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

Authors: Shubham Mahajan; Nitin Mittal; Rohit Salgotra; Mehedi Masud; Hesham A. Alhumyani; Amit Kant Pandit
Journal: Computational and Mathematical Methods in Medicine
 (2022)

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## Abstract

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.


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## Body

## 1. Introduction

Nature-inspired methods are applied in most engineering research problems because of their linear nature, easy implementation, and randomization dependent on population. They are mainly classified into two major types: swarm intelligence (SI) and evolutionary algorithms (EAs). EAs are methods that work on optimization of the research problem, e.g., differential evolution (DE) [1], genetic algorithm (GA) [2], and ant lion optimizer (ALO) [3]. SI is dependent on the swarming nature of various species, e.g., dragonfly algorithm (DA) [4], firefly algorithm (FA) [5], gray wolf optimization (GWO), bat algorithm (BA) [6, 7], and particle swarm optimization (PSO) [8–10].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 thresholdsth 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 above-stated 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 cross-entropy 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-FEThe paper is planned as follows: a detailed introduction of thresholding in multilevel images is discussed in Section2. 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.


## 2. 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 ith the gray level is
(1)pi=hiM×N,where the range of gray level is 0,1,2,3,4,5⋯⋯⋯⋯⋯.L−1, M×N is the image dimension, and hi is the no. of pixels with gray level i, 0≤i≤L−1.Letm be the no. of thresholds present; then, t1,t2,t3,t4,⋯⋯⋯..tm and if we break it inm classes, then
(2)C0=0,⋯⋯.t1−1,C1=t1,⋯⋯.t2−1,C2=t2,⋯⋯.t3−1,C3=t3,⋯⋯.t4−1,:Cm=tm,⋯⋯.L−1.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:
(3)Jt1=H0+H1,where
(4)H0=−∑i=0t1−1piω0lnpiω0,ω0=∑i=0t1−1pi,H1=−∑i=t1L−1piω1lnpiω1,ω1=∑i=t1L−1pi.H0&H1 are partial entropies of histogram.t1 is the gray level, which increases objective function in Equation (3).Now, by Otsu’s method, it is defined(5)Jt1=σ0+σ1,where
(6)σ0=ω0μ0−μT2,σ1=ω1μ1−μT2,ω0=∑i=0t1−1pi,μ0=∑i=0t1−1ipiω0,ω1=∑i=t1L−1pi,μ1=∑i=t1L−1ipiω0,μT=∑i=t1L−1ipi.Therefore,ω0μ0+ω1μ1=μT and ω0+ω1=1 and μT 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 (t1,t2,t3,t4,⋯⋯⋯..tm) are examined by increasing objective function:
(7)Jt1,t2,t3,t4,⋯⋯⋯..tm=H0+H1+H2+H3+H4+⋯⋯⋯.+Hm,where
(8)H0=−∑i=0t1−1piω0lnpiω0,ω0=∑i=0t1−1pi,H1=−∑i=t1t2−1piω1lnpiω1,ω1=∑i=t1t2−1pi,:Hm=−∑i=tmL−1piωmlnpiωm,ωm=∑i=tmL−1pi.Now, by Otsu’s method as in Equation (5), it is defined
(9)Jt1,t2,t3,t4,⋯⋯⋯..tm=σ0+σ1+σ2+σ3+σ4+⋯⋯⋯.+σm,σ0=ω0μ0−μT2,σ1=ω1μ1−μT2,:σm=ωmμm−μT2,ω0=∑i=0t1−1pi,μ0=∑i=0t1−1ipiω0,ω1=∑i=t1t2−1pi,μ1=∑i=t1t2−1ipiω0,:ωm=∑i=tmL−1pi,μm=∑i=tmL−1ipiωm.The value of thresholds ist1<t2<t3<t4,⋯⋯⋯<tm in both methods.


### 2.1. 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 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 entropy-based criteria will suffer from the negative effects of high complexity. Tao et al. [36] introduced a fuzzy entropy-based 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 setX=x1,x2,⋯⋯,xn, is defined in
(10)A=x,μAx∣x∈X,0≤μAx≤1,whereμA is the membership function.For dealing with vulnerability, a number of membership values are used in fuzzy type II sets rather than value as in(11)A=xμAhighx,μAlowx∣x∈X,0≤μAhighx,μAlowx≤1,where μAhighx and μAlowx are the upper and lower membership functions.


#### 2.1.2. Image Segmentation with Fuzzy Type II

Thresholding is the simplest method for segmenting an image. Thresholding is as simple as using a thresholdth value and adding it to a histogram until an optimal condition is reached. Equation (12) describes the thresholding method using a histogram.
(12)Isr,c=IGrr,cifIGrr,c≤th1,thk−1ifthk−1<IGrr,c≤thk,k=2,3,⋯.nt,IGrr,cifIGrr,c>thnt,where Isr,c is the segmented image with gray value, IGrr,c is the original image with gray value, and r,c is the position of pixels.


## 2.1. 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 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 entropy-based criteria will suffer from the negative effects of high complexity. Tao et al. [36] introduced a fuzzy entropy-based 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 setX=x1,x2,⋯⋯,xn, is defined in
(10)A=x,μAx∣x∈X,0≤μAx≤1,whereμA is the membership function.For dealing with vulnerability, a number of membership values are used in fuzzy type II sets rather than value as in(11)A=xμAhighx,μAlowx∣x∈X,0≤μAhighx,μAlowx≤1,where μAhighx and μAlowx are the upper and lower membership functions.


### 2.1.2. Image Segmentation with Fuzzy Type II

Thresholding is the simplest method for segmenting an image. Thresholding is as simple as using a thresholdth value and adding it to a histogram until an optimal condition is reached. Equation (12) describes the thresholding method using a histogram.
(12)Isr,c=IGrr,cifIGrr,c≤th1,thk−1ifthk−1<IGrr,c≤thk,k=2,3,⋯.nt,IGrr,cifIGrr,c>thnt,where Isr,c is the segmented image with gray value, IGrr,c is the original image with gray value, and r,c is the position of pixels.


## 2.1.1. Different Fuzzy Type II Sets

Type I fuzzy, with finite setX=x1,x2,⋯⋯,xn, is defined in
(10)A=x,μAx∣x∈X,0≤μAx≤1,whereμA is the membership function.For dealing with vulnerability, a number of membership values are used in fuzzy type II sets rather than value as in(11)A=xμAhighx,μAlowx∣x∈X,0≤μAhighx,μAlowx≤1,where μAhighx and μAlowx are the upper and lower membership functions.


## 2.1.2. Image Segmentation with Fuzzy Type II

Thresholding is the simplest method for segmenting an image. Thresholding is as simple as using a thresholdth value and adding it to a histogram until an optimal condition is reached. Equation (12) describes the thresholding method using a histogram.
(12)Isr,c=IGrr,cifIGrr,c≤th1,thk−1ifthk−1<IGrr,c≤thk,k=2,3,⋯.nt,IGrr,cifIGrr,c>thnt,where Isr,c is the segmented image with gray value, IGrr,c is the original image with gray value, and r,c is the position of pixels.


## 3. 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
(13)Yji=Sj+c1ubj−lbjc2+lbjC3≥0,Sj−c1ubj−lbjc2+lbjC3≤0,where Yji is the leader/first salp, Sj is the food source at jth dimensions, ubj and lbj are the upper and lower boundary, c1,c2,c3⋯⋯. are random values.Balance between exploitation and exploration is maintained byc1 coefficient parameter, as shown in
(14)c1=2e−4iI2,where i is the current iteration, I is the no. of iterations, and c2 and c3 are uniformly distributed random value coefficients in 0,1.The next position injthdimension is determined by utilizing these positions when moving in +ve&−ve∞.Now, followers’ updated position is shown in(15)Yjk=12at2+v0t,where k≥2 and Yjk is the kth follower position in the jth dimension.
(16)v0=speed,t=time,a=vfinalv0.If we putv0=0 in Equation (15), then
(17)Yjk=12Yjk+Yjk−1,where k≥2 and Yjk is the kth salp follower in the jth 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 parameterc1 is needed for optimum function, but there are 3 parameters c1, c2, and c3 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:
(i)
For appropriate exploitation and exploration in SSA, a division depend concept was introduced in ASSA(ii)
The major advantage is the inclusion of the logarithmic distributed (LD) parameterc1 in SSA. Randomized LD-dependent parameter is useful in shifting it towards the exploitation stage(iii)
Balance b/w exploitation and exploration is improved by changingc1 in SSA to LD, which is useful in shifting it towards the exploitation stage(iv)
The total no. of evaluation functions is reduced by reducing population size. It reduces computational complexity burdenThe initialization of the algorithm starts in a fixed range and is presented in mathematical form as(18)xi,j=xmin,j+U0,1×xmin,j−xmax,j,where xi,j is the ith solution for the jth dimension.
(19)i=1,2,3,4,⋯⋯,n,j=1,2,3,4,⋯⋯⋯..,d.xmax,j and xmin,j are the upper and lower limits.U0,1 is the uniform rand. no. in 0,1.Position in ASSA is updated by modifying exploitation and exploration function of SSA, and it overall increases the performance and is presented as(20)x1=xi−A1C1·xnew−xit,x2=xi−A2C2·xnew−xit,x3=xi−A3C3·xnew−xit,xnewt+1=x1+x2+x33,xnewt+1=xnewt+α×Lλxbest−xnewt,where xnew is the new solution, A1,A2,A3 and C1,C2,C3 are derived from A=2a·r1−a and C2·r2, α and Lλ are uniformly and Levy distributed rand. no., and r1 and r2 are rand. no. distribution in 0,1.Step size dependent on Levy flight is(21)Lλ~λΓλsinπ2λπ1s1+λ;s≫s0≫0,where s=U/V1/λU~N0,σ2.
(22)V~N0,1,σ2=Γ1+λλΓ1+λ/2.sinπλ/22λ−1/2.λΓ is the gamma function.
(23)λ=1.5.Nis derived from Gaussian distribution with variance=σ2 and mean=0.Basic functions of SSA and ASSA are shown in Table1. 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 Fxit with xit, the solution is mathematically denoted as
(24)xnewt+1=xnewifFxnew<Fxit,xitotherwise.Table 1
Basic functions of SSA and ASSA.
Basic functionsSSAASSAInitialization of populationRand. no.Decreasing adaptive populationExploitationStandardStandardExplorationStandardCombination of CS [6] and GWO [7]Parameters for controllingRand. no.LD w.r.t. iterationsIn controlling parameter balance b/w exploitation and exploration is improved by changingc1 in SSA to LD, which is useful in shifting it towards the exploitation stage. In this range, upper and lower cmax&cmin is 0.950.05 represented as
(25)c1=cmax+cmin−cmax×log10a+10ttmax,where c is the weight of inertia, a is the rand. no. in 0,1, and t and tmax 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(26)ng+1=roundnmin−nmaxFEsmax·FEs+nmax,where FEs is the max. no. of iterations and nmin−nmax is the min. and max. population size.


## 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
(13)Yji=Sj+c1ubj−lbjc2+lbjC3≥0,Sj−c1ubj−lbjc2+lbjC3≤0,where Yji is the leader/first salp, Sj is the food source at jth dimensions, ubj and lbj are the upper and lower boundary, c1,c2,c3⋯⋯. are random values.Balance between exploitation and exploration is maintained byc1 coefficient parameter, as shown in
(14)c1=2e−4iI2,where i is the current iteration, I is the no. of iterations, and c2 and c3 are uniformly distributed random value coefficients in 0,1.The next position injthdimension is determined by utilizing these positions when moving in +ve&−ve∞.Now, followers’ updated position is shown in(15)Yjk=12at2+v0t,where k≥2 and Yjk is the kth follower position in the jth dimension.
(16)v0=speed,t=time,a=vfinalv0.If we putv0=0 in Equation (15), then
(17)Yjk=12Yjk+Yjk−1,where k≥2 and Yjk is the kth salp follower in the jth 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 parameterc1 is needed for optimum function, but there are 3 parameters c1, c2, and c3 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:
(i)
For appropriate exploitation and exploration in SSA, a division depend concept was introduced in ASSA(ii)
The major advantage is the inclusion of the logarithmic distributed (LD) parameterc1 in SSA. Randomized LD-dependent parameter is useful in shifting it towards the exploitation stage(iii)
Balance b/w exploitation and exploration is improved by changingc1 in SSA to LD, which is useful in shifting it towards the exploitation stage(iv)
The total no. of evaluation functions is reduced by reducing population size. It reduces computational complexity burdenThe initialization of the algorithm starts in a fixed range and is presented in mathematical form as(18)xi,j=xmin,j+U0,1×xmin,j−xmax,j,where xi,j is the ith solution for the jth dimension.
(19)i=1,2,3,4,⋯⋯,n,j=1,2,3,4,⋯⋯⋯..,d.xmax,j and xmin,j are the upper and lower limits.U0,1 is the uniform rand. no. in 0,1.Position in ASSA is updated by modifying exploitation and exploration function of SSA, and it overall increases the performance and is presented as(20)x1=xi−A1C1·xnew−xit,x2=xi−A2C2·xnew−xit,x3=xi−A3C3·xnew−xit,xnewt+1=x1+x2+x33,xnewt+1=xnewt+α×Lλxbest−xnewt,where xnew is the new solution, A1,A2,A3 and C1,C2,C3 are derived from A=2a·r1−a and C2·r2, α and Lλ are uniformly and Levy distributed rand. no., and r1 and r2 are rand. no. distribution in 0,1.Step size dependent on Levy flight is(21)Lλ~λΓλsinπ2λπ1s1+λ;s≫s0≫0,where s=U/V1/λU~N0,σ2.
(22)V~N0,1,σ2=Γ1+λλΓ1+λ/2.sinπλ/22λ−1/2.λΓ is the gamma function.
(23)λ=1.5.Nis derived from Gaussian distribution with variance=σ2 and mean=0.Basic functions of SSA and ASSA are shown in Table1. 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 Fxit with xit, the solution is mathematically denoted as
(24)xnewt+1=xnewifFxnew<Fxit,xitotherwise.Table 1
Basic functions of SSA and ASSA.
Basic functionsSSAASSAInitialization of populationRand. no.Decreasing adaptive populationExploitationStandardStandardExplorationStandardCombination of CS [6] and GWO [7]Parameters for controllingRand. no.LD w.r.t. iterationsIn controlling parameter balance b/w exploitation and exploration is improved by changingc1 in SSA to LD, which is useful in shifting it towards the exploitation stage. In this range, upper and lower cmax&cmin is 0.950.05 represented as
(25)c1=cmax+cmin−cmax×log10a+10ttmax,where c is the weight of inertia, a is the rand. no. in 0,1, and t and tmax 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(26)ng+1=roundnmin−nmaxFEsmax·FEs+nmax,where FEs is the max. no. of iterations and nmin−nmax is the min. and max. population size.


## 4. 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 evolutionary algorithms like PSO, PPA, PFA, DE [3–10], 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.Figure 1
Step-by-step working of the proposed method.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 Table2. Finally, the problem’s dimension size is defined as 2 times total number of thresholds.Table 2
Parameter settings.
AlgorithmParametersPSONP=10×D; D=2×PR=2×3,5,7; Gmax=50; Wmax=0.9, Wmin=0.4, Ac1=Ac2=2DENP=10×D; D=2×PR=2×3,5,7; Gmax=50; F=0.5PPANP=10×D; D=2×PR=2×3,5,7; Gmax=50; Nmax=7PFANP=10×D; D=2×PR=2×3,5,7; Gmax=50; σ=5HPFPPA-DNP=10×D; D=2×PR=2×3,5,7; Gmax=50; Nmax=7; σ=5ASSANP=10×D; D=2×PR=2×3,5,7; Gmax=50Here, NP is the population size,D is the dimension of problem, Gmax is the number of iteration, Nmax is the maximum number of runners, σ is the standard deviation, bp is the breeders’ probability, and PR are different threshold levels.For each of the segmentation approaches, three criteria have been used to determine their quality. The peak signal-to-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. Table3 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.Table 3
Thresholds achieved after applying the ASSAs and competitive algorithms to segment the set of benchmark images using TII-FE.
ImPRASSAHPFPPA-DPSOPFADEPPA41004329 104 22433 66 13734 144 23535 104 19335 100 18536 86 152545 86 135 167 24734 100 135 174 23336 78 114 181 23535 100 136 174 23239 78 115 158 20935 105 151 191 236719 62 98 124 157 20241 84 115 146 178 21020 46 71 91 135 17843 78 112 143 176 21142 86 101 133 155 18735 83 106 134 156 188237233217234234228176035338 118 19547 113 19874 138 19949 116 19957 106 18148 108 194536 73 118 142 21251 93 139 184 22036 73 136 187 22254 96 141 187 22151 93 137 185 22264 109 136 171 213724 52 81 117 183 20649 90 117 145 170 19540 78 114 136 171 20743 80 105 132 163 19247 79 106 133 157 18451 100 116 143 180 200215224231224219223225017324 116 23668 134 19568 136 19670 138 19767 138 199103 168 209523 72 154 201 22921 76 128 162 21625 75 108 142 21321 76 137 166 21127 78 131 169 21533 83 135 177 208720 37 90 115 127 18422 44 78 112 147 18220 84 129 146 165 19221 43 81 118 153 19021 41 79 115 139 16329 79 107 143 186 209218219233223204236241004346 100 14284 164 21784 161 21484 164 21785 165 21690 161 210528 84 135 167 22547 102 158 183 21843 82 111 155 21650 105 162 195 22544 100 144 166 21861 110 161 199 229712 28 42 79 132 17344 68 98 127 156 18646 75 91 113 157 19743 97 143 170 199 21650 80 109 138 163 18947 87 109 121 138 171196219227232220212385028388 118 21776 132 19477 157 21774 128 19276 133 19466 110 186544 93 135 169 21956 93 133 173 21456 119 165 198 23154 90 119 156 21058 98 136 175 21545 86 133 169 221756 86 117 135 162 20254 88 114 139 167 19642 66 99 139 172 20353 86 112 137 166 19353 86 112 133 160 18842 72 117 160 182 206226226231225222224388016354 132 20452 97 17551 128 20546 121 20451 95 17050 111 181556 104 148 204 24649 91 133 176 21441 97 120 159 21749 91 138 182 21750 90 135 182 21530 68 88 136 210746 84 104 128 149 19847 87 116 147 173 19648 95 117 139 168 19047 88 113 142 170 19343 81 110 141 170 19337 78 123 147 178 2032202242212242222332092336 162 19441 97 17536 96 18041 97 17540 98 17453 108 167534 62 120 212 24831 61 94 127 18130 62 92 119 18132 63 92 121 17430 62 96 127 17531 74 97 128 179734 70 78 112 158 19024 47 65 88 112 13236 71 105 144 172 19425 52 67 85 112 13721 46 72 96 115 13620 41 88 131 140 15622718521718917420214037396 178 21658 105 18057 145 22096 183 21957 102 17866 109 183544 92 148 184 21660 109 148 187 22156 105 156 202 22956 104 148 189 22355 99 144 188 22248 95 141 185 221738 104 141 152 181 19843 75 103 131 161 19052 98 133 165 187 20838 69 99 126 161 19243 70 103 135 165 19229 73 117 142 167 19122322323222422422255067344 180 19640 79 14840 79 14940 79 14740 79 14741 94 179533 63 84 118 16438 63 99 135 17039 84 119 159 20337 63 100 137 17238 62 98 135 17337 81 100 137 177728 53 84 125 169 18740 63 82 112 139 16736 55 77 113 161 19140 61 81 112 139 17037 59 82 107 146 18040 69 102 123 146 1682372002062052002011690123106 167 21078 139 19765 130 19780 142 19980 139 19792 150 209525 36 59 80 14355 100 137 180 22051 87 122 165 21652 98 136 177 21859 103 143 187 22263 117 152 175 219738 64 102 130 164 19240 74 105 137 165 19743 90 114 128 162 19041 74 100 132 168 19740 74 103 129 160 19539 66 88 112 170 209219229223227226232Table 4
Parameters of TII-FE found by the proposed ECA and ASSA.
ImPRASSAHPFPPA-DPSOPFADEPPAancnancnancnancnancnancn41004328 79 20830 129 2360 66 6666 66 2080 78 21467 210 2557013869 138 2480 70 13070 130 2402 81 9569 91 209527 78 133 15663 94 137 1780 68 132 13867 131 138 2100 77 79 15271 78 148 2092 68 132 13967 132 139 2090 78 80 14978 78 149 1676 76 147 16763 133 154242252210255215255210254167250219215 252711 47 89 12127 78 107 1270 83 84 14681 84 145 1460 41 51 9140 50 90 917 78 81 14278 78 142 1441 85 86 11782 86 116 1492 71 97 12667 95 115 142142 177 229173 228 245146 210 210209 210 25591 178 178178 178 255144 211 212208 211 255150 161 212159 212 255142 174 211170 201 244176035312 114 19364 122 1988 86 14086 140 25515 137 143132 139 2558 90 14290 142 2558 106 106106 106 25510 87 13485 128 254531 61 112 12342 86 124 1629 93 93 18493 93 184 1848 65 85 18664 81 186 18712 95 96 18695 96 185 18710 93 93 18292 93 181 18822 108 113 158106 110 158190234185255189255187254188255184184 242718 45 71 10230 59 92 1329 89 90 14489 90 144 14516 65 91 13664 91 136 1368 79 81 12978 80 128 13515 79 79 13278 79 132 13310 92 109 12492 108 122 162171 201 213195 211 218145 194 195194 195 253138 206 207203 207 255136 190 194190 193 254135 181 188179 187 250166 194 209193 209 236225017320 46 23128 186 2421 134 134134 134 2551 36 136135 136 2551 138 138138 138 255134 143134 142 25545 167 170160 169 248520 64 126 19026 80 183 2120 43 108 14742 108 147 1760 49 101 11549 100 114 1690 42 110 16541 109 164 1660 60 95 16654 95 166 1727 62 104 17459 103 165 180215244177255170255166255174255181234717 30 70 11423 45 111 1171 44 44 11243 44 112 1120 41 128 13040 127 129 1620 42 45 11742 43 117 1192 41 43 11440 41 114 1153 65 96 12755 92 118 159120 175 206134 193 230112 181 183181 182 255162 172 211168 211 255120 188 191185 191 255115 162 163162 163 245175 196 224196 222 248241004332 90 11860 110 16621 146 181146 181 25221 149 173146 172 25521 146 181146 181 25222 148 181148 181 25141 150 182138 172 237520 65 124 15036 103 147 18522 72 133 18371 132 183 18321 65 105 13464 98 117 17522 77 132 19277 132 191 19822 68 134 15366 132 153 17931 98 128 19591 121 193 20221323818425117725519825118425220625178 24 30 6116 32 55 9721 68 68 12767 68 127 12721 71 80 10371 79 102 12322 66 130 15864 128 156 18123 78 81 13877 81 137 13826 72 105 11567 101 113 127127 169 191137 177 202128 185 186183 186 251124 194 20319,01,99,251183 215 216214 216 247139 188 190186 190 249127 155 188148 187 235385028381 115 18295 121 25219 132 132132 132 25518 136 179135 177 25519 128 129128 128 25518 133 133133 133 25531 102 122101 117 250518 90 111 16570 96 159 17318 93 93 17393 93 172 17318 96 141 18894 141 188 20719 89 90 14888 90 148 16319 96 99 17496 99 173 17521 74 103 16469 98 162 174201238173255207255165254175255190252754 76 115 13158 96 120 14019 88 88 13988 88 139 13922 63 69 13762 68 129 14020 85 87 13785 87 136 13726 81 91 13380 91 132 13319 67 82 15865 76 152 161161 189 220163 216 233139 195 197195 196 254142 202 206201 203 255140 192 195192 194 254134 187 189186 188 254162 205 209202 206 239388016334 101 19874 163 2107 97 9797 97 2521,06,15810,21,50,2524 87 15587 155,2527 95 9695 95 2442 105 12198 117 240543 98 138 20469 110 158 2057 90 91 17690 91 174 1760 91 104 13881 103 136 1797 90 93 18290 91 182 18210 90 90 18289 90 179 1825 61 75 10755 74 101 165240253177250181252183251182248170250730 80 98 11362 88 110 1437 87 87 14586 87 144 1493 94 95 13993 95 139 1399 86 90 13685 89 135 1477 80 85 13678 81 135 1455 71 108 13969 85 137 155147 195 210151 201 230150 196 198196 196 249147 189 190189 190 252149 192 196191 193 252148 192 197191 193 247156 201 215199 204 2502092312 134 18459 190 2040 82 11182 111 2380 77 11872 115 2410 82 11182 111,2390 80 11679 115 23113 97 11993 118 214530 52 111 20438 72 130 2200 61 61 12761 61 126 1270 61 65 11960 62 118 1191 62 63 12162 63 120 1211 61 65 12659 62 126 1274 59 96 10157 89 98 15424525112723512024112222612922115520273 65 75 8265 76 81 1420 47 47 82 9347 47 82 930 71 72 13971 71 138 1490 51 52 82 8850 52 82 88 1360 45 49 96 9642 47 95 966 35 50 12734 46 125 134146 178 225170 202 229132 133131 132 237150 194 195194 194 239137 138137 240136 136134 136 212135 145 167144 167 23714037364 150 212128 205 21911 105 105105 105 2558 106 184106 183 25510 182 183182 183 25511 102 102102 102 25427 108 115105 109 251540 74 126 18048 110 170 18811 109 109109 109 1868 104 110 201104 106 20111 103 189101 105 18912 98 101 18897 100 187 18815 86 114 17881 104 168 192205227186 187187 255202202 255190189 255190254195247733 80 138 15043 128 144 15411 74 76 13174 75 130 13111 94 102 16592 101 164 16511 64 74 12364 73 123 12917 68 73 13468 72 133 13613 49 100 13445 96 133 149170 194 215192 203 232131 190 191190 190 255165 208 209208 208 255130 191 193191 192 254138 191 193191 192 255152 191 203182 191 24055067324 176 19164 184 20113 73 8466 84 21113 75 8367 82 21513 73 8566 84 20913 74 8466 83 21019 63 14362 125 214524 62 78 11042 65 89 12614 62 63 13562 63 135 13514 64 105 13263 104 132 18613 62 64 13761 64 135 13716 61 64 13560 62 131 13511 74 91 11963 87 108 155133195135205186220139204135211159195718 43 74 8938 63 94 16216 63 64 10163 63 100 12219 52 59 9552 58 95 13119 61 61 10061 61 100 12415 59 59 10558 59 104 10912 69 84 12167 69 119 125166 176 223173 199 251124 154 181153 180 219132 190 191190 191 220125 152 189152 188 220112 180 180179 180 219136 158 188155 177 214169012387 126 196126 186 22517 139 139139 139 2558 122 139122 138 25518 141 142141 142 25520 139 139139 139 25542 142 162141 157 255524 32 45 8027 40 74 819 100 100 175100 100 17415 87 89 15587 87 154 1758 96 100 17395 99 172 18114 103 103103 103 18328 100 138 16797 134 165 18395192185185 255176255181255185 188188 255185255715 50 82 11961 78 122 1418 72 76 13571 76 134 13911 74 106 12274 106 122 1339 72 76 12572 76 123 1398 73 76 12972 74 129 12924 64 69 11054 67 107 114160 179 192168 205 247139 191 202191 202 255133 190 190190 190 255141 196 198195 197 255129 192 198191 198 254134 208 210206 210 254Table 5
Mean of objective function values attained by the proposed ASSA method for segmentation of digital images using TII-FE.
ImPRASSAHPFPPA-DPSOPFADEPPA41004317.386417.386317.215617.278217.279116.9104524.211724.211523.960024.139024.035222.8482731.142731.142629.442430.932529.994828.8107176035317.760117.760117.583417.749517.748917.6123525.217025.216824.451225.137825.144724.2853731.342731.342630.501931.121130.894729.5311225017318.095118.095118.079218.092618.074717.4896524.889124.889024.532624.802724.675223.7939731.746831.746830.592231.566931.162829.1164241004317.843817.843917.324217.830017.816716.8263524.355824.356023.123724.176224.040423.4730730.544230.544429.679129.585230.027028.1811385028318.424118.424018.178918.403218.406117.8249525.034625.034524.645724.955724.956023.7739731.395231.395230.509431.182830.994529.1722388016317.714417.714317.364217.582517.686017.1471525.000725.000423.564624.943124.828923.3324731.142231.142230.529530.893830.558928.85782092317.242117.241917.064717.230917.220716.8108524.093624.093323.885423.976023.821822.3837729.594929.584928.224129.350029.188627.388114037318.070318.070217.645817.829418.052417.2870525.490225.489724.979125.358025.284923.4466731.533631.533530.958631.295331.112129.209555067316.816616.816516.682416.754516.769315.8787523.071423.071522.178022.931722.872621.4793728.367628.367627.659828.164728.064026.3183169012318.346518.346418.243818.332118.338218.0177525.146425.146324.997525.111825.102624.4865731.410931.410931.027731.243131.279429.4929Table 6
Comparison of the SSIM, MSE, and PSNR value of ASSA applied over benchmark images using the TII-FE.
ImPRMSEPSNRSSIMASSAHPFPPA-DPSOPFADEPPAASSAHPFPPA-DPSOPFADEPPAASSAHPFPPA-DPSOPFADEPPA4100433.55E+023.56E+024.06E+023.83E+023.63E+025.75E+022.27E+012.26E+012.20E+012.23E+012.25E+012.05E+018.76E−018.76E−018.70E−018.73E−018.74E−018.61E−0151.37E+021.38E+021.28E+0021.74E+021.30E+022.15E+022.71E+022.70E+012.57E+012.70E+012.48E+012.67E+019.21E−019.21E−019.07E−019.12E−018.84E−019.12E−0178.69E+018.71E+011.02E+021.05E+028.91E+011.17E+022.92E+012.87E+012.79E+012.86E+012.80E+012.74E+019.23E−019.22E−019.15E−019.22E−019.22E−019.13E−0117603533.07E+023.09E+023.64E+023.68E+023.94E+023.57E+022.37E+012.35E+012.32E+012.26E+012.25E+012.22E+018.52E−018.53E−018.45E−018.34E−018.29E−018.12E−0151.28E+021.30E+021.69E+021.32E+021.30E+021.89E+022.72E+012.70E+012.59E+012.69E+012.70+012.54E+018.71E−018.71E−018.57E−018.70E−018.71E−018.53E−0178.03E+018.04E+018.25E+011.00E+028.16E+011.29E+022.91E+012.91E+012.81E+012.90E+012.90E+012.70E+018.98E−018.98E−018.84E−018.95E−018.94E−018.76E−0122501733.30E+023.31E+023.19E+023.27E+023.41E+023.51E+022.31E+012.31E+012.30E+012.28E+012.27E+012.29E+018.47E−018.48E−018.45E−018.39E−018.36E−018.44E−0151.41E+021.43E+021.59E+021.71E+021.49E+021.79E+022.67E+012.66E+012.58E+012.64E+012.61E+012.56E+019.01E−019.01E−018.91E−019.00E−018.97E−018.75E−0178.87E+018.89E+019.53E+011.09E+028.94E+011.25E+022.86E+012.86E+012.78E+012.86E+012.83E+012.72E+019.23E−019.22E−019.16E−019.22E−019.21E−019.16E−0124100432.13E+022.15+022.18E+022.18E+022.19E+022.17E+022.49E+022.47E+012.48E+012.48E+012.48E+012.47E+018.97E−018.97E−018.97E−018.96E−018.96E−018.95E−0151.39E+021.40E+021.78E+021.88E+021.95E+021.74E+022.57E+012.54E+012.67E+012.57E+012.56E+012.52E+018.91E−018.91E−018.71E−018.87E−018.83E−018.80E−0177.78E+017.79E+011.01E+028.68E+019.55E+011.35E+022.95E+012.92E+012.83E+012.81E+012.87E+012.68E+019.29E−019.30E−019.20E−019.15E−019.21E−018.92E−0138502833.18E+023.19E+023.29E+023.28E+023.32E+023.20E+022.42E+012.40E+012.31E+012.30E+012.31E+012.29E+017.85E−017.86E−017.82E−017.67E−017.69E−017.62E−0151.25E+021.26E+021.76E+021.41E+021.38E+022.08E+022.71E+012.71E+012.57E+012.66E+012.67E+012.49E+018.69E−018.68E−018.44E−018.46E−018.48E−018.17E−0177.14E+017.15E+017.27E+017.57E+017.25E+011.02E+022.99E+012.96E+012.93E+012.95E+012.95E+012.81E+019.07E−019.07E−019.02E−019.06E−019.03E−018.74E−0138801633.51E+013.54E+025.32E+023.76E+025.49E+023.60E+022.11E+012.09E+012.26E+012.24E+012.26E+012.07E+017.47E−017.44E−017.39E−017.33E−017.38E−016.89E−0151.43E+011.46E+021.51E+021.53E+022.13E+021.49E+022.68E+012.66E+012.65E+012.64E+012.63E+012.48E+018.29E−018.29E−018.25E−018.21E−018.20E−017.94E−0178.02E+028.04E+018.25E+018.35E+018.19E+018.88E+012.92E+012.91E+012.89E+012.90E+012.90E+012.86E+018.81E−018.82E−018.72E−018.78E−018.77E−018.70E−01209233.03E+013.06E+023.10E+023.15E+023.48E+023.10E+022.32E+012.31E+012.33E+012.32E+012.32E+012.27E+018.83E−018.82E−018.82E−018.82E−018.82E−018.79E−0151.28E+021.32E+021.51E+021.48E+021.55E+021.80E+022.71E+012.69E+012.64E+012.62E+012.63E+012.56E+019.22E−019.22E−019.22E−019.17E−019.20E−019.14E−0176.89E+017.00E+018.19E+018.37E+017.03E+019.61E+012.96E+012.97E+012.89E+012.97E+012.90E+012.83E+019.52E−019.52E−019.28E−019.51E−019.46E−019.20E−011403733.12E+013.13E+023.58E+023.51E+029.28E+023.47E+022.38E+012.36E+012.32E+012.27E+012.27E+011.85E+018.11E−018.11E−018.03E−017.92E−017.99E−017.15E−0152.10E+012.12E+022.23E+022.32E+022.20E+022.41E+022.49E+012.49E+012.45E+012.47E+012.47E+012.43E+018.36E−018.38E−018.09E−018.21E−018.13E−018.02E−0177.28E+027.31E+018.78E+019.31E+018.33E+011.70E+022.94E+012.95E+012.84E+012.89E+012.87E+012.58E+018.97E−018.97E−018.75E−018.86E−018.77E−018.36E−015506733.75E+013.76E+023.87E+023.84E+023.84E+024.07E+022.26E+012.24E+012.23E+012.23E+012.23E+012.20E+019.45E−019.44E−019.41E−019.42E−019.44E−019.41E−0158.85E+028.88E+011.10E+021.10E+021.08E+021.18E+022.88E+012.86E+012.77E+012.78E+012.77E+012.74E+019.61E−019.63E−019.52E−019.60E−019.60E−019.36E−0174.24E+024.26E+014.66E+015.30E+014.53E+016.91E+013.19E+013.18E+013.09E+013.16E+013.14E+012.97E+019.67E−019.67E−019.59E−019.61E−019.60E−019.57E−0116901232.69E+012.72E+023.01E+022.79E+022.75E+023.10E+022.41E+012.38E+012.33E+012.37E+012.37E+012.32E+018.05E−018.05E−017.83E−018.03E−018.05E−017.75E−0151.46E+011.47E+021.65E+021.65E+021.53E+021.90E+022.63E+012.64E+012.60E+012.63E+012.60E+012.53E+018.51E−018.47E−018.41E−018.43E−018.41E−018.35E−0178.44E+028.45E+011.02E+028.58E+018.57E+011.26E+022.88E+012.89E+012.80E+012.88E+012.88E+012.71E+018.92E−018.91E−018.81E−018.90E−018.91E−018.66E−01Figure2 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.Figure 2
Segmented test images along with equivalent histogram and convergence plots by ASSA combined with type II fuzzy entropy for 3, 5, and 7 levels.Table5 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.


## 5. 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 state-of-the-art algorithms MBO [48], IOA [49], and CASF [50], which is needed in real-time applications.



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*Source: 2794326-2022-01-29.xml*