-consuming, computation expensive, and unable to produce good segmentation accuracy with increased threshold numbers. To overcome these problems, the classical thresholding methods are utilized as objective functions with nature-inspired metaheuristic algorithms such as whale optimization algorithm (WOA), simplified swarm optimization (SSO), sine cosine algorithm (SCA), BAT algorithm, WOA-thresholding, and black widow optimization (BWO) to determine optimal multiple thresholds. Nature-inspired metaheuristic algorithms are widely used to search for an optimal solution for global optimization problems. WOA is widely used to find the optimal solution in search space. WOA suffers from entrapment into local optima due to premature convergence behavior. We introduce hybridization of WOA with Levy flight trajectory and named as hybrid whale optimization algorithm-Levy flight (HWOAL), which is utilized to find optimal multiple thresholds for multilevel image segmentation. Levy flight trajectory is utilized to increase diversity in the swarm population. The efficacy of HWOAL is tested on 23 benchmark optimization functions (F1 to F23) and compared with WOA, SSO, SCA, and BAT algorithms. Experiment arms that HWOAL is efficient and makes WOA faster, enhances the ability of exploitation and exploration phase, and can avoid getting stuck into local optima. The segmentation performance of the proposed HWOAL method has been compared with other algorithms, such as WOA, SSO, SCA, BAT, and other two recent segmentation algorithms, such as WOA-TH and BWO on several benchmark images (BSD 300). The experimental result is carried in 30 trials and analyzed based on objective fitness value, optimal multilevel threshold values, segmentation quality measures, such as mean square error, peak signal-to-noise ratio, structural similarity index, average difference, and computation time to compute optimal multilevel threshold values. The experiment conducted by the authors shows that the proposed HWOAL method is efficient, produces better fitness value, and segmentation metrics for multilevel image segmentation than other algorithms.