Kapur’s Entropy for Underwater Multilevel Thresholding Image Segmentation Based on Whale Optimization Algorithm

Multilevel thresholding is an effective and indispensable technology for image segmentation that has attracted extensive attention in recent years. However, the multilevel thresholding method has some disadvantages, such as a large computational complexity and low segmentation accuracy. Therefore, this paper proposes a whale optimization algorithm (WOA) based on Kapur’s entropy method to solve the image segmentation problem. The WOA can effectively balance exploration and exploitation to avoid falling into premature convergence and obtain the global optimal solution. To verify the segmentation performance of the WOA, a series of experiments on underwater images from the experimental pool of Harbin Engineering University are conducted, and the segmentation results are compared with those of the BA, the FPA, MFO, the MSA, PSO and WWO by maximizing the fitness value of Kapur’s entropy method. The fitness value, peak signal-to-noise ratio (PSNR), structure similarity index (SSIM), execution time and Wilcoxon’s rank-sum test are used to evaluate the overall performance of each algorithm. The experimental results reveal that the WOA is superior to the other comparison algorithms and has a higher segmentation accuracy, better segmentation effect and stronger robustness. In addition, the feasibility and efficiency of the WOA are verified.


I. INTRODUCTION
In recent years, unmanned underwater vehicles (UUVs) with vision systems have been widely used to gather image information for analysis and research, in which underwater image segmentation is difficult to accomplish in machine vision. The quality of image segmentation directly affects the accuracy of target feature extraction and target detection [1]- [3]. The three-dimensional model of a UUV equipped with a vision system is given in Fig 1. Image segmentation is a fundamental and important technology in image processing and robotic vision, which is a key operation from image processing to image analysis, as well as one of the key target feature extraction, recognition and tracking. The purpose is to segment a given original image into several independent and special-quality parts with respect to feature, colour, texture, The associate editor coordinating the review of this manuscript and approving it for publication was Huazhu Fu . histogram, grayscale and edge, and then to extract the target of interest. The grey values of pixels in same area are approximately the same, whereas, the grey values of pixels in different areas are significantly different. The quality of image segmentation directly affects the stability and reliability of the feature extraction and the object recognition. The common methods of image segmentation include the thresholdingbased method, region-based method, edge-based method, clustering-based method and graph-based method [4]- [8]. The thresholding-based method has been widely used to solve the image segmentation problem. Bi-level thresholding and multilevel thresholding are applied to process the simple images and complex images, respectively [9], [10]. Multilevel thresholding can find accurate target regions and obtain the segmentation effects. Various techniques have been proposed to determine the appropriate thresholds [11], such as Otsu's method, Kapur's entropy, minimum cross entropy, fuzzy entropy, Tsallis entropy, Shannon entropy and Renyi entropy. Kapur's entropy is an effective and feasible image processing technology and is used to carry out image segmentation. As the thresholds increase, the computational complexity increases exponentially. To overcome this shortcoming, many meta-heuristic algorithms are used to solve the multi-threshold image segmentation, such as the bat algorithm (BA) [12], flower pollination algorithm (FPA) [13], moth flame optimization (MFO) [14], moth swarm algorithm (MSA) [15], particle swarm optimization (PSO) [16], and water wave optimization (WWO) [17].
Zhou et al. applied the moth swarm algorithm based on Kapur's entropy method to solve the multi-threshold image segmentation problem, and the proposed method has proved the robustness and effectiveness according to numerical experimental results and image segmentation results [18]. Aziz et al. designed a whale optimization algorithm and moth flame optimization algorithm to improve the multithreshold search ability, and the methods provided a good balance between exploration and exploitation in all segmentation images and obtained a better segmentation effect [19]. Quadfel et al. proposed the social spider algorithm and flower pollination algorithm to optimize the objective function value and Kapur's method to perform multi-threshold image segmentation [20]. Díaz-Cortés et al. tried to solve the multi-level thresholding image segmentation problem using a dragonfly algorithm, and the experimental results indicated that the proposed algorithm obtained better optimization performance [21]. Sambandam et al. provided a self-adaptive dragonfly algorithm based on Kapur's entropy method for image segmentation, and the results indicated that the algorithm achieved higher segmentation accuracy and strong robustness [22]. Sun et al. proposed a hybrid optimization algorithm comprising the gravitational search algorithm and genetic algorithm to solve the image segmentation problem. The hybrid algorithm achieved complementary advantages and found the global optimal solution [23]. Shen et al. achieved multi-threshold image segmentation through a modified flower pollination algorithm, and the proposed algorithm had a strong global search ability and obtained the best segmentation effect [24]. Gao et al. introduced an improved artificial bee colony algorithm to solve the multi-threshold image segmentation problem, and the algorithm had high segmentation accuracy and fast convergence efficiency [25]. Pare et al. conducted a study on the firefly algorithm and Lévy flight strategy to conduct image segmentation, and the results showed that the proposed algorithm obtained the best threshold values and segmented VOLUME 9, 2021 images [26]. Satapathy et al. combined the bat algorithm with the chaotic strategy for image segmentation, and the results verified the stability and feasibility of that combination [27]. Akay et al. conducted a study on the particle swarm optimization algorithm and artificial bee colony algorithm for image segmentation, and the overall optimization performance of the proposed algorithms was significantly better than that of other algorithms [28]. Bao et al. proposed the colour image multilevel thresholding method based on the Harris hawks optimization algorithm for image segmentation, and the image segmentation effect of the proposed algorithm was the best [29]. Jia et al. applied a modified moth flame algorithm to solve the multilevel thresholding image segmentation problem, and the results indicated that the proposed algorithm found the optimal objective fitness values and achieved the best segmentation effect [30]. Bohat et al. tried to combine the TH heuristic with swarm intelligence algorithms for colour image segmentation, and the proposed algorithms had superior segmentation performance [31]. Lu et al. employed and validated a neutrosophic c-means clustering method, which was effective and able to solve the image segmentation problem [32]. Li et al. presented the MapReducebased fast fuzzy c-means algorithm to conduct large-scale underwater image segmentation, and the results indicated that the proposed algorithm obtained the best solution [33]. Elaziz et al. created a multi-objective multi-verse optimizer  to solve the image segmentation problem and obtained the optimal fitness value by maximizing the Kapur and Otsu objective functions [34]. Oliva et al. proposed a BNMTH method for multilevel image segmentation, and the results indicated that the BNMTH method had better segmentation performance [35]. Rodríguez-Esparza et al. proposed the Harris hawks optimization algorithm based on the minimum cross-entropy to solve the image segmentation problem, which was found to be an effective and feasible method [36]. Alwerfali et al. combined the salp swarm algorithm with fuzzy entropy for multilevel image thresholding, and the results indicated that the segmentation performance of the proposed algorithm is significantly better than that of other algorithms [37].
The whale optimization algorithm (WOA) is mainly used to simulate the bubble-net attacking behaviour of humpback whales in nature for global search and contains three important operations: encircling of the prey, the bubblenet attacking method and the search for prey [38]. The WOA has faster convergence speed and higher calculation accuracy. The WOA based on Kapur's entropy method is  used to solve the underwater multilevel thresholding image segmentation problem. The proposed algorithm can effectively avoid premature convergence and balance exploration and exploitation to obtain the optimal fitness value. Fourteen underwater images are used as test objects to verify the optimization performance of the WOA in solving the image segmentation problem, it is compared in this paper with other algorithms, i.e., the BA [12], the FPA [13], MFO [14], the MSA [15], PSO [16], and WWO [17]. The experimental results reveal that the WOA not only achieves a better segmentation effect and strong robustness, but also is an effective and feasible segmentation method. This research work will lay a good foundation for image extraction and image recognition.
This article is divided into the following sections: Section 2 introduces the multilevel thresholding. Section 3 reviews the WOA. In Section 4, the proposed WOA-based multilevel threshold method is described in detail. The experimental results and analysis are presented in Section 5. Finally, the conclusions and future research directions are discussed in Section 6. VOLUME 9, 2021

II. MULTILEVEL THRESHOLDING
Image threshold segmentation is mainly divided into two categories: a bi-level thresholding method and a multilevel thresholding method. The bi-level thresholding method involves a threshold value, which divides the image into a foreground and background to process simple images. The multilevel thresholding method is a crucial and unsupervised image processing technology that can not only solve complex image segmentation but also achieve better segmentation results.
Kapur's entropy method is a nonparametric threshold technique, which is applied to classify the image into the multiple classes by comparing the entropy of histogram, and a higher entropy value indicates more homogeneous classes. The proposed method has attracted the attention of many scholars and has been proved to be superior than other thresholding-based methods. The Kapur's entropy method has the following unique advantages: low required number of computations, easy implementation, strong stability, fast processing speed, and high segmentation accuracy. The entropy of a given image indicates the compactness and separateness among distinctive classes. Kapur's entropy can effectively obtain the optimal threshold values by maximizing the objective function and has been widely applied to accomplish image segmentation [39]. Assume that n threshold values from the optimal threshold values [t 1 , t 2 , . . . , t n ] are used to divide the image into various classes. The probability p i can be defined as: where i denotes the grey level, h i denotes the number of pixels, N denotes the total number of pixels, and L denotes the number of levels.

III. WOA
The WOA is a novel swarm intelligence optimization algorithm based on the bubble-net attacking behaviour of humpback whales, which mainly simulates encircling of the prey, the bubble-net attacking method and the search for prey to perform an efficient global search. In the WOA, each humpback whale denotes a candidate solution. The search mechanism of the WOA is used to screen the candidate solutions to obtain the global optimal solution. The model of the bubblenet feeding behaviour is given in Fig. 2.

A. ENCIRCLING PREY
A humpback whale can find the position of prey and quickly encircle them. The position of the optimal solution is unknown, and it is assumed that the current position of the humpback whale is the target prey or a suboptimal solution. After determining the position of the optimal humpback whale, other whales will update their positions according to the optimal position. The position update can be defined as: where t denotes the current iteration, X * denotes the position vector of the optimal solution, X denotes the current position vector, || denotes the absolute value, and · denotes an elementwise multiplication. − → A , − → C denote coefficient vectors and can be defined as: where − → r denotes a random vector in [0, 1] and − → a denotes a linear decrease from 2 to 0.

B. BUBBLE-NET ATTACKING STRATEGY (EXPLOITATION PHASE)
The bubble-net attacking strategy can be divided into the shrinking encircling mechanism and the spiral position updating. The shrinking encircling mechanism is used to reduce the distance between the global optimal position and the current optimal position according to a random vector − → A and control variable a. The humpback whales swim towards their prey according to the updated spiral position and capture the prey by calculating the distance between the whale position and the prey position. The position updating can be defined as: where − → D denotes the distance between whale and prey, l denotes a random number in [−1, 1], and b denotes a constant for defining the shape of the logarithmic spiral.
Humpback whales update their positions to capture prey, and there is a probability of 50% that either the shrinking encircling mechanism or the logarithmic spiral position updating is carried out. The position updating can be defined as: where p denotes a random number in [0, 1].

C. SEARCH FOR PREY (EXPLORATION PHASE)
To avoid falling into the local optimum, the WOA performs a random search strategy to find the prey by adjusting the vector , the WOA has a strong exploration ability to obtain the global optimal solution. The position updating can be defined as: where −−→ X rand denotes a random position vector (a random whale) selected from the current population.
The WOA can balance the exploration ability and the exploitation ability to find the global optimal solution. To better describe the solution process, the pseudo-code of the WOA is shown in Algorithm 1.

Algorithm 1 WOA Algorithm
Begin Step 1. Initialize the whale population X i (i = 1, 2, . . . , n) Step 2. Calculate the fitness of each search agent Obtain the best search agent X * Step 3. while (t < t max ) do for each search agent Update a, A, C, l, and p if1 (p < 0.5) if2 (|A| < 1) Update the position of the current search agent by Eq. (8) else if2 (|A| ≥ 1) Select a random search agent (X rand ) Update the position of the current search agent by Eq. (15) end if2 else if1 (p ≥ 0.5) Update the position of the current search agent by Eq. (12) end if1 end for Check if any search agent goes beyond the search space and amend it Calculate the fitness of each search agent Update X * if there is a better solution

IV. WOA-BASED MULTILEVEL THRESHOLD METHOD
For each whale or search agent, its position denotes the threshold value of a given image segmentation. A whale changes its position to obtain the optimal solution by setting the threshold level. The WOA based on image segmentation is shown in Algorithm 2. The flowchart of the WOA for multilevel thresholding is shown in Fig. 3.

Algorithm 2 WOA Based on Image Segmentation for Kapur Entropy
Begin Step 1. Initialize the whale population X i (i = 1, 2, . . . , n) Step 2. Calculate the fitness of each search agent by Eq. (2) for the Kapur-based method Obtain the best search agent X *

B. SPACE COMPLEXITY
The space complexity of an algorithm is defined as the storage space consumed by the algorithm. The WOA adopts N search agents to calculate the space complexity, and the dimensionality of the solved problem is D. Therefore, the total space complexity of the WOA is O (N  *  D); hence, the space efficiency of the WOA is good.

V. EXPERIMENTAL RESULTS AND ANALYSIS A. EXPERIMENTAL SETUP
All the algorithms are programmed in MATLAB R2018b, and the numerical experiment is set up on an i7-8750H 2.2 GHz processor with 8 GB of memory.

B. TEST IMAGES
The computer vision system and the image processing technology are inseparable, and they are used to solve reconstruction and modeling, tracking and segmentation, and mitigating unnecessary image artifacts. The processing of the    were carefully selected from the experimental pool of Harbin Engineering University and are shown in Fig. 4.

C. PARAMETER SETTING
To verify the effectiveness and feasibility of the WOA, the proposed algorithm is applied to accomplish underwater multilevel thresholding image segmentation, and the WOA is compared with other optimization algorithms, such as the BA, the FPA, MFO, the MSA, PSO and WWO. The control parameters of the comparison algorithm are important empirical values and derived from the original articles; they are shown in Table 1.

D. SEGMENTED IMAGE QUALITY MEASUREMENTS
Five important measures are used as performance evaluation indicators to detect the segmented image and further verify the overall superiority of the WOA:

1) FITNESS VALUE
The amount of information of the segmented image depends on the size of the fitness value. A larger fitness value means that the segmented image contains more information.

2) PEAK SIGNAL-TO-NOISE RATIO (PSNR)
The PSNR is used to detect the difference between the segmented image and the original image based on the intensity value of the image. The larger the PSNR value is, the better the image segmentation effect. Due to the difference in visual acuity of the human eye, a segmented image of a higher PSNR value may be worse than a segmented image of a lower PSNR value. The PSNR can be defined as [40]: where MSE denotes the mean squared error and can be defined as: where I (i, j) and K (i, j) denote the original and segmented images with size M × N , respectively.

3) STRUCTURE SIMILARITY INDEX (SSIM)
The SSIM is used to detect the similarity between the segmented image and the original image according to brightness, contrast and structural similarity. As the SSIM value approaches one, the image segmentation effect improves. The SSIM can be defined as [41]: where µ x and µ y denote the mean intensity of the original image and that of the segmented image, respectively. σ 2 x and σ 2 y denote the standard deviation of the original image and that of the segmented image, respectively. σ xy denotes the covariance between the original image and the segmented image. c 1 and c 1 are constants.

4) EXECUTION TIME
The execution time is based on each comparison algorithm after 30 independent runs, which can reflect the convergence speed. The shorter the time is, the higher the efficiency of the algorithm.

5) WILCOXON'S RANK-SUM TEST
Wilcoxon's rank-sum test is used to detect whether there is a significant difference between two algorithms [42]. If p < 0.05, then there is a significant difference. If p > 0.05, then there is no significant difference.

E. RESULTS AND ANALYSIS
For all algorithms, the size of the population is 30, the maximum number of iterations is 100, and the number of independent runs is 30. The threshold numbers are set to 4, 5, 6, 7 and 8. The experimental results of the WOA based on Kapur's entropy are compared to those of the BA, the FPA, MFO, the MSA, PSO and WWO in Tables 2-7 and Figs. 5-8 according to the optimal fitness value, the best threshold value, the PSNR value, the SSIM value, the average execution time and the p-value of Wilcoxon's rank-sum test.
In computational science and mathematics management, optimization is the process of selecting the best solution from the available alternatives. In other words, the purpose of optimization is to obtain the global optimal solution in a given search space by maximizing or minimizing the objective function. In Table 2, for different thresholds, the WOA can obtain more effective and feasible results. The optimal fitness values of the WOA are significantly better than those of the other optimization algorithms. For all algorithms, the optimal fitness values increase as the threshold levels increase, which indicates that an image segmented with a higher threshold level can result in a better segmentation effect. To verify the superiority of the WOA, the ranking is based on the optimal fitness value. The ranking of the WOA is the highest, which indicates that the algorithm obtains the best solution among those of all algorithms. For test images 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13 and 14, the WOA has a strong global search ability, avoiding falling into a local optimum. Compared with those of the other algorithms, the optimal fitness values of the WOA are the best, and all its rankings are first, which indicates that the WOA can successfully handle underwater test images. For test image 2, the optimal fitness value of the WOA is worse than the fitness value of the FPA at K = 4, but the WOA is better than the BA, the FPA, MFO, the MSA, PSO and WWO at K = 5, 6, 7, 8. For test image 12, the optimal fitness value of the WOA is worse than the fitness value of the PSO and WWO at K = 5, but the WOA is better than the BA, the FPA, MFO and the MSA at K = 5, 6, 7, 8. In Fig. 5, the average fitness values increase as the threshold  levels increase, and the fitness values of the WOA are the best among those of all algorithms. To summarize, the WOA has strong exploration and exploitation abilities and thus can achieve a higher calculation accuracy and better segmentation effect than can the other algorithms.
The threshold value plays an important role in image segmentation, as it not only determines the quality of the segmented image but also affects the value of each evaluation index. In this paper, the segmentation thresholds are determined according to Kapur's entropy. An algorithm with a strong search ability can obtain better threshold values and thus can improve the accuracy and quality of the segmented images. Therefore, it is necessary to analyse the optimization performance of each algorithm in solving the multilevel thresholding image segmentation problem. Compared with other algorithms, the WOA has stronger robustness and a better search ability; hence, it can effectively avoid premature convergence and obtain the global optimal solution. For example, the BA affects the calculation accuracy by adjusting the pulse frequency range f , echo loudness A, and decreasing coefficient γ . The FPA uses the switch probability ρ to perform search optimization. MFO seeks the optimal solution by adjusting the control parameters b, t and r. The MSA adjusts the random numbers θ, ε 2 , ε 3 , r 1 and r 2 . PSO uses the constant inertia ω and the acceleration coefficients c 1 and c 2 to update the position and then performs a global search to obtain the best solution. WWO uses the wavelength λ and wave height h max to avoid premature convergence. Although these factors balance the global search and local search in solving the image segmentation problem, the factors are not universal, especially for complex optimization problems. As the number of thresholds increases, the computational complexity increases, and the accuracy of the segmented images increases. The WOA balances the global search and the local search by simulating the encircling of prey, the bubble-net attacking method and the search for prey and avoids falling into a local optimum. The WOA improves the calculation accuracy to a certain extent and obtains the best threshold values, which indicates that the WOA is effective and useful in solving the image segmentation problem.
For multilevel thresholding image segmentation, the larger the number of segmented thresholds, the higher the accuracy of the segmented image is. To better verify the segmentation performance of each algorithm, the PSNR value is regarded as an important evaluation index. The PSNR values of the segmented images obtained by the BA, the FPA,  MFO, the MSA, PSO, WWO and WOA based on Kapur's entropy are given in Table 4. The PSNR values are applied to evaluate the distortion degree of each segmented image. A larger PSNR value indicates a smaller distortion degree. For different threshold levels, the PSNR values of the WOA are better than those of the other algorithms, which indicates that the WOA has certain advantages in solving the image segmentation problem. In Table 4, as the threshold level increases, the PSNR values of each algorithm increases accordingly. To better compare the PSNR values, a ranking is carried out based on the sizes of the PSNR values. The higher the ranking is, the better the PSNR value. For each segmented image, the number of threshold levels is 4, 5, 6, 7 and 8. In other words, each algorithm has 70 PSNR values. For the WOA, the number of first-place rankings is 51, the number of second-place rankings is 13, and the number of third-place rankings is 6. The average PSNR values of the algorithms over all images are given in Fig. 6. The WOA has a higher average PSNR, and the difference between the WOA and the other algorithms becomes increasingly obvious, which indicates that the overall optimization performance of the WOA based on Kapur's entropy is better than that of other algorithms. The experimental results reveal that the WOA not only is suitable for solving the function optimization problem but also has strong practicability in image segmentation.
The SSIM values, which are based on the brightness, contrast and structural information, are used to evaluate the similarity between the original image and the segmented image. The SSIM values of the segmented images obtained by the BA, the FPA, MFO, the MSA, PSO, WWO and the WOA based on Kapur's entropy are given in Table 5. As the threshold level increases, the distortion of the segmented images decreases, and the segmented images become closer to the original image. Similarly, the ranking is based on the size of the SSIM value. A higher ranking indicates that the WOA contains more image segmentation information. Each algorithm has 70 SSIM values. For the WOA, the number of first-place rankings is 57, the number of second-place rankings is 9, and the number of third-place rankings is 4. The SSIM values of the WOA are obviously superior to those of the other algorithms; hence, the WOA obtains better threshold values and global optimal solutions. Compared with the other algorithms, the WOA has better optimization performance and higher similarity. The average SSIM values of the algorithms over all images are given in Fig. 7. The SSIM values of the WOA are superior to those of the other algorithms, and the difference between the WOA and the comparison algorithms is significant. The experimental results reveal that the WOA has a higher calculation accuracy and certain advantages in obtaining optimal or suboptimal SSIM values and has the ability to solve complex images. VOLUME 9, 2021    The average execution time of each algorithm is given in Table 6. As the threshold level increases, the execution time of each algorithm increases accordingly due to the computational complexity of the algorithms, which indicates that the algorithms consume more time at a higher threshold level. Compared with the other algorithms, the WOA has   a faster convergence speed and requires less time because it has a higher search efficiency and thus can avoid premature convergence. The better fitness values, PSNR values and SSIM values show that the WOA has stronger segmentation performance. The average time of the algorithms over all images is given in Fig. 8. In terms of the computing time, the order of the algorithm is WOA < MFO < BA < MSA < PSO < FPA < WWO. The experimental results reveal that the WOA can complete the effective segmentation of images in a relatively shorter time and achieve a higher segmentation accuracy.
To verify the superiority and feasibility of the WOA, for all algorithms, the population size is 30, the maximum number of iterations is 100, and the number of independent operations is 30. In the data statistics, all experimental data based on Kapur's entropy are used for determining the p-values of the Wilcoxon rank-sum. A p-value less than 0.05 indicates a significant difference between the WOA and the other algorithms. If the p-value is greater than 0.05, then there is no significant difference between the WOA and the other algorithms (shown in bold). The experimental results reveal that there is a significant difference between the two groups VOLUME 9, 2021   of data in most cases and that the data are not obtained by accident. The WOA is an effective and feasible method for achieving a better segmentation effect.
Figs. 9-22 show the results of image segmentation of the WOA and the other algorithms under different threshold levels. As the threshold level increases, the overall effect of VOLUME 9, 2021 the image segmentation improves, which indicates that the segmented image contains more information. The segmentation effect of the WOA is obviously superior to that of the other algorithms, and a segmented image at a higher threshold level is closer to the original image. The WOA based on Kapur's entropy obtains the optimal fitness values and the best threshold values, which indicates that the WOA has a higher calculation accuracy and better segmentation effect. The PSNR and SSIM values of the WOA are better than those of the other algorithms, which indicates that the WOA has less image distortion and a higher structural similarity. The execution time of the WOA is less than those of the other algorithms by over 30 runs; thus, the WOA has a faster convergence speed. The p-values of the Wilcoxon rank-sum verify that there is a significant difference between the WOA and the other algorithms. In summary, the WOA has a better segmentation performance and stronger robustness in solving the image segmentation problem.
Statistically, the WOA simulates encircling of the prey, the bubble-net attacking method and the search for prey to obtain the global solution. The WOA can effectively solve the image segmentation problem for the following reasons. First, the WOA not only is simpler to operate, has few control parameters and is easy to implement but also has a wider search space and a stronger search ability; thus, it can avoid falling into a local optimum. Second, the WOA has a good position update mechanism. Once the optimal position of a humpback whale is determined, the remaining humpback whales will swim to the optimal position and constantly update their positions; hence, the WOA has a strong global search ability and robustness. Third, for control parameter , the humpback whale randomly selects the positions of the whales to update its position. This search mechanism expands the optimization space. To summarize, the WOA can effectively switch between exploration and exploitation to enhance the overall optimization performance.

VI. CONCLUSIONS AND FUTURE RESEARCH
The purpose of image segmentation is to consume less time and obtain better segmentation results. This paper presents a WOA based on Kapur's entropy method to achieve multilevel thresholding image segmentation, and the objective function of the WOA is maximized to obtain the optimal threshold values. As the thresholds increase, the difference between the WOA and the other algorithms increases. Compared with the other algorithms, the WOA can switch between the global search ability and local search ability to obtain the optimal solution. The experimental results show that the WOA has a higher segmentation accuracy and faster convergence speed in terms of the fitness value, PSNR, SSIM, execution time and Wilcoxon's rank-sum test. Meanwhile, the WOA has good practicality and strong robustness and thus can effectively complete the image segmentation task.
In future research, the WOA will be used to address higher threshold values or solve the colour image segmentation problem. Underwater image segmentation methods will be applied to meet the needs of image segmentation, such as region-based method, edge-based method, clustering-based method and graph-based method. The thresholding-based method will be compared with other image segmentation methods to further verify the overall performance of the WOA in solving the image segmentation problem. In addition, advanced strategies or combined algorithms will be used to improve the convergence speed and calculation accuracy. JIALING TANG was born in Suining, China, in 1984. He is currently pursuing the Ph.D. degree in control science and engineering with Harbin Engineering University, China. His research interest includes coordination control of multiple unmanned underwater vehicles. VOLUME 9, 2021