Oppositional symbiotic organisms search optimization for multilevel thresholding of color image

Applied Soft Computing Journal 82 (2019) 105577

Contents lists available at ScienceDirect

Applied Soft Computing Journal journal homepage: www.elsevier.com/locate/asoc

Oppositional symbiotic organisms search optimization for multilevel thresholding of color image ∗

Falguni Chakraborty a , , Debashis Nandi a , Provas Kumar Roy b a b

Department of Computer Science & Engineering, National Institute of Technology, Durgapur, West Bengal, India Department of Electrical Engineering, Kalyani Government Engineering College, Kalyani, West Bengal, India

highlights

graphical

abstract

• OSOS applied in the field of multilevel image thresholding.

• The proposed method is applied to find optimum thresholds value for color image. • The efficiency of the proposed OSOS is compared with other algorithms. • Statistical analysis is performed to check the robustness of the proposed algorithm.

article

info

Article history: Received 26 July 2017 Accepted 5 April 2019 Available online 13 June 2019 Keywords: Multi-level thresholding Nature inspired optimization Symbiotic organisms search Color image segmentation Opposition based learning Entropy

a b s t r a c t Selection of optimal threshold is the most crucial issue in threshold-based segmentation. In case of color image, this task is become challenging, because conventional color image segmentation has computational complexity and also it suffers from lack of accuracy. Various techniques such as threshold based, region growing, edge detection, graph cut, pixel classification, neural network, active contour, gray level co-occurrence matrix are proposed so far for image segmentation in the literature. Out of them, threshold-based segmentation is popular for its simplicity. To address the problem of color image segmentation, we propose an enhanced version of metaheuristic optimization algorithm called Opposition based Symbiotic Organisms Search (OSOS) to solve multilevel image thresholding technique for color image segmentation by introducing opposition based learning concepts to accelerate the convergence rate and enhance the performance of standard symbiotic organisms search (SOS). The performance of the proposed OSOS based algorithm is investigated thoroughly and compared with some existing techniques like Cuckoo Search (CS), BAT algorithm (BAT), artificial bee colony (ABC) and particle swarm optimization (PSO). The comparison is made by applying the algorithm to a set of color images taken from a well-known benchmark dataset (Berkeley Segmentation Dataset (BSDS)) and some of the color images collected for the COCO dataset. It is observed from the results that the performance of the OSOS based algorithm is promising with respect to standards SOS and others in terms of the values of objective functions as well as the values of some well-defined quality metrics such as peak signal-to-noise ratio (PSNR), structure similarity index (SSIM) and feature similarity index

∗ Corresponding author. E-mail address: [email protected] (F. Chakraborty). https://doi.org/10.1016/j.asoc.2019.105577 1568-4946/© 2019 Elsevier B.V. All rights reserved.

2

F. Chakraborty, D. Nandi and P.K. Roy / Applied Soft Computing Journal 82 (2019) 105577

(FSIM). The results of the proposed algorithm may encourage the scientists and engineers to apply it into pattern recognition problems. © 2019 Elsevier B.V. All rights reserved.

1. Introduction Color image segmentation play an important role in recognition, understanding, and interpretation of different objects of an image or video and hence used in various applications such as medical diagnosis, pattern recognition systems, remote sensing etc. There exist many image segmentation techniques which are based on color or gray level thresholding, region growing, edge detection, graph cut, pixel classification, neural network, active contour, fuzzy set etc. Recently deep neural networks have shown great potential in semantic segmentation tasks, bringing state-of-the-art performance on large segmentation datasets. In [1] deep convolutional nets were used for semantic image segmentation. In [2], a sixlayer convolutional neural network was exposed to classifying cells in histopathology images by both k-nearest neighbor and a support vector machine approach. But the recent review by Guo et al. [3] of this field pointed out some of the limitation or weakness of this method, which includes doubt regarding working of this method on general imagery, unavailability of labeled datasets in some cases, and also costly GPU based system is required for computation to implement the deep neural network. Because of this color or gray-level thresholding based segmentation method has got importance for its relative simplicity and so many algorithms have been developed since the last few decades [4–6] in this area. Thresholding based segmentation may be performed by computing optimal bi-level or multi-level threshold values. Bi-level thresholding is capable of dividing the whole image only into two homogeneous regions based on intensity level, texture etc., whereas multilevel thresholding partitions the whole image into multiple regions. Hence multi-level thresholding has become more popular than bi-level thresholding in image segmentation applications. The main challenge of thresholding based image segmentation is to find out the optimized threshold values for partitioning the different regions of an image with better accuracy. In general, the optimized threshold values are computed by optimizing a well-defined objective function. Different objective functions are proposed in the literature for this purpose. Entropy now-a-days has been considered as a suitable objective function in the threshold optimization problems. Recent literature shows that it is possible to obtain a number of threshold values which optimize the entropy of the image histogram and is used for decomposing different meaningful regions of the image [6]. Optimization is a huge topic in mathematics and encompasses various types of optimization methods. Classical techniques include Newton’s method, quadratic programming, interior point method, gradient based methods and many more. Beside this, during last few decades many nature inspired metaheuristic algorithms, such as genetic algorithm (GA) [7], improved GA [8], particle swarm optimization (PSO) [9], artificial bee colony (ABC) [10,11], modified ABC [12], ant colony optimization (ACO) [13], cuckoo search (CS) [14] and honey bee mating optimization (HBMO) [15], Social Spider Optimization (SSO) [16], Flower Pollination [16] etc. have been developed and successfully applied to solve multilevel thresholding problems. This is because the classical techniques generally depend on the derivative of the objective function; hence they fail to provide global optimal solution for non-differentiable objective functions. Metaheuristic

optimization techniques are efficient in these cases and may give near global optimal solution to a problem. In view of this, biologically inspired metaheuristic optimization algorithms have got tremendous importance for computing optimal threshold values in multi-thresholding based image segmentation. Some good references in this direction are: Akay [11], a study on PSO and ABC algorithms for multilevel thresholding; Bhandari et al. [12], a multilevel thresholding algorithm for segmentation of gray-level satellite image using modified artificial bee colony algorithm (MABC); Raja et al. [17], improved PSO based multi-level thresholding for cancer infected breast thermal images; Salima et al. [16], Social Spiders Optimization (SSO) and Flower Pollination algorithm for multilevel image thresholding; Agrawal et al. [14], Tsallis entropy based optimal multilevel thresholding using cuckoo search algorithm; Manikandan et al. [18], multilevel thresholding for segmentation of medical brain images using real coded genetic algorithm, Bakhshali et al. [19], segmentation of color lip images using BFO , He and Huang [20], Modified firefly algorithm to find the optimal threshold value; M. Abd El Aziz et al. [21] Whale Optimization Algorithm (WOA) and Moth-Flame Optimization (MFO) to determine the optimal multilevel thresholding for image segmentation. Khairuzzaman and Chaudhury [22], Gray Wolf Optimizer for multilevel thresholding and image segmentation etc. A.K. Bhandari et al. [23], a novel color image multilevel thresholding based segmentation using nature inspired optimization algorithms. Symbiotic Organism Search (SOS) [24] based optimization is another promising nature inspired metaheuristic optimization algorithm where the symbiotic relationship between two organisms for survival and circulation in the ecosystem is utilized to find out the optimal values of an objective function. Since the beginning, SOS has been successfully applied several times to solve different optimization problems in different fields of science and engineering. In 2016, Cheng et al. [25] applied SOS for optimizing multiple resources leveling in multiple projects using discrete symbiotic organism search. The time cost-labor utilization tradeoff problem has been solved by Tran et al. by using SOS. [26]. Eki et al. have used SOS for solving the capacitated vehicle routing problem [27]. Abdullahi et al. have developed SOS-based task scheduling in cloud computing environment [28]. Prasad and Mukherjee have used SOS for solving for optimal power flow in power system with FACTS devices [29]. SOS has been used by Dosoglu et al. for economic/emission dispatch problem in power systems [30]. Panda and Pani have presented hybrid SOS algorithm with an adaptive penalty function to solve multi-objective constrained optimization problems [31]. However, SOS has shown its potentiality to solve various optimization problems but in some cases it stuck in to the local optima. In order to reduction the effect of this problem for SOS this paper, proposes different variants of SOS algorithm using opposition-based learning (OBL) [32] to find the optimal threshold in the field of multilevel color image thresholding to explored its performance in image segmentation by comparing it with some well-established algorithms. The basic perception of opposition-based learning (OBL) was first introduced by Tizhoosh [32], the key concept of OBL is to search the fitter candidate solution by simultaneous evolution of an estimate and its resultant opposite estimate which is closer to the global optimum. The central opposition theorem [33] states that the probability that the opposite of a candidate solution is

F. Chakraborty, D. Nandi and P.K. Roy / Applied Soft Computing Journal 82 (2019) 105577

closer to the global optimum is higher than the probability of a second random guess. Many researchers have utilized the concept of OBL in the combination of different soft computing algorithm, and these include Particle Swarm Optimization (PSO) [34], Artificial Bee Colony (ABC) [35], krill herd algorithm (KH) [36] and Differential Evolution (DE) [37] to solve real life complex optimization problem. In this paper, OBL has been utilized to accelerate the convergence rate as well as enhance the performance of standard SOS. The rest of the paper is structured as follows: Section 2 represents the mathematical model of thresholding by defining Otsu’s between class variance (BCV), Kapur’s and Tsallis entropy objective functions. Section 3 gives a brief description of PSO, ABC, CS, BAT algorithms which are popularly used for multilevel thresholding. Section 4 presents the SOS algorithm, and the proposed OSOS based multilevel thresholding technique discuss in Section 5. Experiments and Results discussion are presented in Section 6 with the help of some well-known quality metrics such as PSNR, SSIM, and FSIM. Finally, the conclusions are drawn in Section 7.

Thresholding based segmentation mostly relies on the principle of partitioning or segmenting the image objects in an image on the basis of the intensity level. For example, in bi-level thresholding, the background and foreground of an image may be separated applying a set of decision rules based on the computed optimal threshold values. But multilevel thresholding techniques are more complex than the bi-level thresholding in the sense that, here, multiple optimized threshold values are to be computed for segmenting multiple objects from an image or video sequence. However, a general mathematical form of segmentation problem based on thresholding is presented in this sub-section for both bi-level and multilevel cases. Bi-level thresholding is performed using the following rules: P
Rbackground ← P

if

Rforeground ← P

if T ≤ P < L − 1

(1)

where threshold value T divides the image in two regions and is the one of the value of pixel in L-level gray scale image. The same concept may be extended to multilevel thresholding techniques also by the following rules: Rregion_1 ← P

if 0 ≤ P < Tthreshold_1

Rregion_2 ← P

if Tthreshold_1 ≤ P < Tthreshold_2

Rregion_(n−1) ← P

if Tthreshold−(n−1) ≤ P < Tthreshold_n

Rregion_n ← P

if Tthreshold_n ≤ P < L − 1

T1 , T2 , . . . . . . , Tn = arg max(f (T1 , T2 , . . . . . . , Tn )) ∗

∗

This is one of the popular methods, proposed by Otsu’s [38] in 1979, for both bi-level and multiple thresholding, it is based on searching the optimal thresholding by maximizing between-class variance of the segmented region which can be expressed as sum of sigma functions of each region by the equation given below: f (t ) = σ0 + σ1

(4)

where

σ0 = ω0 (µ0 − µT )2 and σ1 = ω1 (µ1 − µT )2

(5)

µT in Eq. (5) represents the mean intensity of the whole image and for bi-level thresholding mean of each class can be expressed as, µ0 =

t −1 ∑ ipi ω0

and µ1 =

L−1 ∑ ipi ω1

(6)

i=t

The optimal threshold can be acquired by maximizing between-class variance. t ∗ = arg max(f (t ))

(7)

This method can be extended for multilevel thresholding problem by the following function f (t ) =

m ∑

σi

(8)

i=0

The sigma function can be express through Eq. (9)

σ1 = ω0 (µ0 − µT )2 , σ2 = ω1 (µ1 − µT )2 , σj = ωj (µj − µT )2 and σm = ωm (µm − µT )2

(9)

And mean level can be defined as tj+1 −1 t2 −1 L−1 ∑ ipi ∑ ipi ∑ ipi ∑ ipi µ0 = , µ1 = , µj = , µm = ωi ωi ωi ωi t1 −1

i=t1

i=0

i=tj

(10)

i=tm

Optimal threshold value can be acquired by maximizing the objective function of Eq. (11)

( ⃗t ∗ = arg max

m ∑

) σi

(11)

i=0

(2)

where Tthreshold_1 < Tthreshold_2 , . . . . . . , Tthreshold_(n−1) < Tthreshold_n are the threshold values. For an image with n + 1 number of objects or regions, it is required to determine the n number of threshold values to segment the objects or regions from the image and the main objective is to compute the optimal thresholds so that the objects or regions can be distinguished clearly with minimum error. The optimized threshold values are searched by optimizing one (or more) objective function(s). If an objective function is f (.), the optimal threshold values T1∗ , T2∗ , . . . , Tn∗ can be computed as follows: ∗

2.1. Otsu’s method

i=0

2. Mathematical model of thresholding problem

3

(3)

Selection of objective functions is one of the vital issues in finding out the optimal threshold values. Otsu [38], Tsallis [39] and Kapur’s entropy [40] method are some selected examples of standard objective functions which are broadly used in image segmentation problems discussed in the next subsection.

2.2. Kapur’s entropy method for thresholding methods The most common and extensively used entropy-based method is Kapur’s entropy-based [39] thresholding. It describes the technique to maximize the entropy of the segmented histogram in order that each segmented region has a more centralized distribution [6]. Optimal threshold for bi-level thresholding by Kapur’s entropy can be express as maximizing the following function f (t ) = H0 + H1

(12)

where

⎧ ( ) t −1 t −1 ∑ ∑ pi pi ⎪ ⎪ ⎪ ln , ω = pi H = − 0 ⎪ 0 ⎨ ω0 ω0 i=0 i=0 ( ) L−1 L−1 ⎪ ∑ ∑ ⎪ pi pi ⎪ ⎪ H = − ln , ω = pi 1 ⎩ 1 ω1 ω1 i=t

i=t

(13)

4

F. Chakraborty, D. Nandi and P.K. Roy / Applied Soft Computing Journal 82 (2019) 105577

This method may be extended for multilevel thresholding by using the following equation f ([t1 , t2 , t3 , . . . , tn ]) = H0 + H1 + H2 + · · · + Hn

(14)

where t1 < t2 < t3 , . . . , tn and

⎧ t1 −1 ⎪ ∑ pi ( pi ) ⎪ ⎪ ⎪ ln , H = − 0 ⎪ ⎪ ω0 ω0 ⎪ ⎪ i=0 ⎪ ⎪ ⎪ t2 −1 ⎪ ∑ pi ( pi ) ⎪ ⎪ ⎪ H = − ln , ⎪ 1 ⎪ ⎨ ω1 ω1

t1 −1

ω0 =

∑

pi

ω1 =

i=t1

pi (15)

pi ln (pi )

(16)

where p = {pi } represents the probability ∑ of the system in each k possible state (i) [14]. and 0 ≤ pi ≤ 1 and i=0 pi and k denotes the total number of state. Its Extensive property is S (A + B) = S (A) + S (B)

(17)

The following equation generalized the Tsallis entropy to nonextensive system using the multi-fractal theory:

∑k

(pi )

i=1

(18)

where q is known as Tsallis parameter or entropic index. Tsallis entropy of the system can be defined by a pseudo additivity entropic rule using (19) Sq Ac + Bc = Sq Ac + Sq Bc + (1 − q) .Sq Ac .Sq Bc

)

( )

( )

( )

( )

(19)

This technique is useful for determining the threshold value of the image. Assume that {1, 2, 3, . . . , G} gray level of an image and pi = p1 , p2 , . . . . . . , pg is the probability distribution of the gray level. From these distribution two probability for background (class A) and foreground (class B) can be obtained by p1 p2 pt pt +1 pt +2 pG pA = , ,..., and ps = , ,..., (20) pA pA pA pA pA pA

∑t

∑G

where pA = i=1 pi and pB = i=t +1 pi Tsallis entropy for each class can be expressed as SqA =

1−

1−

q−1 ∑G

i=1 (pi

/p1 )q

i=tM +1 (pi

q−1

,

Sq1

/pM )q

1−

∑t2

= and

i=t1 +1 (pi

q−1

/p2 )q

,

M =m+1

⏐ ⏐ 1 ⏐ ⎧⏐ 1 2 1 2 ⎨⏐⏐p + p ⏐⏐ − 1 < S < 1 − ⏐⏐p − p ⏐⏐ ⏐p2 + p3 ⏐ − 1 < S 2 < 1 − ⏐p2 − p3 ⏐ ⏐ ⏐ ⏐ ⎩⏐⏐ m p + pm+1 ⏐ − 1 < S M < 1 − ⏐pm − pm+1 ⏐

(25)

where p1 , p2 , . . . , pm corresponding to s1 , s2 , . . . , sm+1 can be obtained using T 1 , T 2 , . . . , T m respectively.

Exploration of optimal thresholds is one of the key issues for better segmentation of image. Various optimization techniques are available for this purpose. Since we are interested to apply nature inspired metaheuristic optimizations for their robustness and better performance, we would like to discuss in brief some well-developed and widely-used nature inspired optimization techniques that are recently used or may be used for multilevel image segmentation. 3.1. Particle swarm optimization

q

q−1

(

∑t1

3. Optimization algorithms used for multilevel thresholding

i=1

1−

=

1−

Subject to the following constraints

i=tn

Shannon entropy refers to disorder or uncertainty in a system. It only considers the probability of observing a specific event, so the information it considers is information about the underlying probability distribution. The Shannon entropy can be stated as

Sq =

Sq1

SqM =

2.3. Tsallis entropy method

S=−

(24)

where

( ) tm+1 −1 tm+1 −1 ⎪ ∑ pi ∑ ⎪ pi ⎪ ⎪ pi H = − ln , ω = ⎪ m m ⎪ ⎪ ωm ωm ⎪ i=tm i=tm ⎪ ⎪ ⎪ ( ) ⎪ L−1 L−1 ⎪ ∑ ∑ pi pi ⎪ ⎪ ⎪ H = − ln , ω = pi n n ⎪ ⎩ ωn ωn

k ∑

where S (t ) = S = [SqA (t ) + SqB (t ) + (1 − q) SqA (t ) .SqB (t)] The above formula can be represent as for multi-level thresholding using Eq. (24)

+ (1 − q) Sq1 (t ) .Sq2 (t ) . . . SqM (t)]

i=t1

i=tn

(23)

[T1 , T2 , T3 , . . . , Tm ] = arg max[Sq1 (t ) + Sq2 (t ) + · · · + SqM (t )

i=0 t2 −1

∑

Subject to following constraint:

⏐ A ⏐ ⏐p + pB ⏐ − 1 < S < 1 − |pA − pB |

∑t

i=1 (pi

q−1

/pA )q

, SqB =

1−

∑G

i=t +1 (pi

/pB )q

(21)

q−1

To obtain the optimal thresholding value the information measured between two classes needs to be maximized. The resultant gray level for which this happens is measured to be the optimum threshold value, which can be accomplished by maximizing the objective function for bi-level thresholding: Topt = arg max SqA (t ) + SqB (t ) + (1 − q) SqA (t ) .SqB (t )

[

]

(22)

Particle swarm optimization (PSO) is a stochastic populationbased search algorithm which is inspired by the behavior of biological communities like bird flocking or fish schooling [9]. In the basic PSO method, a swarm of particles moves through an N-dimensional search space where location of each particle represents a probable solution to the optimization problem. The position of each particle is first initialized by using Eq. (26) and then the position and velocity of the particles are upgraded in the search space at each iteration to reach the final solution until certain criteria is met. Each particle in the swarm is characterized by the following terms: xij (t ) : jth dimension of the position of ith particle at time t vij (t): jth dimension of the velocity of ith particle at time t yij (t): jth dimension of the personal best (pbest) position of ith particle at time t yˆ j (t): jth dimension of the global best (gbest) position of the swarm at time t The initial position of particle i in jth dimension is assumed to be xij = xmin + r(0, 1)(xmax − xmin ) j j j

(26) xmin j

In threshold optimization for image segmentation = 0 and xmax = 256 and r (0, 1) is uniformly distributed random j numbers in the range of 0 to 1. After generating the population, the particles start to move in the search space by improving their

F. Chakraborty, D. Nandi and P.K. Roy / Applied Soft Computing Journal 82 (2019) 105577

velocities and positions as per the classical update equations of swarms ((27), (28)).

) ( vij (t + 1) = w (t ) vij (t ) + c1 r1 (0, 1) yij (t ) − xij (t ) ) ( + c2 r2 (0, 1) yˆ j (t) − xij (t )

(27)

xij (t + 1) = xij (t ) + vij (t + 1)

(28)

where w (t) is the inertia weight in the range [0,1] that controls the magnitude of the old velocity. The control parameters c1 and c2 are known as cognitive and social parameters respectively. r1 (0, 1) and r2 (0, 1) are the uniformly distributed random numbers in the range [0,1]. 3.2. Artificial bee colony (ABC) algorithm The ABC algorithm, proposed by Karaboga [10], is another nature inspired optimization algorithm for solving multidimensional and multimodal problems which is based on the behavior of bees in reality. It is a swarm intelligence approach that is inspired by the collective intelligent behavior of bee’s colony. The behavior of honey bees consists of three important components. (1) The amount of nectar of the food source represents the quality of the solution. (2) Employed foragers, rejected worse sources after discovering better sources. (3) Unemployed foragers onliiker and scout are looking for the new food sources. The placing of the onlookers on the food sources are based on probabilistic selection process. The probability of preference of a food source by the onlookers increases if the nectar in the food source increases. The scouts are characterized by low search costs and a low average in food source quality. A control parameter, called ‘‘limit’’, is used to control the selection. If a solution i.e., a food source is not improved by a predetermined number of trials, the food source is treated as abandoned and the employed bee is converted to a scout.

5

(i) Each bat uses echolocation to sense distance, and they also ‘‘know’’ the surroundings in some magical way; (ii) Bats fly randomly with velocity at position with a fixed frequency, different wavelength, and loudness to search for victim. They can automatically regulate the wavelength of their emitted pulses and adjust the rate of pulse emission from, depending on the proximity of their target; (iii) It is assumed that the loudness can be varied from a positive large value to a minimum constant value. 4. Symbiotic organisms search (SOS) algorithm Symbiotic organisms search (SOS) based optimization [24– 31] is one of the new and promising techniques in the field of metaheuristic optimization. SOS algorithm simulates the interactive behavior seen among the organisms in the nature in an ecosystem. In the real world, the organisms live together in an ecosystem with mutual dependencies for their sustenance and survival. This symbiotic relationship helps to adapt the changes in their own environment. Mutualism, commensalism, and parasitism are the most common symbiotic relationships found in the ecosystem. In case of interacting between two organisms, when both get benefited out of the symbiotic relationship, we call it mutualism; when one get benefited and other is unaffected from this relationship, we call it commensalism; and if one get benefited and other actively harmed, we call it parasitism. Unlike other metaheuristic algorithms, SOS algorithm starts with some randomly selected candidate solution in the solution space and reach to the optimal global solution gradually after successive iterations. Here each organism associated with a fitness value that represents a candidate solution in the solution space. Organisms update their fitness value according to mutualism, commensalism, and parasitism symbiosis relationship in the ecosystem. The symbiotic phenomenon is explained in algorithmic form as follows:

3.3. Cuckoo Search (CS) algorithm The CS algorithm was proposed by Yang and Deb is a natureinspired evolutionary optimization algorithm [14], which is used to find the globally optimal solution. This algorithm mimics the parasitic breeding behavior of the Cuckoo bird. The cuckoo bird lays its egg in the nests of other host bird, host bird can react in two ways, either he can take care the egg assuming as its own egg, or if he recognizes the egg then either he can destroy the egg, or leave the nests and build a new nest at a new place. Here a set of the nest with eggs represent the population of each generation. In each generation, a nest is chosen randomly and modified the quality of the egg, if the quality of the egg is better than the other nest then the egg replaces the existing egg. Nest with good quality egg is carried over to the next generation. Mutation probability represents the probability that host nest recognizes the eggs and discards the nest from the further calculation.

Mathematical operations of three symbiosis relationships are discussed in next subsections. 4.1. Mutualism phase

3.4. Bat algorithm Another nature inspired metaheuristic algorithm is the Bat algorithm which has been proposed by Xin-She Yang in 2010 [41]. This algorithm idealizes some of the echolocation characteristics of microbat. In this algorithm, bat uses the echolocation to avoid the obstacle while searching for food or prey. To implement the bat algorithm, following three idealized rules are used to implement the bat algorithm:

Mutualism benefits both the participating organisms. For example, bees fly among flowers, gathering nectar to turn into honey. From this activity, bees get benefited from the flowers. On the other side, flowers also get benefited by distributing pollen by the bees in this process. To formulate this behavior mathematically, let us consider two organisms Xi and Xj , where Xi represents the ith organism in an ecosystem and Xj is randomly selected from the ecosystem

6

F. Chakraborty, D. Nandi and P.K. Roy / Applied Soft Computing Journal 82 (2019) 105577

Fig. 1. (a) lena (b) lake (c) man (d) beer (e) airplane and (f) peppers represents the original images used for experiments and (’), (’’) and (’’’) are represents histogram of the images for red green and blue band respectively.

to interact with each other to increase mutual survival advantage. Then the new candidate solutions Xinew and Xjnew may be calculated from the following equations: Xinew = Xi + r (0, 1) . (Xbest − MV .BF1 )

(29)

Xjnew = Xj + r (0, 1) . (Xbest − MV .BF2 )

(30)

MV =

Xi + Xj

(31) 2 r(0, 1) in Eqs. (29) and (30) is vector of uniformly distributed random numbers. BF1 and BF2 are the benefit factors between the organisms and represent the level of benefit to each organism. The values of

these two factors may not be always same. This is because one organism in the symbiotic relationship may get more benefit than the others. However, these factors are determined randomly as either 1 or 2. MV is known as mutual vector representing the mutual characteristics between the organisms Xi and Xj . If the fitness values for the new candidate organisms Xinew and Xjnew are better than Xi and Xj then Xi and Xj are replaced by Xinew and Xjnew respectively, otherwise Xinew and Xjnew are discarded. It can be represented by the Eqs. (32) and (33).

{ Xi =

Xinew

if f (Xinew ) > f (Xi )

Xi

if f (Xinew ) ≤ f (Xi )

(32)

F. Chakraborty, D. Nandi and P.K. Roy / Applied Soft Computing Journal 82 (2019) 105577

7

Fig. 2. Segmented man images using Ostu’s method. (a–d) proposed OSOS optimization, (e–h) SOS optimization, (i–l) CS and (m–p) BAT.

Xjnew

if f (Xjnew ) > f (Xj )

Xj

if f (Xjnew ) ≤ f (Xj )

{ Xj =

(33)

where f (.) denotes the fitness function. 4.2. Commensalism phase The symbiotic relationship between two organisms in an ecosystem, when one get benefited and other is unaffected or neutral, is known as commensalism relationship. Relationship between remora fish and sharks is an example of this category of relationship. The remora assigns itself to the shark and eats food left overs, thus getting a benefit. The shark is unaffected by remora fish actions and receives minimal benefit from the relationship.

In commensalism phase, between two symbiotically related organisms Xi and Xj , when Xj is selected randomly to interact with Xi , the organism Xi attempts to get benefit from this relationship but Xj remain unaffected. So the new candidate solution can be computed using Eq. (34). Xinew = Xi + r (−1, 1) . Xbest − Xj

(

)

(34)

If the fitness function of Xinew is better than Xi then Xi is replaced Xinew by otherwise Xinew is discarded. This can be represent as (35) Xinew

if f (Xinew ) > f (Xi )

Xi

if f (Xinew ) ≤ f (Xi )

{ Xi =

(35)

8

F. Chakraborty, D. Nandi and P.K. Roy / Applied Soft Computing Journal 82 (2019) 105577

Fig. 3. Segmented lena images using Kapur’s entropy. (a–d) proposed OSOS optimization, (e–h) SOS optimization, (i–l) CS and (m–p) BAT.

4.3. Parasitism phase

parasite). This scenario is represents by (36)

{ The parasitism relationship is one of the symbiotically related organisms that gets benefit out of the relationship whereas the other is actively harmed. An example of parasitism is the plasmodium parasite. This parasite pass between human hosts by using its relationship with the anopheles mosquito and thrives and reproduces inside the human body which cause host suffering from malaria. In this phase, parasite vector is created in the search space by cloning an organismXi that serves as parasite. Afterward, modify the randomly selected dimensions using a random number. Organism Xj is randomly selected from the ecosystem and serves as a host. The fitness values for both the organisms are then evaluated. If the parasite vector has better fitness value than Xj , then Xj is replaced by the parasite vector (i.e. it will kill Xj and establish its position in the ecosystem), otherwise discards the parasite vector (that indicates the immunity of Xj from the

Xj =

PV

if f (PV ) > f (Xi )

Xj

if f (Xj ) ≤ f (Xi )

(36)

PV denotes the parasite vector. 5. Proposed Opposition-based SOS We have enhanced the performance of the SOS algorithm in terms of quality of output and convergence speed by introducing the concept of opposition based learning (OBL) along with SOS. This enhanced algorithm is named as Opposition based Symbiotic Organisms Search (OSOS). The general concept of OBL is briefly discussed in the next sub-section. 5.1. Opposition-based learning (OBL) In general, all the evolutionary algorithms start with a randomly selected initial population and gradually reach to the optimal solution in subsequent iterations and finally stop depending

F. Chakraborty, D. Nandi and P.K. Roy / Applied Soft Computing Journal 82 (2019) 105577

9

Fig. 4. Segmented peppers images using Tallis’ entropy. (a–d) proposed OSOS optimization, (e–h) SOS optimization, (i–l) CS and (m–p) BAT.

on some predefined conditions. The convergence time of the algorithms is linked to the distances of these initial guesses from the optimal solution, If the initial selection is closer to the optimal solution, it converges quickly, otherwise, it takes longer time to converge. This opposition based learning was first introduced by Tizhoosh [39] to improve the initial solution by simultaneously evaluating current candidate solution and its opposite solution and choose the fitter one as the initial solution. The same methods can be useful not only for the starting population but also for each iteration to improve the final solution. Hence, the central idea of OBL in optimization problem is the evaluation of the current candidate solution and its opposite solution simultaneously. This process will accelerate the learning and searching of optimized thresholds. Some useful definitions related to OBL are

a + b − x where x ∈ [a, b] The same concepts may be applied to generate the opposite number in multidimensional case. II. Opposite point Let P = (x1 , x2 , . . . , xD ) be a point in D-dimensional space, where xi ∈ R and xi ∈ [ai , bi ] and i = {1, 2, . . . . . . , D}. The opposition point P(x1 , x2 , . . . , xD ) is defined as x = ai + bi − xi

(37)

The concept of the opposition based optimization by using the idea of opposite point is described below. III. Opposition based optimization Let P = (x1 , x2 , . . . , xD ) be a candidate solution of Ddimensional problem, f (P) is the fitness function for measuring the candidate fitness. P( is ) the opposite point of theP. In maximization problem, if f P ≥ f (P ) then the point P is replaced by the point P. Thus a point and its opposite point are evaluated simultaneously and the fittest one chosen.

given below. I. Opposite number Opposite number (x ) of a real number (x) is defined as x =

5.1.1. Opposition based initial population In opposition based learning, the initial population is generated by marging the population generated by the conventional

10

F. Chakraborty, D. Nandi and P.K. Roy / Applied Soft Computing Journal 82 (2019) 105577

Fig. 5. (a–c) 5-level convergence graph of lena image by Kapur’s entropy for three band red, green, blue respectively. (d–f) 5 level convergence graph of peppers image.

random number generator and its opposite population. Finally, the best subpopulation is selected based on the fitness function and is treated as the initial population. 5.1.2. Opposition based generation by jumping probability The same method may be followed to improve the solution in each iteration. This is done by forcefully changing the current population to its opposite population (which is fitter than the old population) depending on the jumping rate (Jr ). After generating new population in each iteration, the opposite population is generated and is merged with the old population. Then we select the fittest population from the merged population. This fittest population is the new population for next iteration. Selection of optimum jumping rate (Jr ) is a crucial factor in case of opposition based optimization. As per literature [37], jumping rate over Jr ≥ 0.6 is not suitable for many functions as it causes premature convergence, and jumping rate Jr = 0 means no jumping. That means the optimal jumping rate are scattered in the interval [0, 0.6]. In case of our problem we have conducted the test for (Jr ) = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6], it is observed from

the result that jumping rate between [0.3, 0.4] producing the best result for all the images and also increase the convergence rate, so we have set the average of this two value 0.35 as the jumping rate for this experiments. 5.2. OSOS based multilevel thresholding The proposed OSOS algorithm tries to select k threshold values which maximize the fitness functions (Kapur’s, Otsu’s and Tsallis). The initial population for the algorithm is generated using the concept of OBL and of a selected level (k =2, 3, 4 and 5 level). An organism represents a k -dimensional vector from the population. The values of the fitness function in each iteration are calculated using the organisms (k-dimensional vectors) of the current population. The best organism in an iteration is found out from the optimized fitness value of that iteration. The population in each iteration is upgraded by three symbiosis relation phase Mutualism, Commensalism, and Parasitism. And Opposition-Based Generation by jumping probability. The best organism (overall optimal threshold value) over all the iterations is obtained

Algorithm

ABC

Parameter

Value

Parameter

Value

Swam size

20

Algorithm

Population size

20

No. of iterations

100

No. of iterations

Lower bound and upper bound

1,256

Maximum Inertia weight

Value of Fi (ϕ )

[0,1]

Minimum Inertia weight

0.4

Parameter

Value

Parameter

Value

Number of nests

20

Number of Bat

20

100

No. of iterations

100

No. of iterations

10

0.9

Step size

1

Maximum frequency

1.5

Mutation probability value

0.25

Minimum frequency

0

Maximum velocity

+1.0

Scale factor

1.5

Minimum and maximum Pulse emission

0,1

PSO

Algorithm

CS

Algorithm

BAT

Minimum velocity

−1.0

Minimum and maximum Loudness

1,2

Cognitive coefficient (C1 )

1.429

Minimum and Maximum wavelength

0.9 and 0.99

Cognitive coefficient C2 )

1.429

F. Chakraborty, D. Nandi and P.K. Roy / Applied Soft Computing Journal 82 (2019) 105577

Table 1 Parameter used for ABC, PSO, CS and BAT.

11

12

Objective function value

Threshold value

Image

K

OSOS

SOS

CS

BAT

ABC

PSO

OSOS

SOS

Lena

2 3 4 5

12.0721 15.0264 17.6719 20.1768

12.0721 15.0264 17.6716 20.17062

12.0721 15.0246 17.6641 20.1648

12.0721 15.0246 17.6619 20.1758

12.0721 15.0246 17.6517 20.1445

12.0721 15.0231 17.6657 20.1697

134 114 108 108

134 114 108 107

Lake

2 3 4 5

12.1068 15.3544 18.2318 20.8963

12.1068 15.3544 18.2318 20.8955

12.1068 15.3544 18.2317 20.8822

12.1068 15.3544 18.2313 20.8960

12.1068 15.3542 18.1875 20.8955

12.1068 15.3515 18.2316 20.8949

41 41 41 41

Man

2 3 4 5

12.3547 15.5808 18.2438 20.8654

12.3547 15.5808 18.2439 20.8535

12.3547 15.5808 18.2433 20.8443

12.3547 15.5808 18.1818 20.7492

12.3547 15.5808 18.1878 20.8515

12.3547 15.5756 18.2267 20.5799

133 191 88 139 192 58 93 141 192 58 93 138 181 214

133 191 88 139 192 58 93 141 192 56 91 137 179 211

133 191 88 139 192 58 93 139 191 56 90 138 184 212

133 191 88 139 192 48 91 139 193 77 109 139 183 215

133 191 88 139 192 56 87 136 193 58 95 137 180 214

133 191 89 140 191 59 92 141 193 86 111 141 165 196

Beer

2 3 4 5

13.2287 16.5314 19.5740 22.4240

13.2287 16.5313 19.5738 22.0379

13.2287 16.5314 19.5740 22.4239

13.2287 16.5314 19.5568 22.4137

13.2287 16.5281 19.5718 22.3520

13.2287 16.4881 19.4715 22.0185

85 66 52 41

168 127 191 102 153 204 84 123 170 212

85 66 51 38

168 127 191 102 152 203 80 124 166 210

85 66 51 41

168 127 191 102 153 204 83 125 168 212

85 66 55 45

168 127 191 106 155 204 86 126 167 210

85 65 49 32

168 126 194 108 153 204 67 118 166 208

85 50 44 44

168 113 180 107 142 196 118 159 204 231

Airplane

2 3 4 5

12.1414 15.5393 18.1092 20.8582

12.1414 15.3437 18.1090 20.5848

12.1414 15.3437 18.1061 20.5973

12.1414 15.3437 18.1049 20.5889

12.1414 15.3348 18.0851 20.5619

12.1414 15.3437 18.1064 20.3513

77 60 70 57

169 103 162 109 146 182 90 133 163 193

77 73 70 67

169 124 176 110 146 182 99 129 159 186

77 73 70 66

169 124 176 109 147 184 96 125 155 184

77 73 71 68

169 124 176 109 146 183 97 125 154 184

77 71 74 70

169 120 178 114 148 184 101 133 163 191

77 73 71 67

169 124 176 109 145 182 103 140 176 206

Peppers

2 3 4 5

12.5157 15.5393 18.4072 20.9682

12.5157 15.5393 18.4072 20.9617

12.5157 15.5393 18.4070 20.9665

12.5157 15.5351 18.4066 20.9433

12.5157 15.5351 18.3666 20.962462

12.5157 15.5393 18.4064 20.7653

91 60 57 44

156 103 162 97 138 178 75 104 142 180

91 60 57 43

156 103 162 97 138 178 78 107 144 181

91 60 56 43

156 103 162 97 138 178 74 104 143 180

91 57 56 45

156 103 164 97 138 179 73 108 145 182

91 57 52 48

156 103 164 93 140 174 80 108 146 183

91 60 56 26

156 103 162 97 139 178 64 104 155 186

192 159 202 140 172 207 139 169 199 227

137 115 173 93 137 180 82 116 151 186

41 41 41 41

CS 192 159 202 140 171 207 139 168 200 227

137 115 173 92 136 181 83 117 152 186

BAT

134 114 107 107 41 41 41 42

192 159 202 139 170 208 137 170 197 227

137 115 173 94 137 181 80 114 150 183

134 114 106 108 41 41 41 41

ABC 192 159 202 141 173 209 139 167 197 226

137 115 173 92 135 181 81 114 149 185

134 116 109 111 41 41 39 41

PSO 192 159 201 140 169 202 139 170 202 228

137 114 173 84 130 178 82 115 150 186

134 113 105 108 41 41 41 41

192 158 200 139 171 205 139 169 198 227

137 116 176 94 137 181 83 116 150 186

F. Chakraborty, D. Nandi and P.K. Roy / Applied Soft Computing Journal 82 (2019) 105577

Table 2 The highest objective function value and threshold values for red band by the Kapur’s method for the six test images.

Objective function value

Threshold value

Image

K

OSOS

SOS

CS

BAT

ABC

PSO

OSOS

SOS

CS

BAT

ABC

PSO

Lena

2 3 4 5

2393.6473 2597.9820 2675.6610 2709.7936

2393.6473 2597.982 2675.6457 2709.7570

2393.6473 2597.9684 2675.661 2709.7739

2393.6473 2597.7674 2675.6227 2709.7739

2393.6473 2597.7674 2675.6227 2709.4262

2393.6473 2597.9614 2675.6227 2708.6003

78 57 47 46

146 107 160 84 120 165 80 110 139 174

78 57 47 45

146 107 160 85 120 165 80 110 139 173

78 57 47 46

146 106 159 84 120 165 80 111 139 174

78 56 48 46

146 105 159 85 120 165 80 111 139 174

78 56 48 45

146 105 159 85 120 165 81 110 140 173

78 57 48 48

146 106 160 85 120 165 83 113 142 178

Lake

2 3 4 5

5636.6312 5776.7083 5868.0873 5919.3786

5636.6312 5776.7083 5868.0629 5919.3199

5636.6312 5776.7083 5868.0873 5919.3336

5636.6312 5776.7083 5868.0826 5919.354

5636.6312 5776.7083 5868.0824 5919.2018

5636.6312 5776.7083 5868.0827 5918.8749

76 59 53 41

158 119 181 104 162 207 77 123 171 209

76 59 53 42

158 119 181 103 161 207 78 125 172 209

76 59 53 42

158 119 181 104 162 207 78 124 171 209

76 59 52 41

158 119 181 102 161 207 77 123 172 209

76 59 53 42

158 119 181 103 162 207 78 126 173 210

76 59 52 44

158 119 181 103 162 207 81 127 173 210

Man

2 3 4 5

1622.4562 1728.5751 1780.0754 1800.7206

1622.4562 1728.5790 1780.0754 1800.6473

1622.4562 1728.579 1780.0754 1800.7071

1622.4562 1728.579 1780.0754 1783.9565

1622.4562 1728.5790 1780.0754 1800.7125

1622.4562 1728.579 1780.0754 1783.9565

101 180 97 167 181 89 148 182 209 87 143 173 196 214

101 180 96 167 204 89 148 182 209 87 142 173 196 214

101 180 96 167 204 89 148 182 209 87 143 174 196 214

101 180 96 167 204 89 148 182 209 29 92 151 184 209

101 180 96 167 204 89 148 182 209 88 143 173 196 214

101 180 96 167 204 72 123 156 177 29 92 151 184 209

Beer

2 3 4 5

4121.1266 4339.0894 4447.0593 4498.4424

4121.1266 4339.0894 4447.0325 4498.3298

4121.1266 4339.0894 4447.0031 4498.4276

4121.1266 4339.0894 4447.0031 4498.3653

4121.1266 4339.0894 4447.0593 4498.2170

4121.1266 4339.0894 4447.0069 4497.9918

60 43 34 30

144 99 167 77 127 183 65 102 145 193

60 43 35 30

144 99 167 78 128 184 65 101 145 193

60 43 34 30

144 99 167 77 128 184 66 103 146 194

60 43 34 30

144 99 167 77 128 184 65 101 144 192

60 43 34 31

144 99 167 77 127 183 66 104 147 195

60 43 35 32

144 99 167 78 127 184 68 105 147 194

Airplane

2 3 4 5

2436.3585 2534.0753 2587.6512 2619.0543

2436.3585 2534.0753 2587.6273 2619.0543

2436.3585 2534.0753 2587.6512 2619.0363

2436.3585 2534.0753 2587.6087 2619.0543

2436.3585 2534.0753 2587.6512 2619.0543

2436.3585 2534.0753 2587.6040 2619.0543

94 78 67 61

166 138 189 117 165 202 104 143 181 207

94 77 67 61

166 138 189 116 165 202 104 143 181 207

94 78 67 60

166 138 189 117 165 202 104 143 181 207

94 78 68 61

166 138 189 118 166 203 104 143 181 207

94 78 67 61

166 138 189 117 165 202 104 143 181 207

94 78 66 61

166 138 189 117 165 202 104 143 181 207

Peppers

2 3 4 5

5203.9273 5382.5860 5479.7262 5525.4596

5203.9273 5382.5860 5479.6021 5525.4246

5203.9273 5382.5860 5479.7159 5525.4247

5203.9273 5382.5860 5479.6864 5525.408

5203.9273 5382.5860 5479.7159 5525.4220

5203.9273 5382.5860 5479.7159 5525.3437

79 36 32 29

158 99 168 83 141 186 71 116 159 192

79 36 32 29

158 99 168 84 142 187 71 117 160 193

79 36 31 29

158 99 168 83 141 186 71 117 160 193

79 36 32 29

158 99 168 84 142 186 70 115 159 192

79 36 31 29

158 99 168 83 141 186 71 118 160 193

79 36 31 29

158 99 168 83 141 186 72 119 160 193

F. Chakraborty, D. Nandi and P.K. Roy / Applied Soft Computing Journal 82 (2019) 105577

Table 3 The highest objective function value and threshold values for green brand by the Otsu’s method for the six test images.

13

14

Objective function value

Threshold value

Image

K

OSOS

SOS

CS

BAT

ABC

PSO

OSOS

SOS

CS

BAT

ABC

PSO

Lena

2 3 4 5

0.888881 1.296265 1.654242 1.995718

0.888881 1.296265 1.654240 1.995715

0.888881 1.296265 1.654240 1.995712

0.888881 1.296265 1.654240 1.995714

0.888881 1.296265 1.654239 1.995712

0.888881 1.296265 1.654236 1.995710

96 94 82 81

143 133 165 108 138 168 107 133 155 177

96 94 80 83

143 133 165 107 139 170 109 134 156 178

96 94 80 82

143 133 165 107 139 170 109 134 156 179

96 94 80 82

143 133 165 107 139 170 108 133 156 179

96 94 80 82

143 133 165 105 138 167 109 134 156 179

96 94 77 83

143 133 165 105 138 168 110 135 158 178

Lake

2 3 4 5

0.888875 1.296268 1.654270 1.995792

0.888875 1.296268 1.654270 1.995791

0.888875 1.296268 1.654268 1.995788

0.888875 1.296268 1.654268 1.995790

0.888875 1.296268 1.654269 1.995789

0.888875 1.296268 1.654267 1.995786

81 64 53 49

140 116 161 93 130 168 81 111 142 172

81 64 53 49

140 116 161 93 130 168 80 113 141 176

81 64 49 52

140 116 161 96 135 172 85 114 139 170

81 64 49 45

140 116 161 96 135 172 80 113 141 176

81 64 55 52

140 116 161 91 133 170 85 118 144 176

81 64 54 43

140 116 161 92 138 169 74 103 136 175

Man

2 3 4 5

0.888878 1.296264 1.654265 1.995761

0.888878 1.296264 1.654264 1.995759

0.888878 1.296264 1.654260 1.995745

0.888878 1.296264 1.654260 1.995758

0.888878 1.296264 1.654263 1.995757

0.888878 1.296264 1.654258 1.995745

93 86 54 55

135 127 163 87 128 163 87 126 162 199

93 86 54 55

135 127 163 86 126 164 87 126 165 199

93 86 52 49

135 127 163 86 121 164 87 130 163 203

93 86 52 51

135 127 163 86 121 164 87 124 164 199

93 86 53 51

135 127 163 86 125 164 86 121 162 199

93 86 51 49

135 127 163 81 123 162 87 130 163 203

Beer

2 3 4 5

0.888883 1.296282 1.654292 1.995833

0.888883 1.296282 1.654291 1.995832

0.888883 1.296282 1.654291 1.995827

0.888883 1.296282 1.654291 1.995828

0.888883 1.296282 1.654291 1.995830

0.888883 1.296282 1.654280 1.995828

107 173 84 136 186 62 105 148 191 87 143 173 196 214

107 173 84 136 186 70 110 154 196 51 90 125 163 200

107 173 84 136 186 70 110 154 196 50 85 137 172 205

107 173 84 136 186 70 110 154 196 55 85 128 160 194

107 173 84 136 186 70 110 154 196 53 88 129 171 203

107 173 84 136 186 62 89 130 196 50 85 137 172 205

Airplane

2 3 4 5

0.888870 1.296241 1.654216 1.995712

0.888870 1.296241 1.654215 1.995711

0.888870 1.296241 1.654213 1.995710

0.888870 1.296241 1.654213 1.995710

0.888870 1.296241 1.654213 1.995711

0.888870 1.296241 1.654210 1.995709

133 180 109 152 188 99 128 161 190 70 99 128 161 190

133 180 109 152 188 98 124 158 190 70 99 128 162 192

133 180 109 152 188 96 123 154 191 70 97 127 159 190

133 180 109 152 188 96 123 154 191 70 97 127 159 190

133 180 109 152 188 96 123 154 191 70 99 128 162 192

133 180 109 152 188 96 128 155 190 70 99 126 160 187

Peppers

2 3 4 5

0.888876 1.296263 1.654253 1.995764

0.888876 1.296263 1.654253 1.995762

0.888876 1.296263 1.654251 1.995762

0.888876 1.296263 1.654251 1.995761

0.888876 1.296263 1.654251 1.995761

0.888876 1.296263 1.654248 1.995757

95 93 76 71

95 93 77 68

95 93 77 72

95 93 77 67

95 93 77 67

95 93 82 65

169 139 178 114 151 184 101 132 160 188

169 139 178 114 151 184 98 130 158 188

169 139 178 113 148 183 100 131 162 189

169 139 178 113 148 183 97 130 158 187

169 139 178 113 148 183 97 130 158 187

169 139 178 116 155 185 93 128 158 187

F. Chakraborty, D. Nandi and P.K. Roy / Applied Soft Computing Journal 82 (2019) 105577

Table 4 The highest objective function value and threshold values for blue band by the Tsallis method for the six test images.

F. Chakraborty, D. Nandi and P.K. Roy / Applied Soft Computing Journal 82 (2019) 105577

by considering the organisms obtained from all the iterations by finding the best fitness value. The details of the OSOS algorithm for multilevel image thresholding are given as follows

15

brief analysis of the results in terms of quality of the solutions, consistency, computational time and convergence rate, statistical analysis of the proposed algorithm and the other meta-heuristic algorithms are also presented here.

• Define Ecosystem – Number of organism (size of the population), – Dimension of each Organism (number of threshold value) – Maximum generation

• Initialize the ecosystem by the concept of OBL. • Calculate the objective function value for each organism from the gray level image of selected dimension.

• Repeat • Select the best organism which gives the maximum objective function value. – Mutualism Phase

∗ Select two organisms Xi and Xj randomly such that i ̸ = j ∗ Calculate mutual vector by using Eq. (31) ∗ Choose BF1 and BF2 randomly in the range (1, 2) ∗ Calculate new organisms Xinew and Xjnew by using Eqs. (29) and (30)

∗ Calculate fitness value for new modified organ-

6.1. Specifications of experimental setup and details of simulation Simulations and experiments are carried out on a PC with 2.30 GHz CPU and 4.00 GB RAM in Windows 8 environment. The algorithms are implemented using MATLAB software. In our experiment, we have tested on a set of images taken from Berkeley Segmentation and COCO dataset. Here, we present the results of arbitrary taken six color images to show the performance of the different algorithms. These six input images and their histograms are shown in Fig. 1. The selection of images with multimodal histograms will help to evaluate the performance of the algorithms in multilevel thresholding. The effectiveness of the proposed algorithm is compared with conventional SOS and four others recently proposed evolutionary algorithms namely, CS, BAT, ABC, and PSO. To achieve an unbiased assessment of the performance of the algorithms, we have used same number of iterations and same stopping criteria for all the algorithms. The parameters chosen for different algorithms are taken from the literature and are shown in Table 1.

isms Xinew and Xjnew

∗ If the fitness value of Xinew and Xjnew is better than previous values, replace the organisms by the new organisms otherwise reject the new organisms.

– End of mutualism phase – Commensalism Phase

∗ Select two organisms Xi and Xj randomly such that i ̸ = j ∗ Calculate new organism Xinew by using Eq. (34) ∗ Calculate fitness for modified organism Xinew ∗ If the fitness value of Xinew is better than previous value, replace the new organism by the modified organism otherwise reject the modified organism.

– End of Commensalism phase – Parasitism Phase

∗ Select Two organisms Xi and Xj randomly such that i ̸ = j ∗ Create the Parasite Vector Xi by cloning the Xi and modify it by randomly generated number for selected dimension ∗ Calculate the fitness value of new Xj and Parasite Vector ∗ If the fitness value of Parasite Vector is better than Xj , replace Xj with Parasite Vector otherwise reject Parasite Vector. – End of Commensalism phase

• Select the Jumping rate randomly • Change the population by the concept of OBL, if the jumping rate Jr ≤ 0.35. • Until (End of Generation) 6. Experiments and results discussion In this section, we present the specifications of computational unit used for the experiment of the proposed algorithm. The

6.2. Solution excellence In the simulations and experiments, the optimized threshold values are computed for 2, 3, 4 and 5 levels thresholding using different algorithms by maximizing the Otsu’s BCV, Kapur’s and Tsallis entropy objective functions for the test images. The optimized thresholds and the corresponding objective functions values for each band (i.e., Red, Green, and Blue) for all images are shown in Tables 2–4. Optimized thresholds and objective function’s values at optimal thresholds for Red band using the Kapur’s entropy is shown in Table 2. For green and blue bands, Otsu’s BCV and Tsallis entropy are used as the objective functions. The optimal threshold values and functions’ values at the optimal thresholds are shown in Table 3 and Table 4, respectively. The algorithm for which the value of the objective function is highest is considered as the best algorithm. It is observed from the tables that, for the small number of thresholds (2 to 3 levels), the values of the objective functions of all the algorithms are almost same, but for the higher number of threshold levels, OSOS based optimization gives the better solution for all the test images in comparison to the conventional SOS and the other metaheuristic algorithms. For example, in the case of red band, 5 level thresholds values of the lena image by Kapur’s entropy are 20.1768, 20.17062, 20.1648, 20.1758, 20.1445 and 20.1697 for OSOS, SOS, CS, BAT, ABC and PSO respectively which clearly indicate that OSOS based thresholding gives the best result among others. Figs. 2–4 display the threshold images by maximizing the objective functions using the six meta-heuristic optimization techniques. For the man image, Otsu’s BCV is taken as an objective function for segmentation. 2 to 5 level threshold images by applying OSOS, SOS, CS, BAT, ABC, and PSO optimization algorithms are shown in Fig. 2. For thresholding, the lena image, Kapur’s entropy is used as the objective function, and the 2 to 5 level threshold outputs images are shown in Fig. 3. Tsallis entropy is used for thresholding the peppers image, and the threshold outputs are shown in Fig. 4.

16

F. Chakraborty, D. Nandi and P.K. Roy / Applied Soft Computing Journal 82 (2019) 105577

Table 5 Comparison of mean and standard deviation of red after 30 run of each algorithm for the six test images based on Kapur’s method. MEAN

SD

Image

K

OSOS

SOS

CS

BAT

ABC

PSO

OSOS

SOS

CS

BAT

ABC

PSO

Lena

2 3 4 5

12.072100 15.02540 17.670745 20.174645

12.072100 15.019379 17.669459 20.164139

12.072100 15.003607 17.661679 20.142279

12.072100 15.018836 17.653359 20.167219

12.072100 15.018276 17.649159 20.061959

12.072100 15.01661 17.659119 20.161119

1.87244E−15 0.934231689 0.001217477 0.003748188

000000000 0.931269086 0.002273013 0.004651352

000000000 1.523266887 0.002213687 0.042978278

000000000 1.499151015 0.007028286 0.007067755

000000000 1.522271596 0.002297131 0.104589086

000000000 1.525296955 0.00670998 0.010181544

Lake

2 3 4 5

12.10544 15.35440 18.230753 20.894243

12.099779 15.354400 18.130712 20.794561

12.086007 15.242364 18.119677 20.76758

12.004067 15.242377 18.119268 20.683971

12.084747 15.242173 18.075477 20.753247

12.091314 15.239457 18.119579 20.762627

0.002867132 0000000000 0.00426145 0.004346258

0.006222076 0000000000 0.318574018 0.403184903

0.043838874 0.316227562 0.315505551 2.544292283

0.315319317 0.316227562 0.444323811 0.464042485

0.044691302 0.316227562 0.319903638 0.338450481

0.030521882 0.316227562 0.315529474 0.415350603

Man

2 3 4 5

12.354700 15.580800 18.238897 20.860497

12.354700 15.580800 18.005585 20.613161

12.354700 15.58080 18.003561 20.669285

12.354700 15.398585 17.895271 20.462671

12.354700 15.343551 17.994651 20.347851

12.354700 14.654389 17.316889 19.917889

0000000000 0000000000 0.003448750 6.94973E−06

0000000000 0000000000 0.00486420 5.379762E−05

000000000 000000000 0.16797547 3.54276E−05

000000000 0.05654098 0.1864599 4.76974E−03

000000000 1.238105475 0.09322081 3.87883E−03

000000000 1.035765327 3.41207077 2.63467E−04

Beer

2 3 4 5

13.228700 16.531400 19.574000 22.419097

13.228700 16.531300 19.573800 22.169785

13.228700 16.256051 19.270271 22.127171

13.228700 16.244871 19.333461 21.797561

12.942171 16.290961 19.239451 21.786451

12.996651 15.604989 18.647589 21.497489

0000000000 0000000000 0000000000 0.015687543

0000000000 0000000000 0000000000 0.06659764

000000000 1.28538E−06 1.02639865 0.573332452

000000000 6.8437E−07 0.19007534 2.997002211

6.80557E−07 7.19759E−06 3.66348E−07 1.20422532

3.9598E−05 2.85463E−06 5.44863E−06 2.813616647

Airplane

2 3 4 5

12.136377 15.539300 18.106677 20.825474

11.980461 15.343700 17.918061 20.797195

11.854671 14.43078 17.19148 20.664750

11.908327 15.053654 17.822871 20.64635

11.859147 15.150485 17.902847 20.679853

11.22198 15.117884 17.885127 20.623456

0.009915286 0000000000 0.009025209 0.004356756

0.339349224 0000000000 0.368692117 0.019718643

0.474184451 0.472371161 0.415198201 0.116446481

0.42125311 0.52059022 0.478223096 0.054325756

0.521360795 0.42556288 0.478223096 0.98543078

2.862150349 1.545085475 2.884768033 0.175432681

Peppers

2 3 4 5

12.515700 15.539300 18.407200 20.963497

12.515700 15.539300 18.1823857 20.778247

12.515700 15.307451 18.164961 20.719461

12.515700 15.297061 18.174551 20.656831

12.515700 15.248631 18.120131 20.533451

12.515700 14.613589 17.481289 20.040789

0000000000 0000000000 0000000000 0.000232195

0000000000 0000000000 0.003898757 0.006994391

000000000 5.39602E−07 0.386411143 0.05432957

000000000 000000000 0.008987008 0.058798765

000000000 1.14867E−05 0.490006549 0.1697765431

000000000 3.03643E−06 0.049876783 0.1987987654

Table 6 Comparison of PSNR, SSIM, FSIM of red band for OSOS, SOS, CS, BAT, ABC and PSO based by Kapur’s method. PSNR(dB)

SSIM

FSIM

Image

K

OSOS

SOS

CS

BAT

ABC

PSO

OSOS

SOS

CS

BAT

ABC

PSO

OSOS

SOS

CS

BAT

ABC

PSO

Lena

2 3 4 5

23.8937 23.2009 25.9701 26.1549

23.8937 23.2009 25.2707 25.9536

23.8937 23.2009 25.0336 25.6443

23.8937 23.2009 24.6643 25.8633

23.8937 22.6764 25.2579 25.8366

23.8937 22.7527 24.9958 25.6382

0.9943 0.9921 0.9957 0.9962

0.9943 0.9921 0.9951 0.9953

0.9943 0.9921 0.9949 0.9954

0.9943 0.9921 0.9942 0.9956

0.9943 0.9910 0.9951 0.9957

0.9943 0.9909 0.9945 0.9956

0.8854 0.8739 0.9137 0.9299

0.8854 0.8739 0.9127 0.9290

0.8854 0.8739 0.9118 0.9226

0.8854 0.8739 0.9028 0.9255

0.8854 0.8825 0.9274 0.9267

0.8854 0.8753 0.9114 0.9273

Lake

2 3 4 5

19.4009 20.1075 22.2963 24.1245

19.4009 20.1075 21.8966 23.3445

19.4009 20.1075 21.8564 23.2548

19.4009 20.1075 21.8298 23.2991

19.4009 20.0937 22.1371 23.1588

19.4009 19.6851 21.8564 23.1113

0.9359 0.9490 0.9679 0.9798

0.9359 0.9490 0.9670 0.9767

0.9359 0.9490 0.9658 0.9755

0.9359 0.9490 0.9669 0.9760

0.9359 0.9485 0.9669 0.9759

0.9359 0.9466 0.9658 0.9753

0.8221 0.8523 0.9088 0.9292

0.8221 0.8523 0.9009 0.9276

0.8221 0.8523 0.8970 0.9375

0.8221 0.8523 0.8979 0.9272

0.8221 0.8509 0.8989 0.9267

0.8221 0.8411 0.8970 0.9253

Man

2 3 4 5

21.3640 21.8232 21.8280 22.6946

21.3640 21.8232 21.8280 22.4679

21.3640 21.8232 21.5386 22.4476

21.3640 21.8232 20.7894 22.1655

21.3640 21.8232 20.3696 22.1597

21.3640 21.1694 21.1451 22.3210

0.9906 0.9905 0.9904 0.9971

0.9906 0.9905 0.9904 0.9938

0.9906 0.9905 0.9898 0.9916

0.9906 0.9905 0.9869 0.9920

0.9906 0.9905 0.9867 0.9921

0.9906 0.9891 0.9890 0.9919

0.8720 0.8800 0.8779 0.8804

0.8720 0.8800 0.8779 0.8753

0.8720 0.8800 0.8756 0.8740

0.8720 0.8800 0.8707 0.8723

0.8720 0.8800 0.8693 0.8713

0.8720 0.8774 0.8771 0.8261

Beer

2 3 4 5

21.7947 22.1601 22.8370 23.9502

21.7947 22.1601 22.5935 23.4008

21.7947 22.1601 22.4611 23.2632

21.7947 22.1601 22.5350 23.3364

21.7947 21.8059 21.8461 22.6653

21.7947 21.0123 21.4326 20.2305

0.9843 0.9818 0.9803 0.9813

0.9843 0.9818 0.9784 0.9770

0.9843 0.9818 0.9770 0.9763

0.9843 0.9818 0.9772 0.9739

0.9843 0.9806 0.9703 0.9693

0.9843 0.9666 0.9616 0.9512

0.9109 0.9289 0.9414 0.9492

0.9109 0.9289 0.9386 0.9484

0.9109 0.9289 0.9377 0.9463

0.9109 0.9289 0.9395 0.9542

0.9109 0.9232 0.9258 0.9443

0.9109 0.9153 0.9167 0.8975

Airplane

2 3 4 5

20.6638 24.9831 26.9861 28.9726

20.6638 24.4202 26.8726 28.9347

20.6638 24.4202 26.8066 28.7768

20.6638 24.4202 26.8453 28.4817

20.6638 23.9013 26.8551 27.7683

20.6638 24.4202 26.5780 27.8993

0.9786 0.9900 0.9944 0.9966

0.9786 0.9900 0.9944 0.9964

0.9786 0.9900 0.9939 0.9960

0.9786 0.9900 0.9943 0.9933

0.9786 0.9893 0.9939 0.9959

0.9786 0.9900 0.9941 0.9925

0.8441 0.9286 0.9445 0.9647

0.8441 0.9124 0.9440 0.9668

0.8441 0.9124 0.9430 0.9348

0.8441 0.9124 0.9424 0.9651

0.8441 0.9046 0.9386 0.9520

0.8441 0.9124 0.9391 0.9069

Peppers

2 3 4 5

21.2660 20.2499 22.2910 23.5919

21.2660 20.2499 22.2910 23.4716

21.2660 20.2499 22.0630 23.3735

21.2660 19.6358 21.9562 23.2304

21.2660 19.6358 22.1891 23.4586

21.2660 20.2499 22.0759 20.9428

0.9824 0.9698 0.9783 0.9863

0.9824 0.9698 0.9783 0.9852

0.9824 0.9698 0.9770 0.9844

0.9824 0.9639 0.9768 0.9846

0.9824 0.9639 0.9765 0.9838

0.9824 0.9698 0.9770 0.9636

0.8602 0.8672 0.8887 0.9096

0.8602 0.8672 0.8887 0.9092

0.8602 0.8672 0.8871 0.9085

0.8602 0.8570 0.8850 0.9074

0.8602 0.8570 0.8884 0.9081

0.8602 0.8672 0.8872 0.8699

6.3. Steadiness of algorithm Initially, all metaheuristic algorithms start with some randomly selected population. As a result, the algorithms may not produce the same result in each run. Therefore, the performance of an algorithm should be quantified by executing it a good number of times and then taking the mean and standard deviation of the objective functions’ values. Table 5 displays the mean and standard deviation (SD) values of Kapur’s entropy for red band by executing each algorithm 30 times (i.e.30 runs). Higher value of mean indicates the better accuracy whereas lesser value of SD indicates higher stability of the algorithm. The table shows that, in case of peppers image, the mean values of the objective function for red band are 20.963497, 20.778247, 20.719461, 20.656831, 20.533451 and 20.040789 for OSOS, SOS, CS, BAT, ABC, and PSO, respectively, whereas standard deviations are 0.000232195, 0.0069943891, 0.05432957, 0.058798765, 0.1697765431 and 0.1987987654, respectively. The least value of standard deviation for OSOS indicates that OSOS is more stable as compared to the other algorithms.

are employed. It is known that only one quality metric cannot measure the image quality in all respects. Keeping it in mind, we feel that peak signal to noise ratio (PSNR), structural similarity index metric (SSIM) [42], feature similarity index metric (FSIM) [43] are significant for the quality assessment of output image. The definitions of the metrics are given in the subsequent part of this section. 6.4.1. Peak signal to noise ratio (PSNR) The peak signal to noise ratio in dB is defined as,

( PSNR = 10 log10

2552

)

MSE

(38)

where MSE is mean square error, formulated as:

∑M ∑N MSE =

i=1

j=1

|I (i, j) − S (i, j) |

M ∗N

(39)

where I(i, j) and S(i, j) represent the actual and segmented images respectively. Larger value of PSNR indicates better performance.

6.4. Metrics for performance evaluation In order to judge the performance of the algorithms, some quality metrics for evaluating the quality of the output images

6.4.2. Structural Similarity Index Metric (SSIM) SSIM [42] is used to measure the structural similarity between actual and segmented image. The highest value of SSIM

F. Chakraborty, D. Nandi and P.K. Roy / Applied Soft Computing Journal 82 (2019) 105577

17

Table 7 Average CPU time (milliseconds) of OSOS, SOS, CS, BAT, ABC, and PSO of three band by Kapur methods. CPU timing Image

K

OSOS

SOS

CS

BAT

ABC

PSO

Lena

2 3 4 5

60.2 65.8 91.5 129.1

65.5 74.6 98.4 137.5

63.4 72.6 97.3 136.8

66.8 74.8 103.5 141.1

68.9 79.6 100.6 140.3

75.6 79.6 99.8 139.8

Lake

2 3 4 5

50.2 54,6 95.7 132.6

54.9 58.7 98.6 135.3

51.4 56.3 95.7 132.1

56.9 63.7 102.4 138.7

55.8 67.5 100.3 138.9

56.8 64.9 103.8 139.8

Man

2 3 4 5

45.6 58.1 92.3 135.4

47.2 60.3 95.4 137.2

46.3 59.5 93.4 136.4

51.3 62.3 98.4 139.5

48.2 61.4 99.3 140.2

52.3 63.6 100.3 142.6

Beer

2 3 4 5

57.4 70.1 108.4 145.3

60.3 72.6 110.5 147.3

58.2 71.3 108.7 146.7

62.3 74.6 112.5 149.6

63.1 73.6 113.5 151.4

64.7 57.8 115.7 154.3

Airplane

2 3 4 5

46.8 58.7 92.6 132.7

50.7 59.6 94.6 134.5

47.5 56.3 92.4 132.6

52.6 62.8 96.7 137.6

54.7 63.8 97.5 138.4

53.8 63.9 96.9 139.7

2 3 4 5

47.2 65.4 92.4 112.1

49.8 68.6 95.6 115.6

48.2 67.5 94.8 114.7

52.7 70.1 97.5 118.7

51.6 69.4 96.6 117.8

50.3 69.8 96.4 116.5

Peppers

Table 8 Result of Wilcoxon rank sum test of red band for Kapur’s method. Kapur Image

K

OSOS vs. SOS

OSOS vs. CS

OSOS vs. BAT

OSOS vs. ABC

OSOS vs. PSO

p

h

p

h

p

h

p

h

p

h

Lena

2 3 4 5

<0.05* <0.05* >0.05#* <0.05*

1 1 0 1

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

Lake

2 3 4 5

<0.05* <0.05* <0.05* >0.05#

1 1 1 0

<0.05* <0.05* <0.05* <0.05*

1 1 0 1

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

Man

2 3 4 5

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

Beer

2 3 4 5

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

<0.05* <0.05* <0.05* <0.05*

0 1 1 1

<0.05* <0.05* <0.05* <0.05*

0 1 1 1

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

>0.05# <0.05* <0.05* >0.05#

0 1 1 0

Airplane

2 3 4 5

<0.05* <0.05* >0.05# <0.05*

1 1 0 1

<0.05* <0.05* >0.05# <0.05*

1 1 0 1

<0.05* <0.05* >0.05# <0.05*

1 1 0 1

<0.05* <0.05* <0.05* >0.05#

1 1 1 0

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

Peppers

2 3 4 5

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

<0.05* <0.05* <0.05* <0.05*

1 0 1 1

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

<0.05* <0.05* <0.05* <0.05*

1 1 1 1

represents the better performance. SSIM is defined as follows: 2µx µy + c1

( SSIM (x, y) = (

µ2x + µ2y + c1

)(

)(

2σxy + c2

)

σx2 + σy2 + c2

)

(40)

(40) where µx , µy are the mean intensity of actual image and segmented image, respectively; σx , σy are the standard deviation of actual and segmented image; σxy is the co-variance of actual and segmented image; C1 and C2 are two constant, such that he C1 = 0.01 and C2 = 0.03.

6.4.3. Feature similarity index metric (FSIM) FSIM [43] is used to find the structural similarity between actual and segmented image. For two images f1 (X) and f2 (X), the FSIM is given by,

∑ FSIM =

X∈Ω

∑

SL (X) PCm (X)

X∈Ω

PCm (X)

(41)

18

F. Chakraborty, D. Nandi and P.K. Roy / Applied Soft Computing Journal 82 (2019) 105577

where Ω means the whole image spatial domain and SL (X) = SPC (X) SG (X) SPC (X) and SG (X) are given by, SL (X) = SG (X) =

2PC1 (X) PC2 (X) + T1 PC12 (X) + PC22 (X) + T1

and

2G1 (X) G2 (X) + T2

(42)

G21 (X) + G22 (X) + T2

where PC1 and PC2 are the phase congruency maps extracted from two images f1 (X) and f2 (X) respectively; T1 and T2 are constants and taken as T1 = 0.85, T2 = 160. Higher value of FSIMindicates better performance. Table 6 show the values of PSNR (dB), SSIM, and FSIM metrics of the color images for Red brands. It is seen from the tables that PSNR, SSIM and, FSIM value of the segmented images by the proposed OSOS gives a better value than other algorithms. It is observed from the table that the value of PSNR increased as the number of the threshold is increased, and the visual quality segmented images are also improved as the number of the threshold value is increased. For example PSNR value of red brands in case of lena image with 5-level thresholding for Kapur entropy are 26.1549, 25.9536, 25.6443, 25.8633, 25.8366 and 25.6382 for OSOS, SOS, CS, BAT, ABC, and PSO respectively, It clearly indicate that the OSOS based method produces better quality segmentation compared to others algorithm.

7. Conclusions In this article, the OBL concept has been incorporated to enhance the performance and the convergence speed of the standard SOS algorithm. The OBL is used in two phases: in the first phase, the initial population and its opposite population are simultaneously evaluated and the fitter one is chosen as the initial solution and in the second phase, opposition-based generation is performed in each iteration by considering jumping probability which helps for quick convergence of the solution. The merit of OSOS has been examined in the field of multilevel image thresholding, for the segmentation of color image using three popular objective functions such as Otsu’s between class variance, Kapur’s entropy, and Tsallis entropy. The performance of the proposed OSOS algorithm is compared with basic SOS and some other well-known and recently proposed meta-heuristic algorithms like CS, BAT, PSO and ABC using the same objective functions. The performance of the algorithms is verified with 2, 3, 4, 5 level thresholding on a set of images taken from standard Berkeley Segmentation Dataset and COCO dataset. The numeric illustration and reliability assessments for every images considered in this paper reveals that OSOS with Otsu’s between class variance, Kapur’s entropy, and Tsallis entropy outperforms CS, BAT, PSO and PSO. This clearly suggests that the proposed algorithm can be used effectively for multilevel image thresholding. Declaration of competing interest

6.5. Computational time and convergence Fig. 5 shows the convergence graphs of OSOS, SOS, CS, BAT, ABC, and PSO, using Kapur entropy and Otsu BCV objective functions for three color bands of lena and peppers images. It is clearly observed for this figure that the convergence performance of OSOS is superior to the other algorithms. Table 7 shows the average computation time of OSOS, SOS, CS, BAT, ABC, and PSO of red band for all three thresholding methods for 30 run each. It is found that the proposed OSOS is faster than conventional SOS and CS, BAT, ABC, and PSO algorithms. 6.6. Statistical investigation Wilcoxon rank sum [44] test at 5% significant level has been performed for the proposed algorithm to compare it with SOS, CS, BAT, ABC, and PSO. The test is done by running each algorithm 30 times for each bands. In testing we consider two hypotheses. Null hypothesis assumes that there is no major difference between the algorithms whereas alternative hypothesis considers that there is a major difference between the algorithms. Table 8 shows the p and h value for the all algorithms for red band, a value of p > 0.05 or (h = 0) represents the null hypothesis cannot be rejected whereas value of p < 0.05 or (h = 1) indicate null hypothesis can be rejected. The result of Table 8 reveals that OSOS performs better with respect to other algorithms. (Note * indicates a significant difference and # indicate no significant difference.) The segmentation results obtained for test images demonstrate that, regarding solution quality, stability convergence speed, computational time and the quality of the segmented images OSOS has comprehensively outperformed the standard SOS and other algorithms. By observing the promising segmentation results of the OSOS algorithm, other researchers may be motivated to implement the proposed algorithm to solve complex real-life problem.

No author associated with this paper has disclosed any potential or pertinent conflicts which may be perceived to have impending conflict with this work. For full disclosure statements refer to https://doi.org/10.1016/j.asoc.2019.105577. References [1] L.C. Chen, G. Papandreou, I. Kokkinos, K. Murphy, A.L. Yuille, Deeplab, semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs, IEEE transactions on pattern analysis and machine intelligence (2017). [2] N. Hatipoglu, G. Bilgin, Classification of histopathological images using convolutional neural network, in: Proceedings of the International Conference on Image Processing Theory, Tools and Applications (IPTA), 2014, pp. 1–6. [3] Yanming Guo, Yu Liu, Theodoros Georgiou, Michael S. Lew, A review of semantic segmentation using deep neural networks, Int. J. Multimed. Inf. Retr. (2017). [4] P.Y. Yin, Multilevel minimum cross entropy threshold selection based on particle swarm optimization algorithm, Appl. Math. Comput. 184 (2) (2007) 503–513. [5] P.D. Sathya, R. Kayalvizhi, Optimum multilevel image thresholding based on tsallis entropy method with bacterial foraging algorithm, Int. J. Comput. Sci. 7 (5) (2010) 336–343. [6] J.N. Kapur, P.K. Sahoo, A.K.C. Wong, A new method for gray-level picture thresholding using the entropy of the histogram, Comput. Vis. Graph. Image Process. 29 (1985) 273–285. [7] K. Hammouche, M. Diaf, P. Siarry, A multilevel automatic thresholding method based on a genetic algorithm for a fast image segmentation, Comput. Vis. Image Underst. 109 (2) (2008) 163–175. [8] J. Zhang, H. Li, Z. Tang, Q. Lu, X. Zheng, J. Zhou, An improved quantum inspired genetic algorithm for image multilevel thresholding segmentation, Math. Probl. Eng. 112 (2014). [9] P.Y. Yin, Multilevel minimum cross entropy threshold selection based on particle swarm optimization algorithm, Appl. Math. Comput. 184 (2) (2007) 503–513. [10] Y. Zhang, L. Wu, Optimal multi-level thresholding based on maximum tsallis entropy via an artificial bee colony approach, Entropy 13 (4) (2011) 841–859. [11] B. Akay, A study on particle swarm optimization and artificial bee colony algorithms for multilevel thresholding, Appl. Soft Comput. 13 (2013) 3066–3091. [12] A.K. Bhandari, A. Kumar, G.K. Singh, Modified artificial bee colony based computationally efficient multilevel thresholding for satellite image segmentation using Kapur’s, Otsu and Tsallis functions, Expert Syst. Appl. 42 (2015) 1573–1601.

F. Chakraborty, D. Nandi and P.K. Roy / Applied Soft Computing Journal 82 (2019) 105577 [13] W. Tao, H. Jin, L. Liu, Object segmentation using ant colony optimization algorithm and fuzzy entropy, Pattern Recognit. Lett. 28 (7) (2007) 788–796. [14] S. Agrawal, R. Panda, S. Bhuyan, B.K. Panigrahi, Tsallis entropy based optimal multilevel thresholding using cuckoo search algorithm, Swarm Evol. Comput. 11 (2013) 16–30. [15] M.H. Horng, Multilevel minimum cross entropy threshold selection based on the honey bee mating optimization, Expert Syst. Appl. 37 (2010) 4580–4592. [16] S. Ouadfel, A. Taleb-Ahmed, Social spiders optimization and flower pollination algorithm for multilevel image thresholding: A performance study, Expert Syst. Appl. 55 (2016) 566–584. [17] S.M. Raja, S.A. Sukanya, Y. Nikita, Improved PSO based multilevel thresholding for Cancer Infected Breast Thermal Images using Otsu, Procedia Comput. Sci. 48 (2015) 524–529. [18] S. Manikandan, K. Ramar, I.M. Willjuice, K.G. Srinivasagan, Multilevel thresholding for segmentation of medical brain images using real coded genetic algorithm, Measurement 47 (2014) 558–568. [19] M.A. Bakhshali, M. Shamsi, Segmentation of color lip imags by optimal thresholding using bacterial foraging optimization(BFO), J. Compt. Sci. 5 (2) (2014) 251–257. [20] Lifang He, Songwei. Huang, Lifang he songwei huang modified firefly algorithm based multilevel thresholding for color image segmentation, Neurocomputing 240 (2017) 152–174. [21] Mohamed Abd El Aziz, Ahmed A. Ewees, Aboul Ella Hassanien, Whale Optimization Algorithm and Moth-Flame Optimization for multilevel thresholding image segmentation, Expert Syst. Appl. 83 (2017) 242–256. [22] Abdul Kayom Md. Khairuzzaman, Saurabh. Chaudhury, Multilevel thresholding using gray wolf optimizer for image segmentation, Expert Syst. Appl. 86 (2017) 64–76. [23] A.K. Bhandari, A. Kumar, S. Chaudhary, G.K. Singh, A novel color image multilevel thresholding based segmentation using nature inspired optimization algorithms, Expert Syst. Appl. 63 (2016) 112–133. [24] M.Y. Cheng, D. Prayogo, Symbiotic organisms search: A new metaheuristic optimization algorithm, Comput. Struct. 139 (2014) 98–112. [25] M.Y. Cheng, D. Prayogo, D. Tran, Optimizing multiple resources levelling in multiple projects using discrete symbiotic organisms search, J. Comput. Civ. Eng. 30 (3) (2016). [26] D.H. Tran, M.Y. Cheng, D. Prayogo, A novel multiple objective symbiotic organisms search (MOSOS) for timecost-labor utilization tradeoff problem, Knowl.-Based Syst. 94 (2016) 132–145. [27] R. Eki, F.Y. Vincent, S. Budi, A.A.N. Perwira Redi, Symbiotic organism search (SOS) for solving the capacitated vehicle routing problem, Appl. Soft Comput. 52 (2017) 657–672. [28] M. Abdullahi, M.A. Ngadi, S.M. Abdulhamid, Symbiotic organism search optimization based task scheduling in cloud computing environment, Future Gener. Comput. Syst. 56 (2016) 640–650.

19

[29] D. Prasad, V. Mukherjee, A novel symbiotic organisms search algorithm for optimal power flow of power system with FACTS devices, Eng. Sci. Technol. 19 (1) (2016) 79–89. [30] M.K. Dosoglu, U. Guvenc, S. Duman, Y. Sonmez, H.T. Kahraman, Symbiotic organisms search optimization algorithm for economic/emission dispatch problem in power systems, Neural Comput. Appl. (2016). [31] A. Panda, S. Pani, A symbiotic organisms search algorithm with adaptive penalty function to solve multi-objective constrained optimization problems, Appl. Soft Comput. 46 (2016) 344–360. [32] Hamid R. Tizhoosh, Opposition-based reinforcement learning, J. Adv. Comput. Intell. Intell. Inform. 10 (4) (2006) 578–585. [33] S. Rahnamayan, H.R. Tizhoosh, M. Salama, Opposition versus randomness in soft computing techniques, Appl. Soft Comput. 8 (2) (2008) 906–918. [34] Hui wang, Zhijian Wu Shahryar Rahnamayan, Yong Liu, Mario Ventresca, Enhancing particle swarm optimization using generalized opposition-based learning, Inform. Sci. 181 (2011) 4699–4714. [35] Xiaoji Yang, Zhiguo Huang, Opposition-based artificial bee colony with dynamiv Cauchy mutation for function optimizion, Int. J. Adv. Comput. Technol. 4 (4) (2012). [36] Gai-Ge Wang, Suash Deb, Amir H. Gandomi, Amir H. Alavi, Oppositionbased kill herd algorithm with Cauchy mutation and position clamping, Neurocomputing 177 (2016) 147–157. [37] S. Rahnamayan, Hamid R. Tizhoosh, M.M.A. Salama, Opposition-based differential evolution, IEEE Trans. Evol. Comput. 12 (1) (2008). [38] N. Otsu, A threshold selection method from gray-level histograms, IEEE Trans. SMC 9 (1) (1979) 62–66. [39] J.N. Kapur, P.K. Sahoo, A.K.C. Wong, A new method for gray-level picture thresholding using the entropy of the histogram, Comput. Vis. Graph. Image Process. 29 (1985) 273–285. [40] W. Tsai, Moment-preserving thresholding: A new approach, Comput. Vis. Graph. Image Process. 29 (1985) 377–393. [41] Adis Alihodzic, Milan. Tuba, Improved bat algorithm applied to multilevel image thresholding, Sci. World J. (2014). [42] f.W. Zhou, C.B. Alan, S.R. Hamid, S.P. Eero, Image quality assessment: From error visibility to structural similarity, IEEE Trans. Image Process. 13 (4) (2004) 600–612. [43] Z. Lin, Z. Lei, M. Xuanqin, D. Zhang, FSIM: A feature similarity index for image quality assessment, IEEE Trans. Image Process. 20 (8) (2011) 2378–2386. [44] F. Wilcoxon, Individual comparisons by ranking methods, Int. Biom. Soc. 1 (6) (1945) 80–83.