Extraction of radish seed oil (Raphanus sativus L.) and evaluation of its potential in biodiesel production

1.   Introduction

With the emergence of computer technology, image processing has been widely used in many fields. Image segmentation is one of the classical topics in image processing ^[1]. It divides the original image into multiple sub-regions according to intensity, color, texture, and other attributes of the image ^[2]. Image segmentation is often the preprocessing phase of higher-class processing such as: image analysis, object recognition, and computer vision. Consequently, the performance of higher-class processing system depends on the accuracy of the segmentation technique adopted ^[3]. Researchers have proposed a range of segmentations, including edge detection, histogram based thresholding, region, feature clustering, and neural networks ^[4,5,6]. Histogram based thresholding is a simple and the most commonly used image segmentation method ^[7,8]. Thresholding methods can be divided into two categories: bi-level thresholding and multi-level thresholding. Bi-level thresholding means that the target and background can be clearly distinguished by a single threshold value. Multi-level thresholding denotes that the given image can be segmented into various classes by multiple threshold values ^[9,10,11].

Among available image thresholding techniques, Otsu and Kapur's entropy are two state-of-the-art thresholding methods ^[12,13,14]. Otsu and Kapur's entropy find the optimal threshold values according to some preset criteria. Otsu maximizes the variance of the histogram classes, and Kapur's entropy maximizes the entropy of the histogram. These thresholding techniques mentioned above can be easily extended to multilevel thresholding segmentation. However, the exhaustive search makes it inefficient to find the optimal threshold values, and the time complexity increases exponentially when the number of threshold increases. In order to overcome the above drawback, swarm intelligence (SI) algorithms are extensively used in multilevel thresholding problems ^[15,16]. Ibrahim et al. proposed the fish images segmentation model based on salp swarm algorithm, in which Otsu method is used to determine the threshold and extract fish from the original image ^[17]. Ouadfel et al. studied two metaheuristic algorithms: flower pollination algorithm and social spiders optimization. Then the performance of multilevel thresholding methods was evaluated comprehensively ^[18]. Infrared image is of great value in medical research. Díaz-Cortés applied dragonfly algorithm in medical image segmentation technology ^[19]. Satapathy et al. used Otsu method and a novel chaotic bat algorithm (CBA) to address bi-level and multi-level image thresholding problem. The chaotic map was considered to update the position of bat during the optimization search. The proposed CBA offered superior image quality measure values ^[20]. Salvi et al. presented an adaptive method for nuclei segmentation in H & E stained images, named multiscale adaptive nuclei analysis (MANA). High segmentation performances were obtained for different organ images ^[21]. Feng et al. invented a thresholding technique of 3D Otsu based on dimension decomposition rule. The test results on medical images showed that the proposed technique reduced time complexity without the loss of segmentation quality ^[22]. Zhao et al. proposed an improved ant colony optimizer (RCACO) using a random spare strategy and chaotic intensification strategy. The convergence speed and the convergence accuracy were main gains. Furthermore, it was also an excellent multilevel image segmentation algorithm ^[23]. In ^[24], the horizontal crossover search (HCS) and the vertical crossover search (VCS) were introduced into the ant colony optimizer for the first time. The proposed algorithm was named CCACO. The newly proposed algorithm was evaluated in the field of function optimization and image segmentation ^[24]. He et al. introduced the efficient krill herd (EKH) algorithm into image segmentation. The experimental results showed that the presented EKH algorithm was superior to the other algorithms ^[25]. Hilali-Jaghdam et al. proposed a method based on the classical and quantum genetic algorithms to solve the medical images segmentation. The Genetic Algorithm (GA) used a binary coding while the Quantum Genetic Algorithm (QGA) used the qubit encoding of individuals ^[26]. Wu et al. proposed an improved teaching-learning-based optimization algorithm (DI-TLBO) and successfully applied it in casting X-ray image segmentation for multi-level threshold ^[27].

Mirjalili proposed a novel nature-inspired algorithm called ant lion optimizer (ALO) in 2015 ^[28]. Obviously, ALO algorithm simulates the intelligent behavior of antlions in nature, including building traps, catching preys, and rebuilding traps. In 2018, Hadidian-Moghaddam et al. used ALO algorithm to solve the optimal sizing and siting of distributed generation. The results showed that ALO had better performance than particle swarm optimization (PSO) and genetic algorithm (GA) in this field ^[29]. Raju et al. applied ALO algorithm for optimization of the controller gains. The results showed that the controller performed better in stabilization time(s), peak overshoot, and oscillations ^[30]. In 2016, by using ALO algorithm, Saxena et al. solved the problem of antenna current and antenna position optimization ^[31]. In the paper of Umaheswari et al., ALO was first adopted to solve the integrated maintenance scheduling problem ^[32]. Dinakara et al. proposed to determine the optimal distributed generation size by ALO. This approach achieved the purpose of reducing system power loss and improving voltage profile ^[33]. In ^[34], ALO was performed multilevel thresholding based on the contextual information of the image. Contextual information enhanced the quality of the segmented image as it considered not only the pixel value but also its vicinity. Jin et al. proposed a method to image segmentation based on ALO and fuzzy c-means (FCM). The proposed method alleviated the problem that the segmentation results of the images were unsatisfactory due to the presence of noise ^[35]. Yue et al. proposed an improved ALO called BIALO to enhance industrial images. Three strategies improved exploration and exploitation capabilities of the native algorithm ^[36]. In fact, there are still several disadvantages of the native ALO, such as the slow convergence rate, falling easily into local optimum and so on. In view of this phenomenon, it is necessary to improve the performance of the native ALO. In the paper of Wu et al., chaos was introduced into the initialization stage of ALO algorithm ^[37]. The improvement of ALO algorithm by Subhashini was to change the elite weight ^[38]. Majhi et al. proposed a hybrid clustering method based on k-means and ALO algorithm for cluster analysis in 2018 ^[39]. Some authors also include opposition-based learning (OBL) in their methods. This scheme can look for the opposite direction of each candidate solution. If the opposite point is beneficial then it is used as the candidate solution before proceeding to the next iteration. OBL helps in further exploration and better probability to converge to the optimum. Sarkhel et al. embedded OBL into harmony search algorithm, which improved the convergence rate of the algorithm ^[40]. Ewees et al. proposed a grasshopper optimization algorithm based on OBL strategy. Experimental results proved that the modified algorithm was competitive on engineering optimization problems ^[41]. In 2016, Ahandani et al. combined OBL with shuffled bidirectional differential evolution algorithm, which sped up the search process the algorithm ^[42].

Inspired by these successful applications of OBL strategy, OBL strategy is introduced into ALO algorithm to avoid falling into the local optimum. The search accuracy and convergence performance are improved. Then Otsu and Kapur's entropy as objective functions are maximized by MALO to find the optimum threshold values. Finally, the provided images are segmented into some classes. In this paper, IEEE CEC2017 benchmark functions ^[43] are used to evaluate the effectiveness of MALO. 7 traditional algorithms and 4 improved algorithms are selected for comparisons. The quality of the segmented images is evaluated in terms of fitness value, peak signal-to-noise ratio (PSNR) ^[44,45], structural similarity index (SSIM) ^[46,47,48], feature similarity (FSIM) ^[49,50], and computational time. The experimental results confirm that the proposed method can be used effectively for multilevel thresholding.

The remainder of this paper is organized as follows: Section 2 outlines Otsu and Kapur's entropy methods for multilevel thresholding. Section 3 gives an overview of ALO followed by its mathematical model. ALO algorithm based on opposition-based learning for multilevel thresholding color image segmentation is presented in Section 4. Simulation experiments and results analysis are described in Section 5. Finally, Section 6 concludes the work and suggests some directions for future studies.

2.   Materials and methods

Thresholding segmentation processes the histogram of digital images. An algorithm is used as the segmentation criterion. The threshold that satisfies the criterion function is called the optimal threshold. Based on the optimal threshold, the image is divided into target region and background region. The image thresholding method can be summarized into two categories: bi-level thresholding segmentation and multilevel thresholding segmentation. Bi-level thresholding segmentation cannot completely extract the target for a particular image. Multilevel thresholding divides the whole image into multiple regions. Multilevel thresholding segmentation can highlight the features among image regions.

The color image is represented by three different 8-bit gray values of R, G, and B channels. ${{{n}}_{{i}}}$ denotes the number of pixels whose gray level is i. N denotes the total number of pixels. ${{{p}}_{{i}}}$ denotes the distribution probability of the ith gray value. They are defined as follows:

Suppose there are K thresholds of ${t_1}, {t_2}, \cdot \cdot \cdot, {t_K}$. They divide the gray level of a given image into K+1 classes: ${C_0} = [0, 1, \cdot \cdot \cdot, {t_1}{\rm{ -}}1], {C_1} = [{t_1}, {t_1} + 1, \cdot \cdot \cdot, {t_2}{\rm{ -}}1], {C_K} = [{t_K}, {t_K} + 1, \cdot \cdot \cdot, L{\rm{ -}}1]$.

The selection of threshold is related to the quality of the segmentation results. In this paper, Otsu and Kapur's entropy methods are adopted.

2.1.   Otsu method

Otsu is an automatic threshold selection method for image segmentation, which was proposed in 1979. According to the grayscale characteristics of images, Otsu calculates the variance of class and determines the threshold. When the maximum variance of class is obtained, the threshold returned by the objective function is called the optimal threshold.

Equations (4)–(6) represent the probabilities of the class occurrence, the class mean levels, and the total mean level of the original image, respectively.

Then the total variance among the classes is:

When ${\sigma ^2}({t_1}, {t_2}, \cdot \cdot \cdot, {t_K})$ takes the maximum value, $({t_1}^{\rm{*}}, {t_2}^{\rm{*}}, \cdot \cdot \cdot, {t_k}^{\rm{*}})$ is the optimal thresholding group of Otsu method.

2.2.   Kapur's entropy method

In thresholding segmentation methods, Kapur's entropy method introduces the "entropy" of information theory into the segmentation. According to the additivity of entropy, the total entropy of the segmented image is:

where ${{{p}}_{{i}}}$ is the distribution probability of the ith gray value, ${{{P}}_{{k}}}$ is the probability of each class.

Kapur's entropy method finds the optimal threshold values based on maximizing the total entropy. The optimal threshold is determined by the following equation:

3.   Ant lion optimizer

3.1.   Basic concepts

Ant lion optimizer is a novel swarm intelligent optimization algorithm. By simulating the process of antlion preying on ants in nature, the practical optimization problem is solved. The antlion uses its jaw to dig a cone-shaped pit in sand. After digging the trap, the antlion hides underneath the bottom of the cone. Random walks of ants may fall into it. Once an ant falls into trap, the antlion throws sand to the edge of the pit and preys on it. After the antlion eats prey, it rebuilds its trap for the next hunt. Figure 1 shows several antlions and cone-shaped pits with different sizes. The details of the ALO algorithm are discussed as follows.

Figure 1.  Antlions and cone-shaped pits with different sizes ^[28].

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3.2.   Mathematical model

Since ants move randomly in nature, the following equation is established to simulate the random movement of ants.

where the ${{cumsum}}$ function evaluates the cumulative value of an array, ${{r}}({{t}})$ function is defined as follows:

where t shows the number of iterations in this study, ${{rand}}$ is a random number that belongs to [0, 1].

In order to make random walks of ants in the search space, the following equation is needed to normalize Eq (11).

where ${{{a}}_i}$ denotes the minimum of random walk array X(t), ${{{b}}_i}$ denotes the maximum of random walk array X(t), ${{c}}_i^t$ denotes the lower boundary of ith space at tth iteration, and ${{d}}_i^t$ denotes the upper boundary of ith space at tth iteration.

The ants move randomly around the antlion, and the boundary of the area is affected by the position of the antlion. The calculation equations of ${{c}}_i^t$ and ${{d}}_i^t$ are as follows:

where ${{c}}_i^t$ denotes the lower boundary at tth iteration, and ${{d}}_i^t$ is the upper boundary at tth iteration. ${{Antlion}}_j^t$ shows the position of the jth antlion at tth iteration by the roulette wheel selection.

Once the ant enters the trap, in order to prevent it from escaping, the antlion immediately digs out the sand outside the hole to make the ant slide into the bottom of the hole. This process can be seen as the decreasing radius of the ant random walk. The equations are as follows:

where I is the ratio of boundary contraction, and its equation is defined as follows:

where t is the current iteration, T is the maximum of iterations. ω is a fixed value, which can adjust the speed of ant moving to antlion.

According to the elite strategy, the antlion with the highest fitness value is considered as an elite, and the elite can affect the random walks of all ants. The antlion and the elite affect ant walking path. The ant's position update equation is as follows:

where ${{R}}_A^t$ is an ant random walks around an antlion selected by roulette wheel, ${{R}}_E^t$ is this ant random walks around the elite.

If the fitness of the updated ant is better than that selected antlion, which means that the ant is caught and eaten by the antlion. Then the position of the antlion is updated to this position of ant. The two equations are used as follows:

where ${{Ant}}_i^t$ shows the ith ant with the best fitness value at tth iteration, and f is the fitness function value.

4.   Proposed methods

ALO algorithm has drawbacks of falling easily into local optimum and lower search accuracy. In this section, a modified ALO algorithm is proposed. MALO uses opposition-based learning strategy to generate opposite solutions, which is helpful to search more effective regions. And then, MALO maximizes Otsu and Kapur's entropy methods to determine the optimal threshold.

4.1.   Opposition based learning

Tizhoosh et al. proposed the concept of opposition-based learning in 2005. The main idea of this strategy is to generate opposite solutions. By comparing opposite solutions with current solutions, excellent individuals can enter the next generation. Mathematically, the strategy is defined as follows:

Suppose $x = \left({x}_{1}, {x}_{2}, \dots, {x}_{D}\right)$ is a point in the D-dimensional search space (can be regarded as a feasible solution), ${x}_{j} = \left[{a}_{j}, {b}_{j}\right], j = \mathrm{1, 2}, \dots, D$, and its corresponding opposite point $\widetilde{x} = \left({\widetilde{x}}_{1}, {\widetilde{x}}_{2}, \dots, {\widetilde{x}}_{D}\right)$ can be defined as:

The fitness values of the current solution and the opposite solution are calculated. By comparison, the solution with the optimal fitness value is preserved.

4.2.   MALO algorithm

ALO algorithm has the advantages of simple principle, fewer parameter settings and so on. It also has the problems of slower convergence speed, falling easily into the local optimum, and lower search accuracy. In order to improve the exploration and exploitation of the ALO algorithm, OBL strategy is introduced in the native ALO. The probability of convergence to the global optimum is increased. For each iteration, the position of ant $Ant_i^t$ is obtained by Eq (19). However, there may be a possibility that $Ant_i^t$ is opposite or near the optimal position in the search space. Therefore, after each iteration, OBL is applied to generate the opposite solution $\widetilde{An{t}_{i}^{t}}$. The equation is as follows:

where ub denotes the upper bound and lb denotes the lower bound.

The fitness values of the new position and the original position are compared. After the evaluation, the position with high fitness values are retained. After this process, the modification algorithm has more search attempts in each iteration ^[51,52].

The time complexity of MALO is given based on four factors such as the number of search agents N, the number of dimension D, the maximum number of iterations T, the cost of function F. In the initialization process, the time complexity is O(N). The time complexity of sorting mechanism is O(N × logN). The time complexity of function evaluation is O(T × N × F). The time complexity is expressed as O(T × N × D) for the updating the positions. The time complexity of the updating phase by the OBL is O(T × N × D). The overall time complexity of MALO is O(N ×(1 + logN + T ×(F + 2D))).

4.3.   The proposed MALO based multilevel thresholding method

The process of finding the optimal threshold is actually to find the optimal solution. However, it has high time complexity when dealing with multilevel thresholds. In order to achieve efficiency, it is entirely possible to use the modified ALO algorithm to do this. The basic steps are described as follows:

Firstly, test images in JPG format are read and histograms are obtained. The number of search agents and maximum number of iterations are initialized. MALO is implemented considering two different objective functions: Otsu and Kapur's entropy. Then, the fitness of initial population is calculated. The main loop begins with the second iteration. The updating position of ant is determined by a selected antlion by the roulette wheel and the elite. OBL strategy is applied to the obtained position of ant for generating the opposite solution. The fitness of original position and opposite position of ant are calculated and compared. The individual with high fitness value is preserved. If the fitness of ant is better than the antlion, then the position of antlion will be updated to the position of ant. This process is repeated until the maximum number of iterations is completed. The position of elite represents the optimal thresholds. The segmentation is carried out based on the obtained thresholds. Finally, the values of the evaluation measures and the segmented images are output. The pseudo code and the flowchart of MALO algorithm based multilevel thresholding are provided in Algorithm 1 and Figure 2, respectively.

Figure 2.  Flowchart of MALO algorithm based multilevel thresholding.

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5.   Experiments

In this section, in order to evaluate the quality of image segmentation based on MALO, a series of experiments are conducted. Firstly, Section 5.1 indicates the parameter settings of comparison algorithms, test images selected in the experiment, and operating environment. Section 5.2 introduces the metrics used to evaluate the image segmentation performance in the experiment. Section 5.3 uses IEEE CEC2017 benchmark functions to validate the effectiveness of MALO. Section 5.4 compares MALO with some traditional algorithms. The experimental data are analyzed, and the performance of image segmentation based on various algorithms is evaluated. Furthermore, Section 5.5 compares MALO with some improved algorithms. The future research is also conducted.

5.1.   Experimental materials

In this paper, 10 color images are selected from the Berkeley University database ^[53] for performance analysis. Figure 3 shows the original test images and the corresponding histograms. All images are in JPG format with a size of 481 × 321 pixels. Each algorithm runs each image 30 times separately. The number of threshold K includes: 4, 6, 8, 10, and 12.

Figure 3.  Original test images and histograms. (Line a represent images; line b represent histograms.).

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In order to prove the superiority of the MALO algorithm, 7 traditional algorithms and 4 improved algorithms which have been proposed and widely applied to multilevel thresholding segmentation are selected for comparisons, including SSA ^[17], MVO ^[54], DA ^[19], FPA ^[18], PSO ^[55], SCA ^[34], MABC ^[56], IDSA ^[57], WOA-TH ^[58], and BDE ^[59]. These comparison algorithms have different search strategies and mathematical equations. The maximum of iterations for all algorithms is 500 and the population size is 25. We follow the same parameters in the original papers. The main parameters of various algorithms are shown in Table 1.

Table 1.  Parameters for the compared algorithms.

Algorithm	Parameters	Value
SSA	Balance coefficient c1	[0, 2]
	Random number c2, c3	[0, 1]
	Switch possibility	0.5
MVO	Wormhole Existence Probability	[0.2, 1]
	Travelling Distance Rate	[0, 1]
	Random number r1, r2, r3	[0, 1]
DA	Inertial weight ω	[0.5, 0.9]
	Seperation weight	[0, 0.2]
	Alignment weight	[0, 0.2]
	Cohesion weight	[0, 0.2]
	Food factor	[0, 2]
	Enemy factor	[0, 0.1]
FPA	Switch possibility	0.4
	Lévy constant β	1.5
PSO	Maximum inertia weight	0.9
	Minimum inertia weight	0.4
	Learning factors c1, c2	2
	Maximum velocity	+120
	Minimum velocity	−120
SCA	Movement direction r1	[0, 2]
	Movement distance r2	[0, 2π]
	Random weight r3	[0, 2]
	Random number r4	[0, 1]
	Switch possibility	0.5
ALO	Switch possibility	0.5
MABC	Random number r	[0, 1]
IDSA	Random number r	[0, 1]
WOA-TH	Parameter a	[0, 2]
	Constant b	1
	Random number l	[−1, 1]
	Constant a0	13
	Initial value G0	40
BDE	Number of objectives	1
	Number of constraints	0
	Number of decision variables	4
	Scaling factor	0.5
	Crossover probability	0.2

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All the experimental series were carried out on MATLAB R2016b, and the computer was configured as Intel(R) Core(TM) i5-4210U CPU @1.70 GHz, using Microsoft Windows 10 system.

Algorithm 1. Pseudo code of MALO algorithm based multilevel thresholding.
1	Input the image and calculate components of the histogram.
2	Initialize parameters: SearchAgents_no (the number of search agents), T (maximum number of iterations).
3	Calculate the fitness of initial ants and antlions;
4	Find the best antlions and assume it as the elite;
5	While t < T
6	For each ant
7	Select an antlion using Roulette wheel;
8	Update c and d using Eqs (16) and (17);
9	Create a random walk and normalize it using Eqs (11) and (13);
10	Update the position of ant using Eq (19);
11	End for
12	For each the position of ant
13	Generate the opposite solution of the position of ant using Eq (22);
14	Calculate the fitness of original position and opposite position of ant;
15	Compare fitness values and keep ant fitness and position with high fitness value;
16	End for
17	Update antlion positions and finesses based of the ants Eq (20);
18	Update the position of elite if any antlions becomes fitter than it;
19	t = t + 1;
20	End while
21	Return elite fitness and position, which elite position represents the optimal thresholds.
22	Output the values of the evaluation measures and the segmented images.

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5.2.   Evaluation measurements

This paper evaluates the quality of image segmentation from the following five aspects:

1) Fitness value. Since Otsu and Kapur's entropy methods are maximization problem, the fitness values are expected to be as large as possible. The optimal fitness values show that the algorithm has high accuracy and convergence performance.

2) PSNR. It is an objective evaluation measure based on pixel error. A higher PSNR value indicates that the quality of the distorted image is better. However, it is based on the error between corresponding pixels and does not consider the visual characteristics of human eyes. Its calculation equation is as follows:

where L represents the scale range of the image. For an 8-bit image, L = 255. MSE is the mean square error between the original image and the processed image.

where M × N is the size of the image, ${{R}}({{m, n}})$ represents the gray value of coordinates at the reference image (m, n), and ${{I}}({{m, n}})$ represents the gray value of coordinates at the distorted image (m, n).

3) SSIM. It is an objective evaluation measure based on structural similarity. It measures the image similarity from brightness, contrast, and structure. SSIM value range is [0, 1]. If the value is closer to 1, the image distortion is smaller. It is defined as follows:

where ${{{U}}_R}$ and ${{{U}}_I}$ are the average gray values of the original image R and the segmented image I, respectively. $\sigma _R^2$ and $\sigma _I^2$ represent the variance of image R and image I, respectively. $\sigma _{RI}^{}$ is the covariance of image R and image I. ${C_1} = (0.01L)_{}^2$, ${C_2} = (0.03L)_{}^2$.

4) FSIM. Based on SSIM, researchers have proposed a new evaluation measure, namely feature similarity algorithm (FSIM). We use two complementary features of phase congruency (PC) and gradient magnitude (GM) to calculate FSIM.

where Ω is the pixel field of the entire image, ${S_L}(x)$ represents the similarity value of each position x, and $P{C_m}(x)$ denotes the phase consistency measure.

where ${S_{PC}}(x)$ is the similarity measure of phase consistency, ${S_G}(x)$ represents the similarity measure of gradient magnitude, and $\alpha$, $\beta$ are both constants.

where ${T_1}$ and ${T_2}$ are positive constants.

5) Computational time. The smaller the value, the faster the algorithm execution speed.

5.3.   Comparison with traditional algorithms on IEEE CEC2017 benchmark functions

In this subsection, 29 IEEE CEC2017 benchmark functions are chosen to check the efficiency of algorithms. We skip "F2" of IEEE CEC2017 because of its unstable behavior. These functions are divided into four groups: unimodal (F1–F3), multimodal (F4–F10), hybrid (F11–F20), and composition (F21–F30). Furthermore, the relevant composition, dimension, range limitation and optimal position of 29 functions can be found in ^[43]. Meanwhile, all experiments are conducted 30 times.

In MALO, the OBL strategy can developed more in the later search period. Compared with the native ALO, it has excellent exploration and exploitation. For the OBL strategy, putting it into ALO as a strategy can greatly improve the convergence and high efficiency. The performance of algorithms is evaluated according to the mean value (Mean) and standard deviation (Std). The stability of each model is evaluated by Std value. Meanwhile, the best results has been highlighted in boldface in Table 2. From the table above, we can observe that MALO based method gives the satisfied results in general. For example, in the unimodal and multimodal functions, the proposed method gives better results in 10 out of 18 cases (9 functions and 2 indexes). In terms of hybrid functions, the MALO based method outperforms in 12 out of 20 cases (10 functions and 2 indexes) for others. In the composition functions, the proposed method gives better results in 10 out of 20 cases (10 functions and 2 indexes). All the other algorithms show a certain difference with MALO based method. The experimental results above are effectively proved the superior performance of proposed method. The ability to avoid local optimization has enhanced. Thus, it can be said that the proposed method in this paper is more effective than competitors in 29 benchmark functions, so this paper combines MALO with multilevel thresholding segmentation method to improve the image segmentation accuracy.

Table 2.  Comparison of the mean and standard deviation of fitness values obtained.

F		SSA	MVO	DA	FPA	PSO	SCA	ALO	MALO
F1	Mean	2.7525 × 103	2.0775 × 104	5.3030 × 107	9.4246 × 107	2.3768 × 103	1.1165 × 109	1.6205 × 103	2.2691 × 102
	Std	3.1853 × 103	1.0204 × 104	1.3048 × 108	1.6194 × 108	3.3853 × 103	2.6690 × 108	1.6927 × 103	7.5223 × 102
F3	Mean	3.0002 × 102	3.0015 × 102	3.3792 × 103	5.6230 × 103	3.0009 × 102	3.0174 × 103	4.5012 × 102	4.4652 × 102
	Std	8.4151 × 10−2	7.5858 × 10−2	3.5353 × 103	3.7208 × 103	7.7137 × 10−2	1.6524 × 103	3.7837 × 102	3.1829 × 102
F4	Mean	4.0989 × 102	4.0702 × 102	4.2856 × 102	4.6977 × 102	4.0507 × 102	4.6709 × 102	4.1395 × 102	4.0394 × 102
	Std	16.908	9.3281	29.903	61.297	1.2334	30.876	22.338	12.248
F5	Mean	5.2912 × 102	5.2264 × 102	5.1732 × 102	5.6206 × 102	5.4292 × 102	5.5799 × 102	5.2180 × 102	5.1692 × 102
	Std	12.497	1.1788 × 10	8.4145	21.327	14.890	6.6091	13.640	2.8811
F6	Mean	6.1533 × 102	6.0237 × 102	6.0125 × 102	6.3945 × 102	6.1021 × 102	6.2361 × 102	6.1562 × 102	6.7956 × 102
	Std	8.9433	3.1079	1.4272	16.075	8.8947	5.4162	8.8988	10.159
F7	Mean	7.4500 × 102	7.3257 × 102	7.3766 × 102	7.9322 × 102	7.3056 × 102	7.8595 × 102	7.5048 × 102	7.2403 × 102
	Std	15.007	12.483	14.458	26.384	12.387	10.193	26.572	2.3596
F8	Mean	8.2630 × 102	8.2696 × 102	8.1554 × 102	8.4529 × 102	8.2131 × 102	8.4537 × 102	8.2771× 102	8.1001 × 102
	Std	11.690	12.498	7.2712	16.236	7.9025	8.7128	14.163	9.4471
F9	Mean	1.0897 × 103	9.0116 × 102	9.2457 × 102	1.7066 × 103	9.6607 × 102	1.0671 × 103	1.1272 × 103	1.0417 × 103
	Std	2.5134 × 102	2.8801	51.037	6.1484 × 102	1.1193 × 102	81.732	2.2796 × 102	1.8741 × 102
F10	Mean	1.8446 × 103	1.7723 × 103	1.7989 × 103	2.1907 × 103	1.9995 × 103	2.5054 × 103	2.0639 × 103	1.2226 × 103
	Std	2.8235 × 102	2.8547 × 102	3.4047 × 102	3.9008 × 102	2.9524 × 102	2.0358 × 102	3.1110 × 102	1.7148 × 102
F11	Mean	1.1840 × 103	1.1325 × 103	1.2913 × 103	1.2604 × 103	1.1388 × 103	1.2494 × 103	1.2125 × 103	9.3895 × 104
	Std	71.184	27.254	8.0087 × 102	1.1285 × 102	2.7432 × 105	76.249	74.386	24.745
F12	Mean	3.1659 × 106	1.9237 × 106	8.5333 × 105	5.3131 × 106	2.8460 × 109	3.6304 × 107	2.9647 × 106	2.2571 × 104
	Std	3.9918 × 106	2.4011 × 106	1.0164 × 106	5.2872 × 106	1.4432 × 109	4.6673 × 107	3.6635 × 106	3.1055 × 104
F13	Mean	1.7372 × 104	1.2349 × 104	1.6552 × 104	2.3449 × 104	3.2613 × 108	8.9513 × 104	1.3896 × 104	1.1517 × 104
	Std	1.2611 × 104	9.7419 × 103	9.0887 × 103	1.8794 × 104	2.7709 × 108	8.0007 × 104	1.2201 × 104	7.8833 × 103
F14	Mean	3.3621 × 103	3.0338 × 103	4.8484 × 103	2.8067 × 103	2.8688 × 103	2.3311 × 103	2.6070 × 103	2.3278 × 103
	Std	2.7150 × 103	2.3148 × 103	1.8854 × 103	1.4364 × 103	2.1263 × 103	1.0895 × 103	1.6260 × 103	1.2880 × 103
F15	Mean	6.2001 × 103	3.3924 × 103	6.4284 × 103	9.6586 × 103	3.9125 × 103	3.7996 × 103	1.3375 × 104	3.0564 × 103
	Std	4.2086 × 103	3.5797 × 103	5.0026 × 103	7.7162 × 103	3.7024 × 103	2.3791 × 103	1.0871 × 104	2.1255 × 103
F16	Mean	1.8063 × 103	1.8309 × 103	1.7338 × 103	1.9840 × 103	1.8428 × 103	1.8126 × 103	1.8928 × 103	1.8066 × 103
	Std	1.4760 × 102	1.6725 × 102	1.2125 × 102	1.4716 × 102	1.2492 × 102	80.085	1.6074 × 102	1.0356 × 102
F17	Mean	1.7831 × 103	1.7871 × 103	1.7693 × 103	1.8044 × 103	1.7796 × 103	1.7897 × 103	1.7795 × 103	1.7359 × 103
	Std	38.227	56.931	33.562	52.636	59.130	14.372	39.757	34.260
F18	Mean	1.9046 × 104	1.7527 × 104	2.4433 × 104	1.5703 × 104	1.6595 × 104	4.2187 × 105	1.6102 × 104	1.6102 × 104
	Std	1.3350 × 104	1.1493 × 104	1.5706 × 104	1.2231 × 104	1.3320 × 104	4.6787 × 105	1.3045 × 104	1.2885 × 104
F19	Mean	9.3321 × 103	4.8206 × 103	1.1236 × 104	9.2778 × 104	5.1293 × 103	1.0034 × 104	1.6927 × 104	1.9544 × 103
	Std	7.1553 × 103	4.0080 × 103	6.8870 × 103	2.0401 × 105	3.8240 × 103	8.8662 × 103	1.2359 × 104	3.1306 × 103
F20	Mean	2.1580 × 103	2.1181 × 103	2.1072 × 103	2.1974 × 103	2.1351 × 103	2.1393 × 103	2.1520 × 103	2.1017 × 103
	Std	77.357	71.982	59.164	81.489	81.620	37.232	76.695	1.1244 × 102
F21	Mean	2.2892 × 103	2.3067 × 103	2.3146 × 103	2.3260 × 103	2.3033 × 103	2.2951 × 103	2.3181 × 103	2.2919 × 103
	Std	58.652	43.950	23.354	56.359	69.965	67.337	23.092	23.025
F22	Mean	2.3032 × 103	2.4325 × 103	2.3387 × 103	2.3737 × 103	2.3168 × 103	2.3923 × 103	2.3019 × 103	2.2108 × 103
	Std	1.5330	4.0570 × 102	1.5916 × 102	3.0758 × 102	86.302	36.970	14.139	4.3619
F23	Mean	2.6246 × 103	2.6213 × 103	2.6263 × 103	2.6544 × 103	2.6993 × 103	2.6630 × 103	2.6330 × 103	2.6235 × 103
	Std	9.4651	8.4456	11.398	27.680	38.621	9.4154	13.016	8.6164
F24	Mean	2.7448 × 103	2.7399E+03	2.7422E+03	2.7726E+03	2.7821E+03	2.7773E+03	2.7541E+03	2.7242E+03
	Std	48.315	45.915	47.575	55.733	1.1838 × 102	59.112	13.296	10.259
F25	Mean	2.9316 × 103	2.9322 × 103	2.9355 × 103	2.9755 × 103	2.9227 × 103	2.9816 × 103	2.9352 × 103	2.9316 × 103
	Std	30.687	28.163	23.579	53.181	23.221	24.991	28.272	2.7704 × 102
F26	Mean	2.9852 × 103	3.0412 × 103	3.1910 × 103	3.5113 × 103	3.2078 × 103	3.1238 × 103	3.0689 × 103	3.0597 × 103
	Std	2.7007 × 102	3.8042 × 102	3.9782 × 102	4.9123 × 102	5.0084 × 102	37.746	2.7801 × 102	2.5490 × 102
F27	Mean	3.0942 × 103	3.0936 × 103	3.0975 × 103	3.1538 × 103	3.1493 × 103	3.1084 × 103	3.1028 × 103	3.0346 × 103
	Std	3.6648	3.4486	6.0913	55.897	67.675	4.4917	15.597	1.4249
F28	Mean	3.3187 × 103	3.3510 × 103	3.3579 × 103	3.4196 × 103	3.2028 × 103	3.3398 × 103	3.3863 × 103	3.1170 × 103
	Std	1.6379 × 102	1.3529 × 102	95.702	1.6486 × 102	78.068	90.179	1.3401 × 102	1.0508 × 102
F29	Mean	3.2573 × 103	3.2282 × 103	3.2212 × 103	3.4234 × 103	3.2563 × 103	3.2629 × 103	3.2707 × 103	3.1694 × 103
	Std	81.947	83.366	55.368	1.3273 × 102	82.282	33.745	94.979	22.526
F30	Mean	5.4626 × 105	5.5507 × 105	1.0112 × 106	2.2409 × 106	6.8210 × 104	1.7827 × 106	7.0103 × 105	1.5116 × 104
	Std	5.8213 × 105	6.5747 × 105	1.3632 × 106	2.9983 × 106	6.4354 × 104	1.3111 × 106	2.1161 × 106	7.2776 × 104

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 | Show Table

DownLoad: CSV

5.4.   Comparison with traditional algorithms on Berkeley images

The fitness value can be used as an index to evaluate the performance of segmentation method. All the experiments are conducted 30 times on 10 color images. Tables 3 and 4 respectively show average fitness values using Otsu and Kapur's entropy compared with other algorithms. In every line, the maximum is in bold. From these tables, it can be seen that MALO algorithm finds the maximum fitness values more times than other algorithms. However, the same objective function value obtained by several algorithms also occasionally occurs when the threshold value is small (such as K = 4, 6, and 8). Overall, the OBL strategy can improve the calculation accuracy of ALO algorithm, which helps to find the global optimal solution and improve the overall performance.

Table 3.  Comparison of fitness values obtained with each algorithm for Otsu.

Image	K	SSA	MVO	DA	FPA	PSO	SCA	ALO	MALO
Cactus	4	2126.2412	2126.2412	2126.2412	2084.2192	2126.2085	2091.2043	2126.1077	2126.2412
	6	2188.8026	2188.7881	2188.7749	2152.9126	2180.5976	2151.3710	2188.6529	2188.8076
	8	2213.1588	2213.1207	2210.6763	2185.1975	2206.7101	2177.4155	2212.8736	2213.2108
	10	2224.0745	2224.9921	2224.4972	2202.9660	2224.8409	2205.3385	2223.8535	2225.0378
	12	2228.0349	2231.4043	2227.1859	2208.4757	2230.3736	2209.0205	2230.9917	2231.8810
Kangaroo	4	1114.7964	1114.7964	1114.7964	1088.7665	1114.7783	1088.6203	1114.7451	1114.7964
	6	1164.7339	1164.7235	1162.2148	1131.7231	1157.9995	1142.5799	1164.5055	1164.7463
	8	1186.9998	1187.2317	1186.4981	1164.0753	1181.4079	1157.1404	1187.0901	1187.3921
	10	1195.5800	1198.8061	1198.1305	1175.6658	1195.7200	1172.3154	1197.6616	1199.0721
	12	1201.3621	1204.3553	1204.0964	1189.4752	1203.7897	1186.9269	1204.8168	1205.6190
Temple	4	1510.8080	1511.3099	1511.3110	1481.4555	1511.2952	1484.9151	1511.1720	1511.3110
	6	1562.1584	1551.2497	1562.1657	1539.3204	1547.2460	1528.3151	1562.0323	1562.1677
	8	1575.4345	1581.9379	1580.1512	1558.9731	1577.2711	1552.2760	1578.5870	1582.0010
	10	1585.0462	1589.3769	1588.9537	1566.9471	1583.4601	1562.6224	1589.3855	1590.0709
	12	1593.4902	1592.3625	1594.7102	1577.6113	1589.2313	1577.5018	1595.2350	1596.7043
Flower	4	2319.2628	2319.2628	2319.2628	2300.8905	2319.2628	2305.0308	2319.2088	2319.2628
	6	2373.7148	2373.9784	2373.9666	2349.7530	2366.7255	2348.8170	2373.7751	2374.0062
	8	2398.3260	2397.7703	2398.6865	2373.7415	2393.6744	2378.1142	2398.0974	2398.7056
	10	2408.6487	2409.1083	2410.1377	2392.7685	2409.5320	2393.4470	2409.9581	2410.1748
	12	2415.5456	2416.1915	2413.2197	2401.7458	2413.6013	2402.8505	2416.6995	2417.4773
Mountain	4	1922.6304	1922.6304	1922.6304	1880.8725	1922.6304	1899.0075	1922.5604	1922.6304
	6	1966.3537	1969.5924	1969.5227	1950.3434	1964.7413	1937.2954	1969.3259	1969.6134
	8	1987.6882	1987.6512	1987.6006	1971.0006	1982.4353	1963.1189	1987.3940	1989.0684
	10	1998.2296	1998.3989	1999.2217	1976.2590	1995.3262	1980.4772	1998.6023	1999.5736
	12	2002.3212	2003.5176	2003.4479	1991.7908	2002.3326	1987.1898	2003.1927	2004.4332
Tree	4	4836.5287	4836.5254	4836.5287	4811.7023	4836.5184	4799.5909	4836.4226	4836.5287
	6	4910.3426	4910.3170	4910.3328	4881.3483	4899.1851	4889.6357	4909.9888	4910.3389
	8	4938.5519	4938.7280	4939.0548	4895.7628	4932.5126	4897.8287	4939.0439	4939.2738
	10	4954.4191	4954.3250	4954.3494	4931.0184	4950.5741	4925.6878	4953.6297	4954.7408
	12	4961.5040	4962.0370	4961.7003	4947.5680	4958.4948	4933.2448	4961.9255	4962.8681
Horse	4	4169.9500	4169.9500	4169.9475	4146.0648	4169.9500	4125.8875	4169.9152	4169.9500
	6	4223.2790	4226.2869	4226.2925	4206.4679	4226.2960	4184.3739	4226.1384	4226.2981
	8	4251.0736	4247.9571	4250.7202	4224.2255	4242.3477	4224.8735	4251.0627	4251.0806
	10	4264.1067	4264.0484	4263.6881	4245.5168	4263.0609	4242.4543	4263.8776	4264.5464
	12	4271.0552	4270.2470	4270.4589	4253.0366	4270.9270	4255.1561	4269.9287	4272.7303
Bridge	4	4386.0155	4386.0155	4386.0155	4348.0212	4386.0155	4364.6402	4385.8679	4386.0155
	6	4448.8450	4456.6582	4456.6941	4430.7839	4456.6543	4416.6522	4448.6228	4456.6941
	8	4483.9318	4476.1230	4481.9799	4459.7426	4480.7550	4436.7087	4480.4869	4484.0957
	10	4495.8304	4494.1137	4497.7496	4475.7876	4494.2483	4472.8251	4497.6619	4498.1770
	12	4505.0626	4504.6934	4502.9179	4488.9690	4504.8794	4485.6536	4504.6902	4506.5159
Pilot	4	3854.8970	3854.8970	3854.8970	3838.0151	3854.8930	3807.6575	3854.8127	3854.8970
	6	3902.7853	3896.5334	3902.7747	3884.5667	3902.7796	3869.1994	3902.6187	3902.7731
	8	3917.0447	3917.7421	3920.6198	3892.5037	3918.0121	3895.6690	3920.4228	3923.5580
	10	3931.0115	3928.4714	3933.5071	3915.8877	3931.1832	3904.4969	3932.5873	3934.2915
	12	3937.8965	3936.9459	3936.6517	3916.5100	3935.4087	3916.0317	3939.2200	3940.3098
Dog	4	2249.9855	2249.9839	2249.9855	2231.2675	2249.9855	2233.1946	2249.9484	2249.9855
	6	2299.7269	2299.6899	2298.6466	2270.5848	2287.9683	2277.7186	2299.5470	2299.7446
	8	2320.5275	2317.0263	2320.4939	2297.8192	2303.3155	2296.9113	2320.2281	2320.5319
	10	2326.4485	2329.6067	2330.9585	2311.9971	2328.1692	2306.4227	2330.4593	2330.9965
	12	2334.7496	2336.2099	2334.3909	2323.5986	2332.0819	2320.2905	2335.7878	2337.4348

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DownLoad: CSV

Table 4.  Comparison of fitness values obtained with each algorithm for Kapur's entropy.

Image	K	SSA	MVO	DA	FPA	PSO	SCA	ALO	MALO
Cactus	4	18.5843	18.5843	18.5843	18.3930	18.5829	18.4259	18.5832	18.5843
	6	23.8329	23.8233	23.8386	23.2412	23.8389	23.2857	23.8364	23.8420
	8	28.4940	28.3247	28.5120	27.0680	28.4911	27.3938	28.4814	28.5198
	10	32.6224	32.0489	32.7875	30.4517	32.8282	30.7148	32.7883	32.8463
	12	36.7255	35.3654	36.6688	34.7456	36.7983	34.2975	36.6721	36.8450
Kangaroo	4	18.9363	18.9353	18.9361	18.6549	18.9352	18.7771	18.9350	18.9363
	6	24.4683	24.4414	24.4720	23.6425	24.4648	24.0457	24.4563	24.4753
	8	29.3790	29.2133	29.3699	28.7933	29.4014	28.2712	29.4026	29.4202
	10	33.8064	33.4514	33.8602	32.6267	33.1534	32.0603	33.8653	33.9054
	12	37.8707	37.1153	37.9876	36.2125	38.0001	35.4540	37.9065	38.0410
Temple	4	17.8159	17.8201	17.8061	17.4725	17.8046	17.5013	17.8195	17.8204
	6	22.9388	22.7544	22.9388	22.2007	22.8940	22.0680	22.9246	22.9388
	8	27.5032	27.2493	27.4436	25.9640	27.4909	25.5465	27.5208	27.5351
	10	31.6211	30.6718	31.6425	29.5279	31.6160	28.9053	31.6706	31.7574
	12	34.2789	33.0925	35.3472	31.7622	34.7704	32.2631	35.3818	35.6116
Flower	4	18.7000	18.6993	18.7000	18.4447	18.6996	18.4765	18.6980	18.7005
	6	24.0481	24.0186	24.0485	23.6039	24.0429	23.3247	24.0441	24.0511
	8	28.7647	28.6438	28.7955	27.6104	28.7721	27.7280	28.7727	28.8057
	10	33.0270	32.9200	33.1672	31.2963	33.1582	31.3512	33.1673	33.1976
	12	36.8699	35.9637	37.1214	34.8362	37.0372	34.9773	36.9291	37.1549
Mountain	4	17.7231	17.7035	17.7213	17.5421	17.7372	17.4362	17.7390	17.7213
	6	23.1283	23.0802	23.0902	22.5402	23.1001	22.4117	23.1173	23.1119
	8	27.9637	27.6405	27.9315	26.6905	27.9354	26.4147	27.9302	27.9679
	10	32.1404	31.9221	32.3451	30.9813	32.2561	30.0080	32.3415	32.4426
	12	36.3399	34.9350	36.3823	34.0005	35.6920	33.6967	36.1384	36.4707
Tree	4	18.9965	18.9962	18.9965	18.8465	18.9961	18.8254	18.9953	18.9965
	6	24.3933	24.4095	24.4100	23.8731	24.3889	23.4245	24.4083	24.4149
	8	29.2846	28.9004	29.2918	27.8265	29.2753	27.6207	29.2581	29.2936
	10	33.5397	33.0809	33.6613	31.4879	33.6439	31.7828	33.5491	33.6785
	12	37.3776	36.7041	37.4570	35.2858	37.5764	34.8717	37.5111	37.6312
Horse	4	18.6614	18.6259	18.6230	18.3914	18.6252	18.5251	18.6614	18.6619
	6	24.0609	23.8743	24.0802	23.2431	24.0604	22.8699	24.0675	24.0806
	8	28.8403	28.5613	28.8907	27.9542	28.8416	27.6730	28.8914	28.8992
	10	33.2142	32.3696	33.2125	31.1950	33.2741	30.7256	33.2480	33.3135
	12	36.8467	35.6548	37.0718	34.9857	37.0695	33.8890	37.1782	37.3216
Bridge	4	18.1906	18.1436	18.1902	18.0033	18.1903	18.0580	18.1903	18.1907
	6	23.5631	23.5510	23.5679	22.8880	23.5610	22.8246	23.5649	23.5682
	8	28.2604	27.9986	28.2930	27.0830	28.2859	26.7516	28.2786	28.3023
	10	32.5876	32.3366	32.5480	30.9047	32.5740	30.5593	32.5281	32.6189
	12	36.0703	35.4806	36.4991	33.5753	36.4588	33.0662	36.4400	36.5351
Pilot	4	17.9368	17.9352	17.9362	17.6027	17.9362	17.7058	17.9355	17.9168
	6	23.0182	22.9648	23.0443	21.9322	23.0365	21.8927	23.0025	23.0447
	8	27.6539	27.4187	27.6678	26.2966	27.6452	25.7373	27.6307	27.6723
	10	31.6001	30.3305	31.7457	30.5445	31.7701	29.3977	31.7568	31.8639
	12	35.3121	34.3457	35.4310	32.7740	35.6276	31.7852	35.5945	35.7388
Dog	4	18.5258	18.5246	18.4850	18.2690	18.5254	18.2825	18.5244	18.5261
	6	23.6922	23.6586	23.7386	22.7559	23.7121	22.7675	23.7319	23.7420
	8	28.3767	28.0194	28.3553	27.0852	28.3862	26.7027	28.3751	28.4079
	10	32.4951	31.5916	32.6709	31.2171	32.6231	29.8432	32.6604	32.6944
	12	36.4563	36.2405	36.3900	34.1968	35.8826	33.0948	36.5074	36.6079

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DownLoad: CSV

In order to make the experimental data more intuitive, the following experiments are conducted. The relevant convergence curve and boxplot are drawn. As shown in Figure A1 and A2, the evolution curve reflects the convergence speed and the accuracy of the algorithm, thus reflecting the overall performance of the algorithm. It can be seen from the convergence curve that the MALO algorithm can obtain the approximate optimal solution, which further improves the overall performance. For Table A2(d), (h), MALO algorithm and DA algorithm eventually approach the same function value. But for the rest of graphs, it is clear that the MALO algorithm is superior to other algorithms in the optimization process. MALO algorithm can reach the maximum fitness value at nearly the 100th iteration, which is earlier than other algorithms. This phenomenon indicates that the convergence rate of algorithm is improved. On the whole, it also proves that by introducing the OBL strategy, the stability of the algorithm is enhanced. As shown in Figures 4 and 5, the boxplot can effectively reflect the stability of the algorithm. Taking the two images of cactus and kangaroo as examples, it can be seen that the boxplot of MALO algorithm has the most flat shape, the highest position, and no bad points. This shows that the MALO algorithm has the highest stability compared with other algorithms by analysis of the 30 fitness values obtained.

Figure 4.  Boxplots for fitness values using Otsu.

DownLoad: Full-Size Img PowerPoint

Figure 5.  Boxplots for fitness values using Kapur's entropy.

DownLoad: Full-Size Img PowerPoint

Tables A2 and A3 show PSNR values of Otsu and Kapur's entropy respectively. When the PSNR value is larger, the distortion of the segmented image is smaller. Through the data, it can be seen vertically that the PSNR value of high threshold is larger than that of low threshold. We see horizontally that the PSNR value of MALO algorithm is larger than other algorithms in most cases, especially at high threshold level. Tables A4 and A5 show SSIM values of Otsu and Kapur's entropy, respectively. Tables A6 and A7 show FSIM values of Otsu and Kapur's entropy, respectively. When the values of SSIM value and FSIM value are closer to 1, the images before and after segmentation are more similar and the segmentation effect is better. Comparing SSIM value and FSIM value, MALO algorithm is larger and closer to 1 than other algorithms. The maximum value is marked in bold. Most of the evaluation metrics obtained by MALO algorithm are optimal. The modified algorithm makes the image segmentation effect better.

Tables 5 and 6 show the average computational time (in second) of each algorithm using Otsu and Kapur's entropy, respectively. MALO enhanced the native ALO in many aspects, such as fitness value, PSNR, SSIM, and FSIM. However, it can be found from Tables 5 and 6 that MALO has the relatively high time consumption compared to the other algorithms. In fact, the high consumption is mainly caused by the high computational cost of the native ALO. The proposed improvement results in increasing the computational time of MALO as well. In short, in order to improve the overall performance of algorithm, it cannot guarantee to obtain optimal parameters in all cases.

Table 5.  The average computational time (in second) of each algorithm using Otsu.

Image	K	SSA	MVO	DA	FPA	PSO	SCA	ALO	MALO
Cactus	4	0.4100	0.8700	1.8700	0.6900	0.7700	0.7100	1.4050	1.7200
	6	0.2500	0.7000	1.4900	0.6800	0.6700	0.6500	1.8700	2.1455
	8	0.2810	0.7800	1.5200	0.6800	0.7200	0.6800	2.3850	2.6000
	10	0.3200	0.7800	1.5600	0.7300	0.7600	0.7100	2.9545	3.2550
	12	0.3400	1.0600	1.6890	0.8630	0.9000	0.8400	4.8515	4.3270
Kangaroo	4	0.5050	0.8100	1.8420	0.6700	0.7300	0.9580	1.4200	1.5505
	6	0.2690	0.7300	1.5200	0.6800	0.7600	0.6500	1.9600	2.1995
	8	0.3100	0.8300	1.6410	0.7010	0.7500	0.7400	2.4345	2.7155
	10	0.3400	0.8500	1.6000	0.7800	0.8200	0.7400	3.0750	3.3250
	12	0.3700	0.8400	1.6000	0.7800	0.8300	0.7900	3.7580	3.8305
Temple	4	0.3700	0.8540	1.9250	0.6530	1.3210	0.6510	1.4300	1.5605
	6	0.2700	0.7600	1.5690	0.6500	0.7390	0.6510	1.9200	2.1755
	8	0.3000	0.8100	1.5800	0.7400	0.7600	0.6890	3.0805	3.5605
	10	0.4400	1.3800	2.3500	1.0690	0.7600	0.8100	3.7715	4.9285
	12	0.3600	0.8600	1.7200	0.7710	0.8000	0.7300	3.5765	4.2245
Flower	4	0.4250	1.1510	2.8120	0.8400	0.8710	0.8550	2.1855	2.2690
	6	0.2700	0.7900	1.6000	0.7200	0.7700	0.7400	2.0005	3.2575
	8	0.3860	0.9860	2.5490	1.5090	0.8630	0.7330	4.1070	4.4885
	10	0.8540	1.6520	2.4080	0.9010	1.3190	1.5640	4.8340	4.6935
	12	0.5600	1.1700	2.1900	1.1300	0.8700	1.0000	3.7055	4.0505
Mountain	4	0.4700	1.1750	2.8030	0.7110	0.9170	0.8500	2.2840	2.2155
	6	0.5170	0.9080	2.4520	0.7370	0.8370	0.7510	2.5625	2.1245
	8	0.2920	0.8200	1.7150	0.6800	0.9710	0.8810	3.3625	2.8755
	10	0.4300	0.8200	3.4100	0.7100	0.8010	0.8800	5.0305	4.2160
	12	0.4000	0.8820	1.5710	0.7900	1.1500	0.8550	4.4010	3.9205
Tree	4	0.4500	0.9200	1.9700	0.9800	1.5640	0.7900	1.6595	2.3955
	6	0.4300	1.0950	2.6590	1.7460	1.0490	1.6700	3.1700	3.5230
	8	0.3410	1.4480	2.8000	0.9750	0.7530	0.6930	2.6675	3.7390
	10	0.3740	1.2760	2.3920	0.8310	0.8920	0.8130	3.6270	3.5155
	12	0.4500	0.9390	0.9390	0.9390	0.8990	0.8510	3.9570	5.2985
Horse	4	0.4040	0.8970	1.8600	0.6840	0.7480	0.9190	1.7475	1.8105
	6	0.3140	0.8380	1.6460	0.8150	0.7450	0.6850	2.0365	2.2195
	8	0.3010	1.0490	1.8420	0.7300	0.8770	0.7740	3.2820	2.9730
	10	0.3300	0.8560	1.6410	0.7780	0.8540	0.7920	3.7315	3.8360
	12	0.3920	0.9120	1.7110	1.6600	1.6600	1.0670	4.2670	4.8615
Bridge	4	0.4200	1.9550	2.5860	1.7110	0.9140	0.7110	1.6845	1.8555
	6	0.2660	0.8010	1.5530	0.7070	1.3360	1.0980	2.8115	3.0780
	8	0.3210	0.9610	2.7830	1.0120	0.9970	0.7930	4.5400	4.8560
	10	0.4110	1.5550	2.6160	1.0420	1.6320	0.9770	5.2685	5.8515
	12	0.5330	1.2210	2.9890	1.1920	1.9340	1.1170	4.6090	4.1150
Pilot	4	0.4400	0.9200	2.3630	0.7820	1.0780	0.8350	1.8890	1.8405
	6	0.2810	1.6590	2.2270	0.7510	1.3550	0.8610	3.4105	2.8835
	8	0.4400	1.5610	2.2130	0.8350	1.0880	1.2600	3.6285	3.9075
	10	0.3700	1.0850	2.7580	1.2330	1.2590	1.3200	4.9585	5.6945
	12	0.3740	0.9200	1.7840	1.2990	1.1100	1.5060	5.2780	4.0805
Dog	4	0.4500	1.0160	2.4440	0.8390	0.8300	1.3690	1.7170	2.5915
	6	0.2750	1.3830	2.4210	1.2500	0.8100	1.3300	3.1915	3.4480
	8	0.4700	0.9450	1.5800	0.7400	0.7400	0.7510	2.4325	2.8155
	10	0.3490	0.8300	1.5390	0.7190	0.8010	0.7220	3.0855	3.5100
	12	0.3300	0.8720	1.5700	0.7600	0.8700	0.7800	3.7950	4.3600

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Table 6.  The average computational time (in second) of each algorithm using Kapur's entropy.

Image	K	SSA	MVO	DA	FPA	PSO	SCA	ALO	MALO
Cactus	4	0.6400	1.2900	1.9500	0.8000	1.6930	0.7800	1.5150	1.8455
	6	0.4700	0.8500	1.5890	0.8210	0.8910	0.7900	2.0750	2.3905
	8	0.4900	0.9500	1.6810	0.8110	0.8900	0.8080	2.4650	4.2290
	10	0.6230	1.2750	2.0900	1.0400	0.9900	0.8490	3.1220	3.6495
	12	0.5380	1.0030	1.7180	0.9570	1.0110	0.8900	3.6600	4.1195
Kangaroo	4	0.5800	0.9600	1.8620	0.8300	0.8900	1.4690	2.2225	2.3925
	6	0.9260	1.2200	2.6770	1.4180	0.9600	1.0310	3.2235	2.9170
	8	0.4800	0.8900	1.6200	0.8200	0.9000	1.1690	2.5200	3.1900
	10	0.5210	0.9200	1.6400	0.8900	0.8700	0.8400	3.0550	3.6250
	12	0.5200	0.9900	1.7500	0.8800	0.9400	0.8900	3.6400	4.1070
Temple	4	0.6100	1.6350	2.5860	1.2700	1.2480	0.9400	2.4355	2.8155
	6	0.4700	1.0400	2.3770	1.0500	1.2900	0.7900	2.0400	2.4100
	8	0.4700	0.9100	1.6800	0.8000	0.8900	0.8000	2.4900	2.9895
	10	0.5200	0.9300	1.6500	0.8600	1.0000	0.8400	3.1050	3.6095
	12	0.5700	1.0000	1.8200	0.9300	0.9100	0.8700	5.4985	4.5950
Flower	4	0.6000	1.4130	2.6960	1.0000	1.2850	1.3000	2.3625	2.8995
	6	1.0690	0.9900	2.8420	0.9500	0.9390	0.9860	2.6195	2.7010
	8	0.4800	0.9900	1.7200	0.9400	0.9200	0.8700	2.6020	3.0850
	10	0.5300	0.9700	1.8010	0.9100	0.9990	0.9600	3.2255	3.6850
	12	0.6100	1.0700	1.8100	0.9400	1.0000	1.3790	5.1945	4.5065
Mountain	4	0.5600	1.5490	1.9920	0.8570	0.8810	0.8310	1.5315	1.9575
	6	0.4410	0.9230	1.7220	0.9020	0.8820	0.8800	2.0330	2.4990
	8	0.5100	0.9710	1.7300	0.9000	0.9520	0.8420	2.5850	3.1700
	10	0.5480	1.0300	1.7900	0.9040	0.9510	0.9000	5.1080	4.0555
	12	1.0660	1.0420	1.9110	0.9610	1.0690	0.9580	3.9095	4.3645
Tree	4	0.6200	1.3020	2.8450	1.0270	1.2090	1.3510	2.2510	2.7790
	6	0.5000	1.2040	2.6420	1.3380	1.1410	0.8990	2.1775	3.1785
	8	0.5110	0.8790	1.6500	0.8300	0.8800	0.8600	2.4650	2.9350
	10	0.5000	0.9300	1.6800	0.9190	0.8500	0.9000	3.0445	3.5950
	12	0.6700	1.0090	1.8600	0.9100	0.9400	0.9400	3.7930	4.1300
Horse	4	0.6100	1.5700	3.2080	1.5370	1.6130	0.8400	2.5665	2.8115
	6	1.0800	1.2290	2.5900	0.8000	0.8100	0.9800	2.0500	2.4145
	8	0.4600	0.8900	1.6000	0.8300	0.8600	0.8900	2.6550	3.2905
	10	0.5000	0.9900	1.6400	1.1500	0.8900	0.8500	3.0550	3.6400
	12	0.5400	1.9330	2.0100	0.9800	1.0100	1.0000	3.7850	4.4105
Bridge	4	0.6000	0.9500	1.7600	0.7600	0.8100	0.7300	1.4750	1.7950
	6	0.4100	0.8400	1.5700	0.8200	0.8400	0.8000	1.9300	2.3950
	8	0.4400	0.8600	1.5900	0.8700	0.8600	0.7900	2.4900	2.9775
	10	0.4700	0.9100	1.6400	0.7900	0.9100	1.2500	3.7975	3.9840
	12	0.5230	1.0150	2.1800	0.8710	0.9340	0.9500	3.7080	4.3340
Pilot	4	0.5400	0.9400	1.7300	0.7500	1.0100	0.7700	1.4750	1.7600
	6	0.3900	0.8100	1.5500	0.8300	0.8700	0.8800	2.0940	2.5195
	8	0.4600	0.8400	1.8120	0.7760	0.9500	0.8600	2.6975	3.1400
	10	0.5650	1.1600	2.2950	0.9460	0.9790	0.9690	3.5840	4.1245
	12	0.5800	1.3060	2.3550	1.2900	1.0490	1.3350	5.6445	8.5025
Dog	4	0.6600	1.2350	3.0700	1.0100	1.0550	1.6800	2.5700	3.0600
	6	0.5050	1.0870	2.1600	0.9200	0.9200	0.8500	2.2025	2.8425
	8	0.5050	1.2550	2.9380	1.0800	1.8400	1.4900	4.5565	5.3650
	10	0.5920	1.4200	2.2400	0.9200	1.2000	0.9250	3.4000	3.9405
	12	0.5790	1.0750	1.8410	0.9500	0.9990	0.9140	3.8400	4.5330

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Table A8 denotes the PSNR, SSIM and FSIM values obtained by MALO using the Otsu and Kapur's entropy. By comparison, it can be found that the average value of the evaluation metrics obtained by using the Otsu method is higher. For selected 10 images, using the Otsu method is just recommended. Wolpert and Macerday put forward the No Free Lunch (NFL) theorem ^[60]. Of course, Otsu and Kapur's entropy methods have different theoretical foundations, so the types of images they process also have different focuses.

Tables A9 and A10 give the optimal thresholds of MALO under Otsu and Kapur's entropy at 4, 6, 8, 10, and 12 levels. Taking the "Tree" image an examples, the segmented results based on different algorithms using Otsu at 4, 6, 8, 10, and 12 levels are presented in Figure 6. Taking the "Horse" image an examples, the segmented results based on different algorithms using Kapur's entropy at 4, 6, 8, 10, and 12 levels are presented in Figure 7. Different target regions correspond to different threshold ranges. Considering the segmented images presented in Figures 6 and 7, it can be found that the images with high levels contain more information and details than that with low levels. Furthermore, the MALO based method has achieved the desired goal, because the main target areas have been efficiently identified. To sum up, the proposed method is competent for most cases and can still be considered as a competitive technique for the multilevel thresholding color image segmentation.

Figure 6.  Segmented results of "Tree" image obtained by different algorithms using Otsu at 4, 6, 8, 10, and 12 levels.

DownLoad: Full-Size Img PowerPoint

Figure 7.  Segmented results of "Horse" image obtained by different algorithms using Kapur's entropy at 4, 6, 8, 10, and 12 levels.

DownLoad: Full-Size Img PowerPoint

5.5.   Comparison with improved algorithms on Berkeley images

In this subsection, the proposed method is further compared with some improved algorithms, including MABC, IDSA, WOA_TH, and BDE. PSNR and FSIM are utilized for analysis.

For visual analysis, the PSNR values obtained are represented as a line graph in Figures 8 and 9. From the figures we can observe that the MALO based method gives the higher values in general, which indicates that the segmented image is similar to the original image. For example, in the circumstance of "Flower" image through Otsu technique (for K = 12), the PSNR values are 29.5819, 29.4498, 29.3192, 29.6828, and 30.7280 for MABC, IDSA, WOA_TH, BDE, and PSO, respectively. It also can be seen that all algorithms give the similar results when the number of thresholds is small (such as K = 4). Whereas, when the number of thresholds increase, the difference between algorithms becomes greater and the MALO based method outperforms the others. On comparing the FSIM values, which are given in Figures 10 and 11, it can be observed that the values increase as the number of the thresholds increase. In the circumstance of "Temple", "Flower", "Mountain", "Tree", "Bridge", "Pilot", and "Dog" images through Otsu technique (for K = 12), the proposed algorithm is not the best. However, the proposed method gives the highest values on most cases through Kapur's entropy (for K = 12). These results indicate the precise search ability of MALO based method, which is suitable for color image segmentation.

Figure 8.  Comparison of PSNR values for different algorithms using Otsu at 4, 6, 8, 10, and 12 levels.

DownLoad: Full-Size Img PowerPoint

Figure 9.  Comparison of PSNR values for different algorithms using Kapur's entropy at 4, 6, 8, 10, and 12 levels.

DownLoad: Full-Size Img PowerPoint

Figure 10.  Comparison of FSIM values for different algorithms using Otsu at 4, 6, 8, 10, and 12 levels.

DownLoad: Full-Size Img PowerPoint

Figure 11.  Comparison of FSIM values for different algorithms using Kapur's entropy at 4, 6, 8, 10, and 12 levels.

DownLoad: Full-Size Img PowerPoint

6.   Conclusions

In this paper, an ant lion optimizer algorithm based on opposition-based learning for multilevel thresholding color image segmentation is proposed. Among many thresholding segmentation methods, Otsu and Kapur's entropy are adopted. The proposed algorithm is used to find the optimal threshold for 10 color test images. IEEE CEC2017 benchmark functions are performed to verify the performance of the proposed algorithm. Furthermore, 7 traditional algorithms and 4 improved algorithms are selected for comparisons. The fitness value, PSNR, SSIM, FSIM, and computational time are used to evaluate the quality of segmentation. By the convergence curve and boxplot at K = 12, it can be seen that MALO algorithm can find larger objective function value more times at nearly the 100th iteration. In terms of PSNR, SSIM, and FSIM, the value obtained by the MALO algorithm is larger than other algorithms in most cases. It concludes that the segmentation performance based on MALO algorithm is superior. To sum up, a variety of experiments fully proves that MALO algorithm has higher search accuracy and convergence speed. However, high time consumption might be considered a principle limitation of this method.

In the future, the relevant research directions are given as follows:

(1) Explore to introduce other strategies and hybrid other algorithms in improving the performance of the ALO algorithm.

(2) Extend the algorithm to multi-objective problem for obtaining superior segmentation effect.

Acknowledgments

This work was supported by the Harbin Normal University doctoral research initiation fund project (XKB202014), Sanming University introduces high-level talents to start scientific research funding support project (20YG14), Guiding science and technology projects in Sanming City (2020-G-61), Educational research projects of young and middle-aged teachers in Fujian Province (JAT200618), Scientific research and development fund of Sanming University (B202009).

Conflict of interest

All authors declare no conflicts of interest in this paper.

Appendix

Table A1.  The main notations involved in this paper.

Provenance	Symbols	Paraphrase
Color images	L	The gray value
	${n_i}$	The number of pixels with gray value of i
	N	The total number of pixels
	p	The distribution probability of gray value
	K	The total number of threshold
	t	The threshold
	C	The class
	R, G, B	The three channels of color images
Otsu	$\omega$	The probabilities of class occurrence
	$\mu$	The levels of class
	${\sigma ^2}$	The total variance
Kapur's entropy	$\psi$	The total entropy
ALO	X	The array of random walk
	ub	The upper bound of parameter
	lb	The lower bound of parameter
	t	The current iteration
	T	The maximum of iterations
	I	The ratio of boundary contraction
Time complexity	O	The complexity notation
PSNR	MSE	The mean square error
SSIM	R	The original image
	I	The segmented image
	${\mu _R}, {\mu _I}$	The average gray values of image
	$\sigma _R^2, \sigma _I^2$	The variance of image
	${\sigma _{RI}}$	The covariance of image
FSIM	PC	Phase congruency
	GM	Gradient magnitude
	Ω	The entire domain of image
	${S_L}(x)$	The similarity value of each position x
	$P{C_m}(x)$	The phase consistency measure
	${S_{PC}}(x)$	The similarity measure of phase consistency
	${S_G}(x)$	The similarity measure of gradient magnitude

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Figure A1.  Convergence curves for fitness values using Otsu at 12 levels thresholding.

DownLoad: Full-Size Img PowerPoint

Figure A2.  Convergence curves for fitness values using Kapur's entropy at 12 levels thresholding.

DownLoad: Full-Size Img PowerPoint

Table A2.  Comparison of PSNR values obtained with each algorithm for Otsu.

IMAGE	K	SSA	MVO	DA	FPA	PSO	SCA	ALO	MALO
Cactus	4	19.1730	19.1730	19.1730	18.7263	19.1730	18.8974	19.1344	19.1901
	6	21.4834	21.4806	21.4819	20.6216	21.0808	20.2685	21.4733	21.4849
	8	22.9129	23.0452	22.5947	21.8482	22.5738	23.0573	22.9754	23.7403
	10	23.8232	24.1443	23.9252	23.1394	23.9100	23.8865	24.0865	24.1499
	12	24.6895	25.1475	24.8778	24.9636	24.5394	25.1646	25.0007	25.2868
Kangaroo	4	22.0643	22.0643	22.0643	20.7955	22.0643	20.4905	22.0429	22.0797
	6	24.8251	24.8350	24.5043	23.2999	24.4744	23.1015	24.8199	24.8836
	8	26.8199	27.0457	26.8403	24.3867	26.3434	24.2914	26.9047	27.0860
	10	28.1619	28.8131	28.5707	25.1187	28.1677	25.2235	28.4114	28.8186
	12	29.1767	30.0207	29.8385	27.1879	29.8151	26.9052	30.1672	30.3411
Temple	4	17.4713	17.4707	17.4713	19.7885	17.4736	17.1516	17.4005	17.6125
	6	20.7143	19.8002	20.7137	20.7876	19.7566	18.2250	20.7661	21.4589
	8	22.0492	23.5836	22.5695	20.7664	22.5250	23.8550	23.4862	23.9977
	10	23.2619	25.2421	24.2747	23.4468	23.3367	22.7675	24.8846	25.7059
	12	26.8631	26.8151	25.5113	24.5639	24.7817	26.2330	26.4459	27.5232
Flower	4	22.6832	22.6832	22.6832	21.9099	22.6832	22.2661	22.6832	22.6916
	6	25.1802	25.5484	25.5446	23.9499	25.2590	24.5962	25.5240	25.5506
	8	27.5586	27.3846	27.6921	25.3172	27.3576	26.1643	27.5337	27.6960
	10	28.6654	28.8544	29.0249	26.6791	28.8757	26.7323	29.1768	29.2169
	12	29.9882	30.1775	29.8010	28.1115	29.6455	27.8780	30.6120	30.7280
Mountain	4	19.7307	19.7307	19.7307	19.1368	19.7307	19.2754	19.7277	19.7307
	6	21.8240	22.4882	22.3866	20.9344	22.1794	21.8654	22.3347	22.5039
	8	24.8724	24.1574	24.2907	22.8823	24.0400	23.4094	24.7870	24.9053
	10	25.9744	26.1368	26.1295	24.6068	25.8506	23.8109	26.0493	26.3373
	12	27.3911	26.9209	26.9014	25.3515	26.9991	25.7124	26.8751	27.4991
Tree	4	19.9284	19.9265	19.9284	19.3506	19.9206	19.0453	19.9284	19.9364
	6	22.9219	22.9184	22.9126	21.8322	22.4339	22.4819	22.9276	22.9388
	8	25.1296	25.0004	25.0881	22.6562	24.4342	22.7555	25.1489	25.1704
	10	26.7206	26.6709	26.6389	24.1790	26.1891	24.3475	26.5608	26.7213
	12	27.5331	28.0382	27.7147	26.1871	27.2252	24.9152	27.8812	28.0724
Horse	4	19.1095	19.1095	19.1543	18.4918	19.1095	17.8797	19.1095	19.1569
	6	22.6175	22.6343	22.6083	22.4411	22.6441	20.0880	22.5318	22.8301
	8	24.8257	24.6203	24.7383	23.2636	23.7326	22.2812	24.5913	24.8543
	10	26.7272	26.7701	26.3299	23.8301	26.2501	23.7805	26.4699	26.8845
	12	28.0067	27.6999	28.1864	25.0419	28.0623	24.4077	27.5665	28.3129
Bridge	4	18.7684	18.7684	18.7684	18.1883	18.7684	18.3216	18.7562	18.7684
	6	21.0341	21.5192	21.5142	20.6458	21.5142	19.4138	21.0529	21.5346
	8	23.5582	22.9642	23.4355	21.6761	23.3575	20.6855	23.3521	23.7010
	10	25.0709	24.8332	25.2117	22.7421	24.8889	23.3572	25.3971	25.4265
	12	26.3616	26.8858	26.3203	25.5030	26.4849	25.2994	26.1879	27.0756
Pilot	4	16.9918	16.9918	16.9918	16.9571	16.9915	16.9918	17.0028	17.6971
	6	19.4806	19.6603	19.3935	18.8999	19.4660	19.4742	19.4398	21.5230
	8	22.1137	21.7970	21.8114	19.8872	20.9936	20.1921	21.9259	22.4562
	10	23.3937	23.4926	22.5532	23.4677	22.5761	22.8645	23.6086	24.1912
	12	24.6032	24.8457	25.4417	23.3403	23.4735	24.3050	25.6425	25.8213
Dog	4	19.9346	19.9569	19.9346	20.2544	19.9346	18.6387	19.9734	19.9346
	6	22.5690	22.6725	22.3348	21.6363	21.7981	20.9528	22.5891	22.6726
	8	24.3105	24.3265	24.3176	23.0185	22.9836	22.5716	24.3533	24.3548
	10	24.9193	26.0109	25.7454	24.4410	25.5648	23.1901	25.8904	26.4961
	12	26.7167	28.0094	26.3712	24.9053	26.4391	25.6498	27.6947	28.1328

---

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Table A3.  Comparison of PSNR values obtained with each algorithm for Kapur's entropy.

IMAGE	K	SSA	MVO	DA	FPA	PSO	SCA	ALO	MALO
Cactus	4	17.1463	17.1849	17.1849	16.6326	17.1605	16.5963	17.1918	17.2250
	6	18.7054	19.5152	18.8374	17.7723	18.9734	18.9692	18.9353	20.9242
	8	20.2196	21.8061	21.8129	20.2720	20.7186	20.1477	20.8937	23.1098
	10	21.6755	23.5236	23.5035	22.9740	23.3426	23.5817	23.6783	25.6436
	12	24.5328	25.7488	24.2717	25.8229	25.6387	22.2231	25.5971	26.7329
Kangaroo	4	18.7559	18.7559	18.7529	16.9273	18.7030	17.9415	18.7714	18.8067
	6	21.2093	21.9397	21.7227	20.3904	21.8062	20.1191	22.1098	22.3708
	8	23.8181	24.5562	23.9062	20.5802	24.5744	22.1074	24.4808	24.6322
	10	25.1196	26.0125	25.7934	25.0967	25.7309	22.8701	25.9331	26.1974
	12	26.6277	27.4952	27.4380	24.5722	27.3277	24.0530	27.2209	28.0349
Temple	4	16.7418	18.6069	17.9079	17.7575	17.8108	16.4613	18.5579	18.6105
	6	20.3140	20.4895	20.3140	20.7483	20.5577	21.6953	20.6648	23.1506
	8	24.9708	24.0553	23.2965	22.2220	24.5715	23.2979	25.0443	25.1273
	10	25.8405	25.8930	26.0409	23.4840	26.5620	21.8980	26.5010	26.7757
	12	27.0259	26.4958	27.5263	24.8266	27.3391	24.0635	27.5766	28.4027
Flower	4	21.4262	21.4353	21.4262	21.0771	21.4030	21.7291	21.3824	21.4046
	6	23.9954	24.0070	24.0260	22.9845	23.9935	23.7137	24.0223	24.2923
	8	25.0019	25.3825	25.3936	24.4758	25.6350	25.5636	25.5517	26.3947
	10	26.1749	27.0175	26.8094	25.4329	26.9897	26.1739	26.8538	27.6016
	12	26.8429	28.2241	27.8388	25.9058	27.9865	27.9984	27.8198	29.2750
Mountain	4	15.7308	16.1695	16.1695	15.1291	14.6360	17.2397	14.6863	17.7501
	6	19.1293	19.7275	19.3198	20.0548	19.8595	18.9344	19.2375	20.2658
	8	22.2621	22.4482	22.2780	20.3443	22.2996	20.2389	22.1739	23.7160
	10	20.8677	25.1887	23.4748	22.1128	24.6158	22.2042	24.5972	26.2667
	12	25.4993	26.3821	26.2452	24.7312	26.5979	22.1953	26.4684	26.6949
Tree	4	19.3878	19.4098	19.3878	19.4510	19.3660	19.0814	19.3485	19.3878
	6	21.7283	21.9982	21.9410	20.7787	21.7496	20.5382	21.9919	22.0355
	8	23.5510	23.6198	23.4812	22.0054	23.5766	22.2770	23.5404	24.2661
	10	24.8234	25.5643	25.4307	23.3183	25.4128	22.1914	25.4025	25.7360
	12	26.1558	26.7973	26.3433	23.9995	26.5906	24.8922	26.5045	26.8461
Horse	4	18.9208	19.7557	19.0344	18.9208	19.6738	19.4317	19.5801	19.7788
	6	21.2581	21.6962	21.6519	19.7265	21.3967	19.8505	21.6610	21.6974
	8	23.8699	23.6078	24.2314	22.0431	23.2680	21.4611	23.4581	24.2427
	10	25.5023	24.5116	25.5495	23.2916	25.8501	22.6324	26.0431	26.1268
	12	26.4346	25.3050	27.0205	24.1636	27.1689	24.0270	26.9024	27.4180
Bridge	4	17.7375	17.7101	17.7433	17.6562	17.7064	17.2277	17.7680	18.3564
	6	21.0395	21.0300	21.0468	20.0621	21.0612	19.8616	21.0352	21.1004
	8	22.8402	23.4100	23.4820	21.0220	23.3430	21.3364	23.4706	23.6124
	10	24.6074	24.9201	24.1982	23.1209	24.7082	23.6599	24.6209	25.3739
	12	25.4895	26.0580	26.3086	23.1938	26.7399	24.1204	26.4986	27.4320
Pilot	4	15.9241	15.8597	15.9653	15.5965	15.8932	15.9792	15.9532	16.0238
	6	19.9635	19.1615	20.4713	19.5345	20.6783	20.2829	19.8317	20.7123
	8	22.5976	22.0836	22.9972	22.6697	23.0674	22.7085	22.8982	23.1598
	10	24.5888	20.7618	24.7292	23.9268	24.7256	24.0374	24.5571	24.8228
	12	25.6096	24.6046	26.7532	24.9263	25.9880	25.6817	26.4241	27.1095
Dog	4	18.3708	18.4828	17.6137	16.0679	18.2476	18.2657	18.4844	18.2605
	6	20.0477	20.7865	20.6360	19.9191	20.6773	18.4516	20.7274	21.9672
	8	22.3956	22.5129	22.5608	22.6757	22.5483	22.5758	22.3802	24.5205
	10	23.4554	25.3079	24.3555	24.4406	25.4561	21.6361	24.8465	26.3186
	12	25.8139	26.8848	26.0117	23.2895	26.5957	23.0829	26.4860	27.2748

---

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Table A4.  Comparison of SSIM values obtained with each algorithm for Otsu.

IMAGE	K	SSA	MVO	DA	FPA	PSO	SCA	ALO	MALO
Cactus	4	0.6001	0.6001	0.6001	0.5854	0.6015	0.6001	0.5984	0.6063
	6	0.6955	0.6961	0.6950	0.6716	0.6801	0.6568	0.6956	0.6963
	8	0.7438	0.7515	0.7268	0.7278	0.7361	0.7507	0.7487	0.7904
	10	0.7684	0.7838	0.7732	0.7495	0.7745	0.7814	0.7807	0.8391
	12	0.8012	0.8123	0.8157	0.8272	0.7927	0.8022	0.8050	0.8456
Kangaroo	4	0.7735	0.7735	0.7735	0.7156	0.7738	0.7046	0.7725	0.7735
	6	0.8609	0.8615	0.8515	0.8179	0.8525	0.8033	0.8608	0.8627
	8	0.9018	0.9066	0.9029	0.8415	0.8958	0.8431	0.9041	0.9084
	10	0.9219	0.9325	0.9288	0.8581	0.9244	0.8658	0.9262	0.9331
	12	0.9352	0.9466	0.9426	0.9032	0.9449	0.9032	0.9474	0.9495
Temple	4	0.5829	0.5829	0.5829	0.5906	0.5825	0.5492	0.5793	0.6798
	6	0.7234	0.6884	0.7242	0.7222	0.6836	0.6239	0.7249	0.7263
	8	0.7702	0.8149	0.7873	0.7265	0.7843	0.8102	0.8121	0.8152
	10	0.8069	0.8561	0.8329	0.7886	0.8084	0.7752	0.8480	0.8643
	12	0.8823	0.8883	0.8606	0.8254	0.8453	0.8546	0.8753	0.8917
Flower	4	0.4655	0.4655	0.4655	0.4194	0.4655	0.4655	0.4656	0.4916
	6	0.5704	0.6806	0.6789	0.4849	0.6696	0.6800	0.6765	0.7406
	8	0.7883	0.7946	0.7974	0.6136	0.7867	0.7725	0.7911	0.8000
	10	0.8139	0.8286	0.8219	0.7771	0.8206	0.7406	0.8268	0.8294
	12	0.8364	0.8550	0.8310	0.8422	0.8372	0.8203	0.8644	0.8682
Mountain	4	0.6987	0.6987	0.6987	0.6715	0.6987	0.6987	0.6976	0.7081
	6	0.7471	0.7758	0.7691	0.7237	0.7698	0.7761	0.7705	0.7932
	8	0.8293	0.8166	0.8127	0.7688	0.8101	0.8206	0.8311	0.8322
	10	0.8442	0.8536	0.8476	0.8254	0.8524	0.8261	0.8520	0.8603
	12	0.8682	0.8650	0.8626	0.8273	0.8731	0.8511	0.8617	0.8780
Tree	4	0.6406	0.6410	0.6406	0.6162	0.6419	0.6406	0.6412	0.6915
	6	0.7535	0.7538	0.7535	0.6682	0.7420	0.7454	0.7538	0.7546
	8	0.7919	0.7890	0.7901	0.7176	0.7465	0.7515	0.7954	0.7960
	10	0.8229	0.8272	0.8263	0.7932	0.8190	0.8009	0.8258	0.8281
	12	0.8372	0.8505	0.8416	0.8307	0.8387	0.8142	0.8555	0.8579
Horse	4	0.7206	0.7206	0.7203	0.6791	0.7206	0.7155	0.7201	0.7206
	6	0.7543	0.7624	0.7613	0.7617	0.7611	0.7700	0.7591	0.7744
	8	0.8102	0.8062	0.8103	0.7689	0.7945	0.7622	0.8114	0.8117
	10	0.8501	0.8510	0.8505	0.8026	0.8454	0.8162	0.8523	0.8534
	12	0.8709	0.8769	0.8739	0.8233	0.8757	0.8161	0.8686	0.8793
Bridge	4	0.7286	0.7286	0.7286	0.7286	0.7286	0.7293	0.7280	0.7398
	6	0.8032	0.8180	0.8180	0.8022	0.8190	0.7728	0.8030	0.8193
	8	0.8626	0.8512	0.8566	0.8374	0.8604	0.8323	0.8620	0.8691
	10	0.8830	0.8909	0.8903	0.8447	0.8912	0.8886	0.8956	0.8993
	12	0.9021	0.9140	0.9031	0.8986	0.9041	0.9063	0.9087	0.9226
Pilot	4	0.7296	0.7296	0.7296	0.7222	0.7296	0.7296	0.7299	0.7399
	6	0.7854	0.7857	0.7839	0.7540	0.7852	0.7849	0.7855	0.8224
	8	0.8420	0.8385	0.8383	0.7887	0.8218	0.7875	0.8390	0.8424
	10	0.8720	0.8651	0.8607	0.8555	0.8570	0.8401	0.8737	0.8788
	12	0.8905	0.8996	0.8951	0.8581	0.8726	0.8668	0.8947	0.9017
Dog	4	0.7003	0.7031	0.7003	0.7003	0.7003	0.6563	0.6999	0.7428
	6	0.7700	0.7755	0.7624	0.7684	0.7514	0.7104	0.7694	0.7756
	8	0.8188	0.8190	0.8190	0.7735	0.7848	0.7632	0.8213	0.8240
	10	0.8314	0.8572	0.8510	0.8116	0.8470	0.7804	0.8544	0.8655
	12	0.8691	0.8928	0.8643	0.8246	0.8654	0.8566	0.8886	0.8948

---

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Table A5.  Comparison of SSIM values obtained with each algorithm for Kapur's entropy.

IMAGE	K	SSA	MVO	DA	FPA	PSO	SCA	ALO	MALO
Cactus	4	0.4811	0.4831	0.4831	0.4466	0.4818	0.4497	0.4835	0.4858
	6	0.5552	0.5975	0.5613	0.5064	0.5697	0.7353	0.5657	0.5690
	8	0.6254	0.7141	0.7143	0.6989	0.6473	0.6168	0.6574	0.7681
	10	0.7156	0.7719	0.7926	0.7684	0.7661	0.8080	0.7761	0.8677
	12	0.8238	0.8537	0.7953	0.8778	0.8524	0.7282	0.8510	0.8873
Kangaroo	4	0.6080	0.6080	0.6078	0.5032	0.6058	0.5645	0.6083	0.6116
	6	0.7320	0.7635	0.7531	0.6689	0.7565	0.6881	0.7690	0.7782
	8	0.8263	0.8498	0.8304	0.7028	0.8493	0.7534	0.8476	0.8521
	10	0.8632	0.8867	0.8798	0.8570	0.8798	0.7602	0.8843	0.8913
	12	0.8976	0.9150	0.9128	0.8380	0.9111	0.8155	0.9096	0.9254
Temple	4	0.5367	0.6145	0.5713	0.5753	0.5657	0.5101	0.6117	0.6149
	6	0.6933	0.6996	0.6933	0.7056	0.6976	0.7261	0.7014	0.7784
	8	0.8252	0.8034	0.7796	0.7400	0.8173	0.7918	0.8318	0.8465
	10	0.8469	0.8719	0.8522	0.7703	0.8665	0.7311	0.8648	0.8787
	12	0.8733	0.8941	0.8845	0.8153	0.8796	0.8086	0.8915	0.9021
Flower	4	0.3948	0.3985	0.3948	0.3969	0.3976	0.3976	0.3950	0.3994
	6	0.4916	0.5129	0.4916	0.4830	0.4925	0.4923	0.4917	0.5247
	8	0.5171	0.5986	0.5385	0.5047	0.5538	0.5388	0.5387	0.6431
	10	0.5589	0.6425	0.5845	0.5280	0.5968	0.5964	0.5885	0.6606
	12	0.5737	0.6445	0.6168	0.5823	0.6299	0.7444	0.6410	0.7643
Mountain	4	0.4651	0.5563	0.5563	0.4348	0.4186	0.5804	0.4192	0.6240
	6	0.6590	0.6916	0.6673	0.7108	0.6961	0.6653	0.6674	0.7131
	8	0.7628	0.7797	0.7716	0.6980	0.7612	0.7505	0.7695	0.8259
	10	0.7035	0.8433	0.7862	0.7690	0.8408	0.8062	0.8135	0.8792
	12	0.8537	0.8681	0.8645	0.8367	0.8718	0.7863	0.8668	0.9085
Tree	4	0.5888	0.5906	0.5888	0.6081	0.5874	0.5888	0.5866	0.6264
	6	0.6716	0.6898	0.6728	0.6909	0.6708	0.6817	0.6770	0.7219
	8	0.7080	0.7157	0.7126	0.6873	0.7171	0.7503	0.7129	0.7737
	10	0.7271	0.7594	0.7631	0.7740	0.7656	0.6862	0.7653	0.8214
	12	0.7646	0.7871	0.7772	0.7040	0.7822	0.7977	0.8101	0.8792
Horse	4	0.6486	0.6486	0.6637	0.6911	0.6976	0.6675	0.6835	0.7070
	6	0.7287	0.7486	0.7478	0.6954	0.7414	0.7463	0.7487	0.7802
	8	0.7789	0.7930	0.7922	0.7668	0.8010	0.7618	0.8035	0.8335
	10	0.8221	0.8388	0.8247	0.7824	0.8276	0.7849	0.8376	0.8697
	12	0.8410	0.8699	0.8567	0.7938	0.8691	0.8089	0.8598	0.8979
Bridge	4	0.6914	0.6927	0.6902	0.6790	0.6918	0.6897	0.6946	0.7176
	6	0.7909	0.7974	0.7957	0.7433	0.7926	0.7813	0.7979	0.8053
	8	0.8336	0.8532	0.8522	0.7775	0.8505	0.8427	0.8564	0.8820
	10	0.8688	0.8812	0.8598	0.8144	0.8717	0.8636	0.8878	0.9160
	12	0.8836	0.9044	0.9271	0.8634	0.9124	0.8837	0.9116	0.9393
Pilot	4	0.7676	0.7675	0.7665	0.7440	0.7644	0.7686	0.7688	0.7512
	6	0.8059	0.8241	0.8201	0.7920	0.8220	0.8259	0.7979	0.8317
	8	0.8584	0.8617	0.8621	0.8436	0.8620	0.8585	0.8619	0.8672
	10	0.8859	0.8857	0.8839	0.8781	0.8852	0.8787	0.8908	0.8937
	12	0.9031	0.9045	0.9100	0.8703	0.9036	0.8707	0.9009	0.9124
Dog	4	0.6534	0.6534	0.6218	0.5749	0.6510	0.6471	0.6582	0.6599
	6	0.7021	0.7305	0.7252	0.7381	0.7333	0.6472	0.7290	0.7797
	8	0.7768	0.7801	0.7867	0.8020	0.7815	0.7875	0.7823	0.8486
	10	0.8039	0.8538	0.8278	0.8369	0.8574	0.7654	0.8338	0.9002
	12	0.8576	0.8860	0.8706	0.8378	0.8754	0.8326	0.8720	0.8889

---

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Table A6.  Comparison of FSIM values obtained with each algorithm for Otsu.

IMAGE	K	SSA	MVO	DA	FPA	PSO	SCA	ALO	MALO
Cactus	4	0.8104	0.8104	0.8104	0.7856	0.8104	0.7991	0.8103	0.8104
	6	0.8679	0.8673	0.8676	0.8305	0.8585	0.8280	0.8676	0.8681
	8	0.8967	0.8978	0.8936	0.8625	0.8912	0.8869	0.8974	0.8980
	10	0.9133	0.9153	0.9143	0.8868	0.9137	0.9029	0.9148	0.9153
	12	0.9250	0.9261	0.9264	0.9001	0.9218	0.9111	0.9272	0.9287
Kangaroo	4	0.8293	0.8293	0.8293	0.8005	0.8297	0.7913	0.8284	0.8293
	6	0.8998	0.8999	0.8962	0.8585	0.8904	0.8642	0.9000	0.9001
	8	0.9325	0.9328	0.9325	0.8860	0.9246	0.8884	0.9330	0.9335
	10	0.9474	0.9521	0.9534	0.8914	0.9454	0.9055	0.9504	0.9541
	12	0.9607	0.9649	0.9638	0.9358	0.9594	0.9352	0.9630	0.9653
Temple	4	0.7391	0.7391	0.7391	0.7435	0.7388	0.7130	0.7374	0.7840
	6	0.8178	0.7984	0.8181	0.8137	0.7968	0.7606	0.8189	0.8203
	8	0.8420	0.8693	0.8497	0.8270	0.8491	0.8671	0.8709	0.8722
	10	0.8628	0.8929	0.8805	0.8614	0.8615	0.8481	0.8888	0.8994
	12	0.9185	0.9135	0.8967	0.8820	0.8854	0.8994	0.9085	0.9301
Flower	4	0.7838	0.7838	0.7838	0.7604	0.7838	0.7726	0.7838	0.7841
	6	0.8402	0.8413	0.8406	0.8177	0.8356	0.8142	0.8404	0.8418
	8	0.8829	0.8810	0.8864	0.8461	0.8790	0.8524	0.8828	0.8874
	10	0.9041	0.9100	0.9110	0.8639	0.9092	0.8791	0.9114	0.9120
	12	0.9246	0.9269	0.9191	0.8891	0.9195	0.8912	0.9333	0.9347
Mountain	4	0.8006	0.8006	0.8006	0.7658	0.8006	0.7918	0.7999	0.8006
	6	0.8426	0.8561	0.8550	0.8225	0.8494	0.8335	0.8552	0.8563
	8	0.8893	0.8892	0.8866	0.8570	0.8824	0.8672	0.8901	0.8903
	10	0.9074	0.9094	0.9083	0.8789	0.9042	0.8793	0.9078	0.9142
	12	0.9217	0.9217	0.9214	0.8919	0.9211	0.8941	0.9182	0.9253
Tree	4	0.8055	0.8056	0.8055	0.7873	0.8060	0.8055	0.8058	0.8166
	6	0.8562	0.8566	0.8562	0.8218	0.8479	0.8448	0.8562	0.8568
	8	0.8826	0.8825	0.8825	0.8408	0.8680	0.8423	0.8833	0.8840
	10	0.9038	0.9038	0.9041	0.8713	0.8981	0.8729	0.9026	0.9055
	12	0.9149	0.9203	0.9201	0.8984	0.9098	0.8789	0.9186	0.9208
Horse	4	0.8217	0.8217	0.8216	0.7960	0.8217	0.8099	0.8213	0.8217
	6	0.8506	0.8504	0.8503	0.8472	0.8505	0.8388	0.8490	0.8506
	8	0.8849	0.8801	0.8848	0.8555	0.8687	0.8423	0.8827	0.8852
	10	0.9120	0.9082	0.9053	0.8773	0.9053	0.8708	0.9063	0.9122
	12	0.9269	0.9240	0.9279	0.8886	0.9254	0.8801	0.9202	0.9303
Bridge	4	0.8399	0.8399	0.8399	0.8276	0.8399	0.8276	0.8397	0.8399
	6	0.8894	0.8971	0.8968	0.8706	0.8968	0.8613	0.8894	0.8974
	8	0.9235	0.9150	0.9223	0.8951	0.9203	0.8849	0.9202	0.9241
	10	0.9368	0.9350	0.9389	0.9098	0.9346	0.9192	0.9397	0.9398
	12	0.9478	0.9493	0.9470	0.9332	0.9469	0.9341	0.9453	0.9499
Pilot	4	0.7854	0.7854	0.7854	0.7765	0.7854	0.7736	0.7854	0.7855
	6	0.8294	0.8260	0.8290	0.8070	0.8292	0.8290	0.8295	0.8345
	8	0.8623	0.8623	0.8619	0.8278	0.8531	0.8277	0.8617	0.8625
	10	0.8890	0.8819	0.8829	0.8710	0.8788	0.8547	0.8898	0.8918
	12	0.9033	0.9122	0.9079	0.8714	0.8905	0.8787	0.9101	0.9148
Dog	4	0.7911	0.7918	0.7911	0.7911	0.7911	0.7584	0.7911	0.7943
	6	0.8497	0.8519	0.8467	0.8274	0.8347	0.8092	0.8494	0.8521
	8	0.8822	0.8793	0.8823	0.8436	0.8571	0.8452	0.8827	0.8834
	10	0.8932	0.9052	0.9049	0.8720	0.9002	0.8584	0.9050	0.9109
	12	0.9147	0.9277	0.9127	0.8882	0.9109	0.8965	0.9235	0.9288

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