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Determining the optimal threshold value for image segmentation has become more attention in recent years because of its varied uses. Otsu-based thresholding methods, minimum cross entropy, and Kapur entropy are efficient for solving bi-level thresholding image segmentation problems (BL-ISP), but not with multi-level thresholding image segmentation problems (ML-ISP). The main problem is exponentially increasing computational complexity. This study uses the memory-based Gray Wolf Optimizer (mGWO) to determine the optimal threshold value for solving ML-ISP on RGB images. The mGWO method is a variant of the standard grey wolf optimizer (GWO) that utilizes the best track record of each individual grey wolf for the global exploration and local exploitation phases of the problem solution space. The solution candidates are represented by each grey wolf using the image intensity values and optimized according to mGWO characteristics. Three objective functions, namely the Otsu method, Kapur Entropy, and M.Masi Entropy are used to evaluate the solutions generated in the optimization process. The GridSearch method is used to determine the optimal parameter combination of each method based on 10 training images. Evaluation of the performance of the mGWO method was measured using several benchmark images and compared with five standard swarm intelligence (SI) methods as benchmarks. Analysis of the results was carried out qualitatively and quantitatively based on the average PSNR, RMSE, SSIM, UQI, fitness value, and CPU processing time from 30 tests. The results were analyzed further with the Wilcoxon signed-rank test. The experimental results show that the performance of the mGWO method outperforms the benchmark method in most experiments and metrics. The mGWO variant also proved to be superior to the standard GWO in resolving multi-level color image segmentation problems. The mGWO performance results are also compared with other state-of-the-art SI methods in solving ML-ISP on grayscale images and was able to outperform those methods in most experiments when combined with the Otsu method and Kapur Entropy.

The main objective of the thresholding method is to determine the optimal threshold value so that it can divide the image into several regions based on the pixel intensity value of an image. Thresholding methods can be divided into two based on the number of values taken from the histogram of an image, namely bi-level thresholding and multilevel thresholding [3], [6], [18]. When the selected threshold value is one, it is known as bi-level thresholding, whereas when more than one threshold value is selected, it is known as multilevel thresholding [6].
The non-parametric approach to the thresholding method which uses certain criteria to obtain the optimum threshold value has been proven to be better for solving BL-ISP [6]. Otsu's between class variance, minimum cross entropy, Kapur entropy are some of the criteria commonly used to complete BL-ISP [3], [6], [13]. Although these criteria have proven to be very efficient in solving BL-ISP on grayscale images, this approach has proven to be inefficient [20] and impractical [3] to be used to solve ML-ISP. Computational complexity will increase exponentially [7], [14], [15], [20] as the number of specified thresholds increases [3], [4], [6], [7], [14], [15] and performance levels tend to decrease [6]. This is because all possible threshold value pairs must be tried thoroughly in order to meet the specified criteria. Therefore, determining the optimal threshold value at ML-ISP in a short time is a challenge [7].
Determining the optimal threshold value for ML-ISP is included in the NP-hard combinatorial optimization problem [6], [7], [13], [18] and has been a challenge in the last few decades [7], [18]. Several approaches have been proposed to solve this problem, including using an SI-based metaheuristic optimization algorithm. The metaheuristic algorithm is proven to be more efficient in finding the optimal threshold value for solving ML-ISP when compared to exhaustive search [3], [6], [13], [15]. SI-based metaheuristic algorithms have been widely used to reduce computational complexity and have proven to be more accurate in solving ML-ISP when compared to evolutionary algorithms [3].
Problems arise when there is no one optimization method that can provide the same solution for all optimization problems referring to the No Free Lunch (NFL) theory [7]. Several previous studies that utilized the SI method to solve ML-ISP [3], [4], [6]- [9], [15], [20], [21] only tested the method they proposed using one function. just be objective. In fact, it is important to test the robustness and consistency of the performance of the proposed method against different objective functions. Thus, it can be guaranteed that the performance of the proposed SI method is stable against several objective functions used [7].
In addition, many studies that apply the SI method to solve ML-ISP only focus on grayscale images as their test images [2], [3], [6]- [9], [14], [15], [17], [18], [20], [21]. In fact, color images can provide a better description of an image than grayscale images [13]. Research related to the completion of ML-ISP using SI on color images is very little found [4], [13]. Ma dan Yue (2022) [4] have implemented a variant of WOA to solve ML-ISP on color images. However, this study did not explain in detail the steps to complete ML-ISP on color images with the proposed WOA variant. The explanation given in this study is only based on grayscale images using the Otsu method. Borjigin dan Sahoo (2019) [13] have implemented PSO with the objective function Tsallis-Havrda-Charv́t Entropy to solve ML-ISP on color images.
Borjigin and Sahoo's research [13] has inspired this study to adapt ML-ISP solutions to color images using mGWO [21] and GWO [22] as well as three different objective functions to measure the performance stability of the two methods for solving ML-ISP. The SI method that has been applied in previous studies to solve ML-ISP still has some drawbacks, such as early convergence, stuck at local optimum values, and low convergence speed [4], [6], [20]. Therefore, images with good segmentation cannot be obtained with the threshold values obtained [8].
mGWO and GWO are used as proposals in this study because they can balance the exploration and exploitation in solving optimization problems, so as to avoid local optimum values [7]. In addition, GWO can reduce computation time greatly when compared to other optimization methods [14]. In fact, mGWO [21] has been proven to be able to solve global optimization problems better in terms of search efficiency, solution accuracy, and convergence rate when compared to standard GWO [22].
The discussion that has been described in the previous section has motivated this research to take place. This study utilizes the GWO [22] and mGWO [21] methods to solve ML-ISP on RGB color images. Three different objective functions, namely the Otsu method, Kapur Entropy and M.Masi Entropy are used in the evaluation to see the performance stability of the two methods compared to the four SI methods as benchmarks, namely genetic algorithm (GA), particle swarm optimization (PSO), whale optimization algorithm (WOA), and slime mold algorithm (SMA).
GA is implemented because it can substantially reduce computational costs in solving ML-ISP [14]. WOA is used because it is proven to be able to provide the best results in terms of exploration capabilities [8], [18]. In addition, this method has fewer parameter configurations with a simple framework and can avoid local optimum values [18]. SMA is used because it has been proven to be significantly successful in solving optimization problems in the continuous domain when compared to other algorithms [8], [23]. PSO is implemented because it has global optimization capabilities [1], is simple [13] and can achieve convergence in a relatively short time [3], [13].
The main contributions of this research are as follows: (1) This study proposes ML-ISP solutions for RGB color images in the mGWO and GWO frameworks besides using grayscale images.
(2) Three different objective functions namely the Otsu Method, Kapur Entropy, and M.Masi Entropy were tested on mGWO and GWO to measure the stability of their performance on ML-ISP (3) The performance of the method implemented in this study was measured using qualitative and quantitative analysis using benchmark images from the USC-SIPI image database. Qualitative analysis was carried out by segmenting the six test images with each optimal threshold for each level. Quantitative analysis was carried out by calculating the fitness, RMSE, PSNR, SSIM, UQI, and CPU time values of each objective function.
(4) Hyperparameter tuning based on GridSearch is performed to obtain the optimal parameter combination of each SI method involved with the aim of maximizing the Otsu method. (5) Statistical analysis using the Wilcoxon signed-rank test was used to test the significance of differences in the quantitative measurements of the GWO and mGWO methods against the benchmark method assigned to the test images. (6) Comparing the results of the mGWO and GWO performance tests on grayscale images with other state-of-the-art methods in terms of fitness values and CPU Time (seconds). with , , each represents the red, green, and blue components (channels) of an image whose combinations can generate any displayable color [13]. Therefore, an RGB color image is a 3D array of color pixels with size × × 3 [13]. notation is used to show any channel (RGB or grayscale) of an i-th image.

MULTILEVEL THRESHOLDING FOR COLOR IMAGE SEGMENTATION
Suppose is the total number of pixels in with is the number of occurrences of the jth gray level. Normalized histogram of is a probability distribution of each ∈ . The probability that the jth gray level occurs at is defined according to Equation is the gray level of the pixels in the ( , ) coordinates from a 2D image .
which is calculated using Equation 5.
value is the average pixel intensity value in the ( ) region which is calculated using Equation 6. value is the average pixel intensity value in which is calculated using Equation 7.

MATERIAL AND METHODS
This section describes the steps taken to answer the research objectives along with the dataset used in this study as shown in Figure 1.

Benchmark Images
This study uses a standard benchmark dataset from the USC-SIPI image database and Berkeley BSDS 300. There are 10 images as training data and 6 images as test data. The training data is a combination of several image files selected from the train and test folders on the Berkeley BSDS 300 source. These files were chosen because they have multimodal histogram characteristics so that the optimal hyperparameters of each model can be selected objectively. The training data is used for the SI model development process for ML-ISP including the hyperparameter tuning process for each model. The test data that is used in this study are Airplane F16, Lena, Man, Mandrill (baboon), Peppers, and Sailboat on lake. The test data is used to evaluate the performance of the method used. Table 1 displays the names of the image files used as training data, while Figure 2 shows the pixel intensity histogram of the test data.

Grey Wolf Optimizer (GWO)
GWO is a method proposed by Mirjaili et al (2014) [22]. The GWO optimization method is inspired by social intelligence in hunting prey and the social hierarchy of the gray wolf (Canis lupus) [14], [22], [24]. Gray wolves live in groups with 5 -12 wolves in each group [14]. There are four levels or hierarchies in one group, namely alpha ( ), betha ( ), delta ( ), and omega ( ) wolves. Alpha wolves are the highest level in this group whose job is to make decisions about hunting, where to sleep, when to wake up and so on. This wolf dominates the pack. The beta wolf is the second level after the alpha whose job is to help the alpha wolf make decisions and other group activities. The deltha wolf is the third level after betha whose duties are scout, caretaker, hunter, guard and scout. The omega wolf is the lowest level of this group which must submit to orders from all other dominant wolves [24].

Social hierarchy on GWO
The social hierarchy in a pack of gray wolves is divided into , , , and wolves. In the mathematical modeling of the GWO method, the , , and wolves each represent the first, second and third best solutions [24]. The optimization process in this method is guided by the solutions produced by the three wolves, while the remaining wolves follow them [14].

Encircling of prey in GWO
During the hunt for prey, the gray wolves surround their prey. This prey encirclement process is modeled mathematically according to Equations 13 and 14. The t-th iteration is expressed by the value ( ). The values of and are calculated using Equations 15 and 16, respectively.

Hunting process in GWO
The , , and wolves guide the hunting process of all wolves in a group. These three wolves are assumed to have better knowledge of the potential location of a prey (optimal solution). Hence all the other wolves updated their positions based on the information on the three wolves. The mathematical model for the prey hunting process is according to Attacking the prey (exploitation) in GWO Vector and vector in the above equation are used to store the exploration and exploitation abilities of wolves [21]. The process of hunting prey from wolves is completed by attacking prey by wolves. This process is modeled by reducing the value of the vector in the range 2 to 0 during the iteration process. The fluctuation range of will decrease if is also decrease. When | ( ) ⃗⃗⃗⃗⃗⃗⃗ | < 1 and/or | ( ) ⃗⃗⃗⃗⃗⃗⃗ | <

GWO for solving ML-ISP
The GWO algorithm is used in this study to find the optimal threshold value (represented by the position of the wolf) at the mth level so that it can be used to segment images with a maximum of + 1 regions. One wolf in GWO represents a solution for which you want to find the optimal value. The input of this process is the histogram of the image to be segmented, while the output of this process is the optimal position vector of the wolf as * which represents the optimal threshold value.
The positional vector representation of each i-th wolf is written as ⃗⃗⃗ which is initialized according to Equation 22. The total number of wolves initialized is written as N. The value

GWO Pseudocode for solving ML-ISP
Pseudocode of the GWO Algorithm to solve ML-ISP is presented as in Figure 3.   wolves [21]. The wolf pack will find it difficult to get out of the optimum locale when the three wolves are trapped in the optimum locale because they only depend on them [21]. Therefore, Gupta and Deep (2020) [21] proposed an update process of ( ) ⃗⃗⃗⃗⃗⃗⃗ integrating the best track record of each wolf with the positions of the three lead wolves. It aims with the intention of involving the best knowledge of each wolf in the process of exploring the solution space to guide the wolf pack to explore or move into a promising solution space and not get stuck at local optimum values [21].

Memory-based
All the symbols in this section are the same as those in the previous section. In mGWO, the encircling prey process is updated using Equation 23 [21]. Vector

Figure 4. mGWO pseudocode for ML-ISP
Algorithm 3: Segmenting process of using optimal threshold Input: 2D pixels array of image , optimal threshold T Output: segmented image Initialization: row ← row shape of col ← col shape of regionThres ← dictionary() flatCi ← convert 2D of into 1D array // Get lower and upper bound for each threshold boundaries ← reshape flatCi to row and col dimension Return The value is the scale factor used to adjust the effect of subtracting the two position vectors. The value of decreases linearly from 1 to 0 in each iteration which is updated using Equation 26. The crossover process is then carried out in the update stage ( +1) ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ . The process combines information from the three best wolves with each individual wolf according to Equation 27. The crossover probability value is written as CR and random numbers in the range 0 to 1 with a uniform distribution are written as .

mGWO pseudocode for solving ML-ISP
Pseudocode of the mGWO Algorithm to solve ML-ISP is presented as in Figure 4.

Segmentation with Optimal Threshold
Each channel in the test image is then segmented using the optimal threshold value that has been obtained from the SI method-based optimization process. The pseudocode in Figure 5 is used to divide the image into + 1 regions using optimal { 1 , 2 , … , }. The image that has been segmented with the optimal threshold is denoted as for RGB color images and for grayscale images.
is obtained by combining the segmentation results from , , and . Assume thresholding levels for each channel r, g, and b in the RGB image, namely , , and . The SI method is implemented to obtain the optimal threshold value for each channel. Each optimal threshold value is used to segment each channel using the pseudocode in Figure 5. The segmented image for each channel is denoted as , , and such that: Therefore, has the most × × color levels and fewer than [13].

EXPERIMENTS
Experiments in this study were conducted to measure the performance stability of the GWO and mGWO methods to solve ML-ISP using three different objective functions, namely the Otsu method, Kapur Entropy, and M.Masi Entropy. As a comparison, another standard IS optimization method is involved, namely the Genetic Algorithm (GA) [ All methods are programmed and evaluated using the Python3.10 programming language which is implemented in the device environment Windows 10 -64 bit, Intel Core i7-8565U CPU @1.80GHz and 8GB of RAM.

GridSearch Hyperparameter Tuning
The hyperparameter tuning process was carried out to obtain the optimal parameter combination for each method (as shown in Table 2) used in this study. It aims to obtain a fair comparison of performance metrics for each method at the evaluation stage. This study uses the GridSearch scheme for the hyperparameter tuning process. The GridSearch method looks for all possible combinations of each hyperparameter value and then gets the parameter combination that gives the most optimal results based on the predefined metrics.

ISSN 2089-8673 (Print) | ISSN 2548-4265 (Online)
Volume 12, Issue 2, July 2023 Several criteria are set the same in this process to get the optimal combination of parameters from each method used. The metric used is the average fitness value of all training data. The number of thresholds used is 5. The objective function used is the Otsu method.

Evaluation Metrics
Qualitative and quantitative evaluation was carried out on each segmented image. Qualitative measurement is done by visualizing / for each threshold level used and comparing it with the visualization of the original / image. Meanwhile, quantitative measurements are carried out using six metrics, namely peak signal to noise ratio (PSNR), root mean square error (RMSE), structured similarity index metrix (SSIM), universal quality index (UQI), fitness value and CPU processing time. (in seconds).

PSNR
PSNR measures the ratio between the maximum squared gray level and the mean square error (MSE) value. PSNR basically calculates the difference between and using the pixel intensity value of an image [18]. The PSNR is calculated using Equation 28 with the MSE value calculated using Equation 29. The gray level pixels at coordinates ( , ) of the segmented image are represented by ( , ) , while those of the original image are represented by ( , ) . ( 28 )

RMSE
RMSE measures the square root of MSE. The RMSE value is calculated using Equation 30.
The structure of the images that are compared between and cannot be measured using only PSNR. PSNR only measures the comparison of errors between two images [8]. SSIM is used to measure the similarity, distortion, and brightness between the two images. SSIM is calculated using Equation

UQI
UQI is similar to the SSIM measurement which measures the quality of based on structural similarities between and . UQI is measured by Equation 32.

Fitness values
The fitness value is used to measure the performance of the method used against the objective function used. The Otsu method, Kapur Entropy, and M.Masi Entropy are each used to measure the fitness value of each method, each of which is calculated using Equations 3, 8 and 10.

CPU Processing Time
CPU processing time is measured to measure the efficiency of the optimization process time of each method for the results it obtains. To get fair results, calculating CPU processing time starts from the moment the method starts optimizing the optimal threshold value until it gets it, without measuring other computational processes involved (such as variable declarations, value initialization, and so on).

RESULT AND DISCUSSION
This section presents the results of the GWO and mGWO for solving ML-ISP using the Otsu, Kapur Entropy, and M.Masi Entropy methods as objective functions. These results were analyzed from the qualitative and quantitative aspects. The average value of each quantitative metric used is calculated from a total of 30 experiments conducted for each method. The results shown in this section are obtained from testing on RGB images. However, this study also tested grayscale images to obtain comparable results with state-of-the-art methods for solving IS-based ML-ISP from previous studies.

Parameter Setting
This section presents the results of the GWO and mGWO for solving ML-ISP using the Otsu, Kapur Entropy, and M.Masi Entropy methods as objective functions. These results were analyzed from the qualitative and quantitative aspects. The average value of each quantitative metric used is calculated from a total of 30 experiments conducted for each method. The results shown in this section are obtained from testing on RGB images. However, this study also tested grayscale images to obtain comparable results with state-of-the-art methods for solving IS-based ML-ISP from previous studies.

Quantitative Analysis Results
This section describes the performance results of the GWO and mGWO methods to solve ML-ISP with the Otsu, Kapur Entropy, and M.Masi Entropy method objective functions. All methods were tested on RGB and grayscale images. The measurement results displayed in this section are only for RGB image format, while the measurement results displayed for grayscale images are only the average value of fitness and CPU Time as a comparison with other state-of-the-art methods.
The sum of the best performance for each method from 24 total experiments for each metric is summarized in Figure 6. Based on Figure 6 the majority of mGWO outperformed the performance of other methods in almost all metrics. In fact, even the standard GWO method was able to obtain the best performance after mGWO. This shows that the GWO method and its variant, mGWO, are stable when tested with different objective functions.
The interesting thing is that the performance of the GWO method can be matched or even surpassed by the PSO method. For example, based on Figure 6, PSO can offset GWO in terms of SSIM when using the Otsu method. When using Kapur Entropy, PSO was able to outperform GWO in terms of PSNR, RMSE, SSIM and UQI. When using M.Masi Entropy, PSO outperforms GWO in terms of PSNR, RMSE, and SSIM.
The results of testing the average fitness value of mGWO and GWO on grayscale images as shown in Table 12 also show the same thing as testing RGB images. The mGWO and GWO methods got 14 and 6 best results respectively from a total of 24 experiments. PSO cannot match the performance of the two methods because it only gets the 4 best results. In fact, mGWO was able to outperform the other methods in terms of CPU processing time for most experiments when using the Otsu method as the objective function, as shown in Table 13.
Experimental results on RGB and grayscale images show that the mGWO and GWO methods are able to solve intensity-based ML-ISP well. The advantage of solving ML-ISP on RGB or grayscale images using the GWO method is that it is simple and easy to implement [14] compared to a thorough search using only the Otsu, Kapur Entropy, or M.Masi Entropy methods. However, the mGWO method provides more accurate performance than the standard GWO [21]. This is because mGWO is able to increase the global exploration phase, local exploitation, and balance the two during the search for prey [21], so as to avoid local optimum values [7]. In addition, the existence of a new prey hunting mechanism in mGWO can have an impact on wolf packs to explore new areas that are more promising for solutions [21].
The GWO method can produce higher quality solutions when compared to other SI benchmark methods [7]. GWO can balance the exploration and exploitation phases so that it can find better solutions [14]. Parameter configuration of other SI benchmark methods which are relatively more than GWO can cause these methods to get stuck at local optimum when solving problems with high dimensional solution spaces, such as PSO. [14]. The success of finding solutions from GWO is heavily influenced by the , , and wolves [14].
In standard GWO, the prey hunting phase is only guided by the best three wolves, namely , , and wolves. These three wolves might get stuck at local optimum values when the optimization problems being solved are multimodal [21]. It will be difficult for a pack of wolves to get out of the local optimum when the process of hunting for prey depends only on the three best wolves. In mGWO, this problem is solved by utilizing the best track record of each individual gray wolf during the prey hunting phase. This allows for a collaborative information exchange mechanism between each individual and the wolf pack so that the search for optimal solutions can take place efficiently [21]. The best track record of knowledge from each individual wolf is used as a guide besides using the three best wolves to get a more promising solution space and to maintain balance between exploitation and exploration [21]. This is in accordance with the results in this study.
The process of updating solutions by being guided by the best solutions and utilizing the best track record of each individual has proven to perform better in solving ML-ISP on RGB and grayscale images. This is shown through the results of this study and is summarized in Figure 6. The GWO method utilizes solutions from , , and wolves in each iteration in the process of updating the wolf's position in hunting the prey [22]. The PSO method utilizes the best track record of each particle and utilizes the best global position of a set of particles in updating the position and velocity vectors of each particle. The mGWO method updates the wolf's position by combining the GWO and PSO mechanisms. The , , and wolves and the track record of each wolf are used to guide the solution update process on mGWO. The three methods, mGWO, GWO, and PSO, are the three methods that performed best in this study compared to other methods.

Qualitative Analysis Results
This section presents a qualitative analysis. Figure 1 -Figure 4 in supplementary fsiles displays the segmented RGB images of each method for the number of thresholds, namely 2, 3, 4, and 5. We also record the optimal threshold values obtained from each method for the three channels on the the images as a supplementary file. To make comprehensive comparisons, the proposed method is also analyzed qualitatively on the grayscale test images and their graylevel histograms. The results displayed are only the results of grayscale image segmentation at level 3, as shown in Figure 5 and its best threshold in Figure 6.
The visualization results of the segmented images shown show that the optimal threshold values generated by the SI method based on the Otsu, Kapur Entropy, and M.Masi Entropy methods are able to properly separate several classes in the RGB and grayscale test images. The results of 3-level grayscale image segmentation on C6 can show important components that should be in C6 images, such as the sky, trees, sailboats, lakes, parks, and shaped clouds. These components can be segmented properly with optimal threshold values obtained from the SI-based optimization method. The results of the segmentation also do not overlap between components. The results of the 3-level RGB image segmentation as shown in Figure 2 (in supplementary files) show that the objective function with Kapur Entropy can produce segmented images that are relatively brighter and not blurry when compared to the Otsu method. This can be seen in the RGB C2 -C6 image results which have been segmented.

Wilcoxon Signed Rank Test Results
The Wilcoxon signed-rank test was performed as a statistical analysis at the 5% significance level. The fitness and PSNR values generated by the objective function of the Otsu method, Kapur Entropy, and M.Masi Entropy of each method are compared to one another. Each method was run 30 times for this analysis. The null hypothesis (H 0 ) and the alternative hypothesis (H a ) used are as follows [6], [14]. H 0 : The difference between sample pairs is not significant H a : The difference between pairs of samples is significant If the p-values are less than 0.05 (H a ), then the null hypothesis can be rejected at the 5% significance level. Conversely, if the p-values are more than 0.05 (H 0 ), then the null hypothesis is accepted [14].
We calculate p-values using the Wilcoxon signed-rank test on the fitness and PSNR value metrics between the mGWO method and the comparison method to solve the multi-level color image segmentation problem. The results are presented as a supplementary file. The p-values of mGWO which show better results than other methods are marked with a sign (*). Based on those results, when combined with the Otsu method, mGWO obtained significantly better results than SMA, WOA, GA, PSO, and GWO of 24, 23, 22, 13, and 0 respectively out of a total of 24 experiments. When combined with Kapur Entropy, mGWO obtained significantly better results than SMA, WOA, GA, PSO, and GWO by 23, 16, 18, 13, and 3 respectively out of a total of 24 experiments. When combined with M.Masi Entropy, mGWO obtained significantly better results than SMA, WOA, GA, PSO, and GWO of 23, 22, 24, 12, and 2 respectively out of a total of 24 experiments. Although the performance of mGWO is better than GWO, in most statistics it does not show a significant difference. The first comparison was made by comparing the performance of the SI method in terms of objective function values when using the Otsu method. The proposed mGWO method was able to give the best results for 12 out of a total of 24 experiments. This result outperforms the results given by the GWO [14] and KHO [15] by 3 and 9 out of a total 24 experiments, respectively. Furthermore, the mGWO method was able to outperform all test cases at various levels when compared to WOA and MFO [18]. The mGWO method is also proven to provide better performance when compared to GWO [14] in the majority of test cases. Some methods like KHO [15], WOA, MFO [18], and GWO [14] does not report the research results at several threshold levels from the same test image. The performance of these methods has not been tested for solving ML-ISP on RGB images.

Comparison with other state-of-the-art algorithms
The second comparison was made by comparing the performance of the SI method in terms of objective function values when using Kapur Entropy. In contrast to the results of the Otsu method, the KHO method [15] did not perform better when compared to the mGWO method in this study. The mGWO and GWO methods [14] respectively gave the best results in 17 and 4 out of 24 experiments. This also shows that the mGWO method is also proven to provide better performance when compared to GWO [14].  GWO [14] is relatively faster when compared to mGWO because in mGWO there are several additional processes that were not previously available in standard GWO [14], [22]. Some of them, namely the process of initializing the matrix to store the best track record, the process of updating the track record of each individual wolf, the process of updating the best fitness value of each grey wolf individu in each iteration and the crossover process in hunting prey [21]. This causes the computational time of the mGWO to increase when compared to the standard GWO [14], [22].

CONCLUSION
Determining the optimal threshold value for solving color ML-ISP can be viewed as an optimization problem using the Otsu, Kapur Entropy, and M.Masi Entropy methods as objective functions. Therefore, the SI method, namely mGWO as a variant of GWO, is proposed to solve this problem. The objective of this method is to determine the optimal threshold value for each channel by maximizing the specified objective function. This study compared the experimental results of mGWO against the PSO, GA, WOA, and SMA methods using six metrics, namely PSNR, RMSE, SSIM, UQI, fitness value, and CPU time (seconds).
The experimental results show that the performance of the majority of mGWO and GWO is superior to other methods in almost all metrics, but the mGWO method is still better than GWO. In addition, mGWO performance is stable when tested with different objective functions. In fact, the results of a comparison of the mGWO method against state-of-the-art WOA and MFO to solve ML-ISP on grayscale images show the best performance of a total of 24 experiments. The increase in the global exploration and local exploitation phases of mGWO can help find a better optimal threshold value for solving color ML-ISP. Statistical testing using the Wilcoxon signed-rank test showed that mGWO gave a significant difference in results compared to other methods in most experiments.
The next research will examine the performance of mGWO to solve color ML-ISP with the multi-objective optimization problem paradigm. In addition, a dynamic approach in determining the optimal number of threshold levels for color ML-ISP will be designed and implemented to obtain better segmentation results.          1929.065 1897.497 1909.297 1936.467 1828.987 1936.467 5 1954.269 1924.743 1948.911 1964.592       (a) Figure 6. Sum of the best performance (out of a total of 24 experiments) of each method on each metric to measure performance stability when tested using different objective functions named (