An Efficient Adaptive Salp Swarm Algorithm Using Type II Fuzzy Entropy for Multilevel Thresholding Image Segmentation

Salp swarm algorithm (SSA) is an innovative contribution to smart swarm algorithms and has shown its utility in a wide range of research domains. While it is an efficient algorithm, it is noted that SSA suffers from several issues, including weak exploitation, convergence, and unstable exploitation and exploration. To overcome these, an improved SSA called as adaptive salp swarm algorithm (ASSA) was proposed. Thresholding is among the most effective image segmentation methods in which the objective function is described in relation of threshold values and their position in the histogram. Only if one threshold is assumed, a segmented image of two groups is obtained. But on other side, several groups in the output image are generated with multilevel thresholds. The methods proposed by authors previously were traditional measures to identify objective functions. However, the basic challenge with thresholding methods is defining the threshold numbers that the individual must choose. In this paper, ASSA, along with type II fuzzy entropy, is proposed. The technique presented is examined in context with multilevel image thresholding, specifically with ASSA. For this reason, the proposed method is tested using various images simultaneously with histograms. For evaluating the performance efficiency of the proposed method, the results are compared, and robustness is tested with the efficiency of the proposed method to multilevel segmentation of image; numerous images are utilized arbitrarily from datasets.

Segmentation is aimed at distinguishing several essential parts that define objects. Segmentation, a challenging step in image processing, plays a key role in detecting objects and pattern recognition [11]. It is necessary to develop an image segmentation algorithm that does not require human intervention and minimal computational resources. The solution to the problem previously proposed relies on C and K-means clustering algorithms [12,13]. But the cluster number computation was its key drawback, along with the fact that the system's computing complexity increased exponentially.
Furthermore, histogram-based thresholding has provided the solution to the image segmentation, where the number of thresholds ðthÞ and histograms would be used together with objective function. The two broadly employed objective functions proposed presently are the Kapur criteria for entropy [14] and Otsu class variance [15]. The abovestated methods are useful but also increase the computational cost when used with multilevel thresholding. Various methods of optimization have been used by researchers from a while to solve this problem.
Some drawbacks of Kanpur entropy were overcome in firefly optimization algorithm (FOA) This approach recreates the behavior of fireflies and bioluminescent interaction processes in nature [5]. Horng also proposed the use of honey bee mating optimization (HBO) in multilevel image thresholds with Kapur's entropy (KE) [16]. The problem of class variance function and the optimization of the entropy criterion in multilevel thresholding was overcome by the bacterial foraging algorithm (BFA) [17,18] and harmony search optimization system (HSO) [19], but Tuba and Brajevic preferred the use of FOA [11] and cuckoo search (CS) [6]. The CS system and Kapur entropy segmentation of satellite images were used. Otsu's approach was tested with the firefly algorithm (FA) [20] for multilevel image thresholds. Tuba and Alihodzic [21] used a bat algorithm (BA) with Otsu and Kapur in multilevel image thresholds. Effective results were obtained when the Tsallis, Kapur, and Otsu methods were optimized using the modified artificial bee colony system for multilevel thresholding images [21]. Subsequently, multilevel picture thresholding was used for the gray wolf optimization process (GWO); an objective function was dependent on Otsu's class variance method [22] and Kapur's entropy. Animal migration optimization (AMA) and social spider (SSA) algorithm were used to optimize class variance for thresholding multilevel images using Otsu class variance methods and Kapur entropy [23,24]. Interdependence has been reduced using an adaptive balance optimizer (AEO) with a multilevel threshold [25]. Additional segmentation of images was carried out using the exchange market optimization (EMO) approach with a minimum crossentropy threshold [26]. Elaziz et al. [27] used a hyperheuristic approach to threshold multilevel images by optimizing class variance to address the drawback of a metaheuristic method. While optimization approaches used so far have been effective with the user-defined threshold value, we have not achieved a completely programmed segmentation method.
When multilevel thresholding, a separate method is used along with peak detection, which relies on the information in the histogram, so the objective function where the cluster center is the peak value of the histogram and the valley is the upper and lower limit of the cluster determined by the intensity level of the histogram, it can be said that the pixel intensity between successive valleys is taken as a cluster in the picture [28,29]. Methods for detecting peaks in the histogram were proposed by Tsai, where Gaussian kernel smoothing was used to eliminate variable peaks and valleys [30], which are the best methods for finding two peaks not fail to detect more than two peaks in the image.
In this article, a novel technique of ASSA along with thresholding methods is proposed for image segmentation, which is an area of research with high accuracy in segmentation. It is practically validated by testing the accuracy of outputs and computational time taken by many other existing, state-of-the-art algorithms like GA [2], PSO [8], FPA [5], BA [6,7], CS [9], DE [1], and MPA [10].
The main contributions of this paper are as follows: (1) The use of ASSA for optimum multilevel thresholding with TII-FE: experiment results indicate that ASSA produces better results than PFA-, DE-, PPA-, PSO-, MPA-, and HPFPPA-D-dependent techniques (2) The computation of multilevel thresholding is significantly reduced by using ASSA-based TII-FE The paper is planned as follows: a detailed introduction of thresholding in multilevel images is discussed in Section 2. The fundamentals of ASSA are described in Section 3. Results are detailed in Section 4. At last, in Section 5, the conclusion and future scope of the work is discussed.

Thresholding in Multilevel Images
Optimal thresholding techniques [11] are employed in image processing to determine thresholds, so the clusters formed on histograms follow the target objectives. The probability of i th the gray level is where the range of gray level is f0, 1, 2, 3, 4, 5 ⋯ ⋯ ⋯ ⋯ ⋯ :L − 1g, M × N is the image dimension, and h i is the no. of pixels with gray level i, 0 ≤ i ≤ ðL − 1Þ.
Let m be the no. of thresholds present; then, t 1 , t 2 , t 3 , t 4 , ⋯ ⋯ ⋯ ::t m and if we break it in m classes, then Optimal thresholds are achieved by increasing the objective function that is based on specified parameters of thresholds. The most widely applied optimum thresholding techniques are Otsu's and Kapur's methods [14,15]. The objective function in bilevel thresholding is selected as per Kapur's approach: Computational and Mathematical Methods in Medicine H 0 &H 1 are partial entropies of histogram. t 1 is the gray level, which increases objective function in Equation (3). Now, by Otsu's method, it is defined where Therefore, ω 0 μ 0 + ω 1 μ 1 = μ T and ω 0 + ω 1 = 1 and μ T is the mean intensity.
Thresholding for multilevel images can be increased by Kapur's entropy; m-dimensional optimization problem is optimal [11] in which m-optimal thresholds (t 1 , t 2 , t 3 , t 4 , ⋯ ⋯ ⋯ ::t m ) are examined by increasing objective function: where : Now, by Otsu's method as in Equation (5), it is defined : : The value of thresholds is t 1 < t 2 < t 3 < t 4 , ⋯ ⋯ ⋯ < t m in both methods.

Multilevel
Thresholding with Fuzzy Type II Sets. The segmentation obtained by multilevel thresholding methods works by grouping pixels based on intensity values to facilitate image analysis. The segmentation criteria can be divided 3 Computational and Mathematical Methods in Medicine into two types: parametric and nonparametric. In comparison to nonparametric parameters, metric methodologies are considered to produce more computational weight. As a result, nonparametric techniques are often preferred due to their intensity and simplicity, maximum entropy, and the most well-known between-class variance.
Researchers paid close attention to entropy-based data utilized to separate the image's histogram. To start with, the data hypothesis allowed us to apply Shannon's entropy to the thresholding problem [31]. Regarding this trend, several different methodologies, such as Tsallis entropy [32], Renyi's entropy [33], cross-entropy [34], and finally a fuzzy entropy-based approximation [35], were suggested. Segments are used to remove artifacts from images.
Moreover, when many edges are used, most entropybased criteria will suffer from the negative effects of high complexity. Tao et al. [36] introduced a fuzzy entropybased method to improve Zhao's [37] work. An image is thresholded using histogram segments with specified fuzzy membership values; these segments are used to eliminate objects in an image.
2.1.1. Different Fuzzy Type II Sets. Type I fuzzy, with finite set X = ðx 1 , x 2 , ⋯ ⋯ , x n Þ, is defined in where μ A is the membership function.  Here, NP is the population size, D is the dimension of problem, G max is the number of iteration, N max is the maximum number of runners, σ is the standard deviation, bp is the breeders' probability, and PR are different threshold levels.  Figure 1:

Image Segmentation with Fuzzy Type II.
Thresholding is the simplest method for segmenting an image. Thresholding is as simple as using a threshold ðthÞ value and adding it to a histogram until an optimal condition is reached. Equation (12) describes the thresholding method using a histogram.
where I s ðr, cÞ is the segmented image with gray value, I Gr ðr, cÞ is the original image with gray value, and ðr, cÞ is the position of pixels.

Adaptive Salp Swarm Algorithm
3.1. Salp Swarm Algorithm. The SSA method is SI inspired by navigation and foraging activity of salps present in oceans [38]. Body configuration of salps is very closely linked to jellyfish present in oceans and practices the same technique to step forth and pump water across their bodies. SSA is ultimately inspired by the swarming action of the salps under which the swarm of the salps produces a chain of salps. The leader salp is present in front, and the rest who follow the leader are known as followers. The position of salps in search space is determined by the presence of food source S and leader's position by where Y i j is the leader/first salp, S j is the food source at j th dimensions, ub j and lb j are the upper and lower boundary, Balance between exploitation and exploration is maintained by c 1 coefficient parameter, as shown in where i is the current iteration, I is the no. of iterations, and c 2 and c 3 are uniformly distributed random value coefficients in ½0, 1. The next position in j th dimension is determined by utilizing these positions when moving in +ve&−ve∞: Now, followers' updated position is shown in where k ≥ 2 and Y k j is the k th follower position in the j th dimension.
If we put v 0 = 0 in Equation (15), then where k ≥ 2 and Y k j is the k th salp follower in the j th dimension search area.
Some main disadvantages of SSA [39] are as follows: (1) The computational cost of the method increases due to usage of only one parameter of optimization.
Although it is said that only parameter c 1 is needed for optimum function, but there are 3 parameters c 1 , c 2 , and c 3 present and defined (2) It has weak convergence and local optimization problems that need to be modified to increase efficiency and decrease computational cost (3) SSA should be adaptive to reduce the user depend parameter initialization and make it more effective and self-adaptive 3.2. Adaptive Salp Swarm Algorithm. To overcome the above-stated drawbacks of SSA, an ASSA was proposed. Some major changes done to overcome drawbacks of SSA [38,39] are as follows:  c n a n c n a n c n a n c n a n c n a n c n   Im PR ASSA HPFPPA-D PSO PFA DE PPA a n c n a n c n a n c n a n c n a n c n a n c n The initialization of the algorithm starts in a fixed range and is presented in mathematical form as where x i,j is the i th solution for the j th dimension.
x max,j and x min,j are the upper and lower limits. Uð0, 1Þ is the uniform rand. no. in ½0, 1. Position in ASSA is updated by modifying exploitation and exploration function of SSA, and it overall increases the performance and is presented as Á , where x new is the new solution, A 1 , A 2 , A 3 and C 1 , C 2 , C 3 are derived from A = 2a · r 1 − a and C2 · r 2 , α and LðλÞ are uniformly and Levy distributed rand. no., and r 1 and r 2 are rand. no. distribution in ½0, 1.    Computational and Mathematical Methods in Medicine Step size dependent on Levy flight is where s = ðU/ðjVj 1 /λÞÞ U~Nð0, σ 2 Þ.
N is derived from Gaussian distribution with variance = σ 2 and mean = 0.
Basic functions of SSA and ASSA are shown in Table 1. In the selection step, greedy selection (GS) is executed to find the proposed solution optimum or not compared with already proposed methods. For a minimization method with fitness Fðx t i Þ with x t i , the solution is mathematically denoted as In controlling parameter balance b/w exploitation and exploration is improved by changing c 1 in SSA to LD, which is useful in shifting it towards the exploitation stage. In this range, upper and lower c max &c min is ½0:95 0:05 represented as where c is the weight of inertia, a is the rand. no. in ½0, 1, and t and t max are present and max. no. of iterations.
In population adaptation, the total no. of evaluation functions is reduced by reducing population size. It reduces computational complexity burden and is represented as where FEs is the max. no. of iterations and n min − n max is the min. and max. population size.

Result and Discussion
For simulations, MATLAB R2020a is installed on a workstation with an Intel i5-4210 CPU running at 1.70 GHz. The ASSA technique is evaluated in conditions of image segmentation, focusing on the thresholding with fuzzy II entropy. Natural images with diverse histogram distributions are used to test the suggested method. The proposed multilevel thresholding utilizing ASSA is compared to other evolution-ary algorithms like PSO, PPA, PFA, DE [3][4][5][6][7][8][9][10], and HPFPPA-D [32] on ten benchmark images with varied attributes and complexities [40]. The complete step-by-step overview and working of the proposed model are represented in Figure 1. Because evaluated algorithms contain stochastic operators, results must be studied in a statistical framework. The results of all tests are presented in this work after 30 independent runs, with parameter values for competing algorithms listed in Table 2. Finally, the problem's dimension size is defined as 2 times total number of thresholds.
For each of the segmentation approaches, three criteria have been used to determine their quality. The peak signalto-noise ratio (PSNR) compares the segmented and original images for similarity. The PSNR is focused on the mean squared error (MSE) of each pixel [41][42]. To compare the segmented image structures, the structural similitude index (SSIM) is used. The higher SSIM number, the better the original image segmentation [43,44].
The ASSA's results for optimizing TII-FE for thresholding are presented and analyzed in this section. Table 3 shows best ASSA-generated thresholds for various numbers of thresholds on the benchmark images [45,46]. The fuzzy parameters of membership functions used for threshold level estimation are described in Table 4. Tables 4 and 5 additionally include the best results produced using PSO, HPFPPA-D, DE, PPA, and PFA for comparison. Table 6 lists the type II fuzzy entropy values achieved by each algorithm so that performance parameters can be compared. In most circumstances, the suggested ASSA outperforms comparative techniques by obtaining solutions with higher fitness values. Figure 2 shows the results of ASSA-dependent segmentation graphically. Every segmented image [47] includes a histogram image and a threshold location. It is clear to notice how the output improves as the number of thresholds increases on resultant images. For evaluating the effectiveness of evolutionary computing methods, the fitness value is not the sole criteria. The convergence curve is frequently evaluated and compared to other algorithms. Figure 2 also shows the fitness evolution of the competitive approaches for benchmark image set across 50 iterations. The graphs show that the proposed strategy converges faster than other alternatives in vast majority of situations. Table 5 displays quality metric values to demonstrate the superior quality of the images acquired with ASSA and TII-FE than any other equivalent methodologies in the segmented images. The ASSA performs better over its peers for most of the experiments in terms of MSE metric, PSNR, and SSIM. This means that there is less noise in threshold images created in this work using the method outlined and the structures which depict the images' objects are appropriately preserved.
A new approach of image threshold based on type II entropy (TII-FE) and ASSA is presented in this paper. A number of benchmark images were used to test the performance of the proposed ASSA-based threshold method. The threshold approach is evaluated against competitive methods based on image accuracy, convergence characteristics, and segmented image quality. In terms of MSE, PSNR, and SSIM, the quality of segmented image is measured. The results show that TII-FE ASSA is an effective image thresholding approach.

Conclusion and Future Scope
This paper presents an image segmentation method of thresholding using ASSA combined with type II fuzzy entropy. ASSA's fuzzy entropy type II results are more efficient than PFA, PPA, DE, PSO, and HPFPPA-D. Optimal image thresholding is accomplished by increasing the value of entropy, which is a time-consuming process. As a result, the proposed methodology is examined and studied using several performance characteristics such as MSE, PSNR, and SSIM. The results are compared to known approaches, and the robustness and effectiveness of the proposed strategy to multilevel picture segmentation are evaluated.
In the future, more precise segmentation of image with less computational time can be achieved by improving the method further and comparing the same with other stateof-the-art algorithms MBO [48], IOA [49], and CASF [50], which is needed in real-time applications.

Data Availability
The data that support the findings of this study are available on request from the corresponding author.

Conflicts of Interest
The authors declare that they have no conflicts of interest to report regarding the present study.