Expert Systems With...

Expert Systems With Applications 83 (2017) 242–256

Contents lists available at ScienceDirect

Expert Systems With Applications

journal homepage: www.elsevier.com/locate/eswa

Whale Optimization Algorithm and Moth-Flame Optimization for

multilevel thresholding image segmentation

Mohamed Abd El Aziz

a , b , Ahmed A. Ewees c , ∗, Aboul Ella Hassanien

d

a Department of Mathematics, Faculty of Science, Zagazig University, Egypt b School of Computer Science and Technology, Wuhan University of Technology, Wuhan, China. c Department of Computer, Damietta University, Egypt d Faculty of Computers and Information, Cairo University, Egypt

a r t i c l e i n f o

Article history:

Received 20 November 2016

Revised 8 April 2017

Accepted 9 April 2017

Available online 22 April 2017

Keywords:

Whale Optimization Algorithm (WOA)

Moth-Flame Optimization (MFO)

Image segmentation

Multilevel thresholding

a b s t r a c t

Determining the optimal thresholding for image segmentation has got more attention in recent years

since it has many applications. There are several methods used to find the optimal thresholding val-

ues such as Otsu and Kapur based methods. These methods are suitable for bi-level thresholding case

and they can be easily extended to the multilevel case, however, the process of determining the optimal

thresholds in the case of multilevel thresholding is time-consuming. To avoid this problem, this paper ex-

amines the ability of two nature inspired algorithms namely: Whale Optimization Algorithm (WOA) and

Moth-Flame Optimization (MFO) to determine the optimal multilevel thresholding for image segmenta-

tion. The MFO algorithm is inspired from the natural behavior of moths which have a special navigation

style at night since they fly using the moonlight, whereas, the WOA algorithm emulates the natural co-

operative behaviors of whales. The candidate solutions in the adapted algorithms were created using the

image histogram, and then they were updated based on the characteristics of each algorithm. The solu-

tions are assessed using the Otsu’s fitness function during the optimization operation. The performance

of the proposed algorithms has been evaluated using several of benchmark images and has been com-

pared with five different swarm algorithms. The results have been analyzed based on the best fitness

values, PSNR, and SSIM measures, as well as time complexity and the ANOVA test. The experimental re-

sults showed that the proposed methods outperformed the other swarm algorithms; in addition, the MFO

showed better results than WOA, as well as provided a good balance between exploration and exploita-

tion in all images at small and high threshold numbers.

© 2017 Elsevier Ltd. All rights reserved.

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1. Introduction

Thresholding is one of the popular techniques in image seg-

mentation. It has two categories: bi-level and multilevel ( Bhandari,

Singh, Kumar, & Singh, 2014; Sarkar, Nayan, Kundu, Das, & Chaud-

huri, 2013 ). The bi-level thresholding splits the image into two

classes, whereas multilevel is used to segment complex images and

it can produce multiple thresholds such as tri-level or quad-level,

which split pixels into multiple similar parts based on intensity

( Guo & Li, 2007; Zhang & Wu, 2011 ). Bi-level thresholding can pro-

duce adequate outcomes in the case that the image contains only

two principal gray levels, but the foremost restriction is the time-

consuming computation which is often high when it is extended to

multilevel thresholding ( Dirami, Hammouche, Diaf, & Siarry, 2013 ).

∗ Corresponding author.

E-mail addresses: [email protected] (M.A.E. Aziz), a.ewees@hotmail.

com , [email protected] (A .A . Ewees), [email protected] (A.E. Hassanien).

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http://dx.doi.org/10.1016/j.eswa.2017.04.023

0957-4174/© 2017 Elsevier Ltd. All rights reserved.

Basically, two approaches namely parametric and nonparamet-

ic ( Hammouche, Diaf, & Siarry, 2008 ) are used to determine

he optimal thresholds. In the first one, some statistical param-

ters (e.g. time-consuming, and their accuracy) should be com-

uted for the classes in the image. In the second one, the opti-

al thresholds are determined by maximizing some criteria such

s the Otsu’ criterion ( Otsu, 1979 ) and Kapur’s entropy ( Kapur, Sa-

oo, & Wong, 1985 ). In the Otsu-based method, the best thresh-

ld is the one that maximizes the between-class variance of the

egions. Kapur’s entropy measures the homogeneity of the classes

y using the maximization of the entropy. So, the selection of op-

imal thresholds in multilevel is a NP-hard problem ( Marciniak,

owal, Filipczuk, & Korbicz, 2014 ), and it has been considered as

challenge over decades ( Dirami et al., 2013; Sarkar et al., 2013 ).

hen the threshold number is small, classical techniques are suit-

ble; but if this number increases, the accuracy of segmentation

ill be affected. Therefore, to avoid this weakness, many swarm

ntelligence (SI) techniques have been applied and combined


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M.A.E. Aziz et al. / Expert Systems With Applications 83 (2017) 242–256 243

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ith thresholding algorithms; such as Genetic Algorithm (GA)

Elsayed, Sarker, & Essam, 2014 ), Particle Swarm Optimization

PSO) ( Kennedy & Eberhart, 1995 ), Ant Colony Optimization (ACO)

Kaveh & Talatahari, 2010 ), Firefly Algorithm (FA) ( Yang, 2009 ), and

ocial Spider Optimization (SSO) ( Cuevas, Cienfuegos, ZaldíVar, &

éRez-Cisneros, 2013 ). For example, Pruthi and Gupta (2016) pre-

ented an algorithm based on GA and its combination with Otsu to

vercome segmentation drawbacks. Also, PSO is applied to deter-

ine the multilevel thresholding for image segmentation ( Ghamisi,

ouceiro, Benediktsson, & Ferreira, 2012; Ye, Hu, Wang, & Chen,

011 ). Naik and Gopal (2016) used PSO as a preprocessing tech-

ique prior to the image segmentation. The image is preprocessed

o get the optimum pixels and then k-means clustering is applied

n the image for segmentation. Whereas, Erdmann, Wachs-Lopes,

allão, Ribeiro, and Rodrigues (2015) presented a firefly algorithm

FA) method for multilevel thresholding segmentation, and the im-

roved FA (IFA) is used to enhance the performance of FA to solve

multilevel image thresholding problem as in Chen et al. (2016) .

he IFA used Cauchy mutation and neighborhood strategy to in-

rease the global search ability and accelerate the convergence.

FA also is utilized to search for multilevel global best thresholds

nd segment images into background and objects ( Horng, 2011 ). In

ddition, Fayad, Hatt, and Visvikis (2015) developed and validated

n image segmentation approach based on ACO algorithm. On the

ther hand, Agarwal, Singh, Kumar, and Bhattacharya (2016) de-

loyed histogram based on bi-modal and multi-modal threshold-

ng for a gray image using SSO. They employed SSO to maximize

apur’s and Otsu’s functions values. Furthermore, there are many

ther swarm algorithms, that were used for image segmentation

ncluding: bacterial foraging algorithm (BFO) ( Bakhshali & Shamsi,

014; Sanyal, Chatterjee, & Munshi, 2011 ), honey bee mating opti-

ization (HBMO) ( Horng, 2010 ), wind driven optimization (WDO)

Bayraktar, Komurcu, Bossard, & Werner, 2013 ), cuckoo search (CS)

Agrawal, Panda, Bhuyan, & Panigrahi, 2013 ), artificial bee colony

ABC) ( Akay, 2013; Bhandari, Kumar, & Singh, 2015 ), harmony

earch (HS) algorithm ( Oliva, Cuevas, Pajares, Zaldivar, & Perez-

isneros, 2013 ), and hybrid swarm (FASSO) ( Abd El-Aziz, Ewees,

Hassanien, 2016 ). However, most of these algorithms have slow

onvergences to the global optimal solution (i.e. can get stuck in

ocal optimal) and the quality of segmentation becomes poor when

he number of thresholds is increased. In addition, before applying

hem, their parameters must be fine-tuned.

Recently, two new swarm algorithms namely, the Whale Op-

imization Algorithm (WOA) and the Moth-Flame Optimization

MFO) are introduced. The WOA is introduced by Mirjalili and

ewis (2016) to solve the global optimization problem by emu-

ating the behavior of humpback whales. The humpback whales

ave a unique hunting method called bubble-net feeding ( Mirjalili

Lewis, 2016 ). This behavior works in three different phases,

amely, coral loop, lobtail, and capture loop ( Mirjalili & Lewis,

016 ). More information about this behavior can be found in

oldbogen et al. (2013) .

The WOA has been used in several applications such as in

aveh and Ghazaan (2016) , Cherukuri and Rayapudi (2016) , and

ouma (2016) , these studies have showed that the WOA algorithm

ives a better accuracy when it is compared to other state-of-the-

rt evolutionary algorithms such PSO and GA. WOA includes ex-

loration and two approaches of exploitation that make it be flex-

ble and gradient-free mechanism as well as it has an ability to

void local optima and get the global optimal solution that makes

t suitable for real applications. In addition, it does not need struc-

ural adjustments in the algorithm for solving different optimiza-

ion problems because it has only two main parameters to be

dapted ( Mirjalili & Lewis, 2016 ).

On the other hand, Mirjalili (2015) had presented MFO, it is a

ew metaheuristic algorithm based on the behavior of the moths.

oths have special navigation style at night since they fly using

he moonlight. The moth in nature flies by calculating a fixed an-

le with respect to the moon and eventually converges towards the

ight which makes moths fly in a straight line; but when there

s an artificial light, the moths fly spirally around the light, since

his light is very close compared to the moon ( Mirjalili, 2015 ). The

ower of MFO algorithm is appeared by increasing exploration of

he search space and decreasing the possibility of being trapped

n local optima, since it assigns each moth a flame and updates

he series of flames in every iteration, as well as, saves the best-

btained position in flames so they never get lost and works as

uides for the moths ( Mirjalili, 2015 ). In Mirjalili (2015) , Li, Li,

nd Liu (2016) , Nanda et al. (2016) , and Parmar et al. (2016) , the

FO was compared with other swarm algorithms to solve several

ontinuous and discrete optimization problems. Its results proved

igh exploitation capability, applicability to solve real problems,

nd ability to optimize search spaces with infeasible regions.

To sum up, these algorithms have many advantages such as:

aving a small number of parameters, simple frameworks, and

bility to avoid the problem of getting stuck in the local optima.

herefore, they can be suitable for many real applications and can

olve several global optimization problems without changing the

tructure of the original algorithm. In addition, both MFO and WOA

lgorithms have operators to balance between exploration and ex-

loitation, unlike other optimizations (e.g. PSO and GA) they apply

ne equation to update the agent’s position, which can increase

he trapping probability in local optima. Based on the success of

oth the proposed algorithms (WOA and MFO) in several applica-

ions, this study further illustrates their power to solve image seg-

entation problems using multilevel thresholding. The Otsu’s cri-

erion is used as a fitness function to assess the solutions in each

opulation of the two algorithms and then determine the best ac-

uracy of the segmented images. In addition, MFO and WOA al-

orithms tune their control parameters through searching for the

lobal solution which avoids the problem of pre-defined control

arameters that can be unsuitable for solving the problem.

The main contributions of this study are two-fold: (1) intro-

uce Whale Optimization Algorithm (WOA) and the Moth-Flame

ptimization (MFO) algorithms for selecting an optimal threshold

alue. (2) Compare between WOA and MFO in such context. To the

est of our knowledge, this concept has not been investigated yet.

The two proposed algorithms generate random solutions in do-

ain bounded by the image histogram. During the updating pro-

ess, the quality of each solution is evaluated using the between-

lass variance function. According to the fitness function value, the

et of solutions is updated based on the characteristics of the WOA

nd MFO until a termination criterion is satisfied. The results of the

OA and MFO algorithms have been compared with other meta-

euristic algorithms. The performance of the different algorithms

as been assessed on various images using the best fitness val-

es and two other criteria namely: the peak-to-signal-noise ratio

PSNR) and the structural similarity index (SSIM), as well as the

ime complexity which is taken into account; in addition, the anal-

sis of variance between all the algorithms has been tested using

n ANOVA test.

The rest of this paper is arranged as follows: in Section 2 , the

roblem formulation and the definition of Otsu’s method are intro-

uced. The proposed algorithms for multilevel thresholding based

n WOA and MFO algorithms are illustrated in Section 3 . The ex-

eriments and results are given in Section 4 . Finally, the conclusion

nd future work are listed in the last section.

. Problem definition

In this section, the definition of multilevel thresholding prob-

em is illustrated which is defined mathematically by considering

244 M.A.E. Aziz et al. / Expert Systems With Applications 83 (2017) 242–256

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a gray level image I to be segmented consisting of K + 1 classes.

Therefore, K thresholds { t 1 , t 2 , . . . , t K } are required to divide the

image into subregions as in Eq. (1) ( Bhandari et al., 2014; Yang,

2014 ):

C 0 = { g(i, j) ∈ I | 0 ≤ g ( i, j ) ≤ t 1 − 1 } C 1 = { g(i, j) ∈ I | t 1 ≤ g ( i, j ) ≤ t 2 − 1 } ,

. . .

K = { g(i, j) ∈ I | t K ≤ g ( i, j ) ≤ L − 1 } (1)

where C k represents the k th class of image, t k ( k = 1,…, K ) is the

k th threshold value, g ( i, j ) is the gray level of the pixel ( i, j ) and L

is the gray levels of I , these levels are in the range (0, 1…L - 1).

The essential purpose of multilevel thresholding is to locate the

threshold values which split pixels into various groups; that can be

determined by maximizing the following equation:

∗1 , t

∗2 , . . . , t

∗K = max

t 1 , ... ,t K F ( t 1 , . . . , t K ) (2)

where F ( t 1 , . . . , t K ) is the Otsu’s function that defined as ( Chen

et al., 2016 ):

F =

K ∑

i =0

A i (ηi − η1 ) 2 , (3)

A i =

t i +1 −1 ∑

j= t i P j , (4)

ηi =

t i +1 −1 ∑

j= t i i

P j

A j

, where P i = h (i ) /N p (5)

where η1 is the mean intensity of I with t 0 = 0 and t K+1 = L . The

h ( i ) and P i are the frequency and the probability of the i th gray

level, respectively. N p represents the total number of pixels in I .

3. The proposed algorithms for multilevel thresholding

In this section, we introduce two algorithms that will be used

to determine the optimal multilevel thresholding for image seg-

mentation that maximizes the Otsu’s objective function.

3.1. Whale Optimization Algorithm

The Whale Optimization Algorithm (WOA) was proposed by the

authors of Mirjalili and Lewis (2016) inspired from the behavior of

the humpback whales.

For the multilevel thresholding problem, the goal of the WOA

algorithm is to determine the position in the search space (the

optimal threshold values) that optimizes the considered objective

function given by Eq. (2) . The input to this algorithm is the image

histogram and the output is the optimal position

� X ∗ that repre-

sents the optimal threshold. Each individual whale � X i (i = 1 , . . . , N)

is represented as a vector of possible real values corresponding to

thresholds as follows ( Mirjalili & Lewis, 2016 ):

� X i = (x i, 1 , x i, 2 , . . . , x i,K )

T , sub ject to 0 < x i, 1 . . . < x i,K < L (6)

where x i , 1 corresponding to t 1 in Eq. (2) . The position of each indi-

vidual whale of the population is generated randomly in the range

[ g min , g max ], where g min and g max are the minimum and the maxi-

mum gray levels in the image histogram, respectively. This can be

expressed by the following equation ( Mirjalili & Lewis, 2016 ):

x i, j = g min + rand(0 , 1) × (g max − g min ) , x i, j ∈

� X i , j = (1 , 2 , . . . , K)

(7)

Then the fitness function for each whale is computed and the best

fitness function F g is determined and its corresponding position

is � X ∗. The whales attacking their prey � X ∗ in either encircling or

ubble-net methods after searching for � X ∗ ( Mirjalili & Lewis, 2016 ).

n the encircling behavior ( Mirjalili & Lewis, 2016 ), the whales up-

ate their position based on the best location as follows ( Mirjalili

Lewis, 2016 ):

�

i = | � B � � X

∗(ν) − � X i (ν) | (8)

�

i ( ν + 1 ) =

� X

∗(ν) − � A � �

D i (9)

here � is a multiplication of elements (e.g. [ a 1 , a 2 , . . . , a n ] �

b 1 , b 2 , . . . , b n ] = [ a 1 b 1 , a 2 b 2 , . . . , a n b n ] ), � D i represents the distance

etween the position of � X ∗(ν) and

� X i (ν) , and ν represents the

urrent iteration. � A and

� B are coefficient vectors and determined

s follows ( Mirjalili & Lewis, 2016 ):

�

= 2

� a � �

r − � a (10)

�

= 2

� r (11)

here � r is a random vector and its elements are generated in

0, 1], and the value of � a is linearly decreased from 2 to 0 as it-

rations proceed as ( Mirjalili & Lewis, 2016 ) � a =

� a − ν �

a νmax

, where

max is the maximum number of iterations.

There are two strategies to simulate the bubble-net behavior.

he first is the shrinking encircling given by decreasing the value

f � a in Eq. (10) , also, � A is decreased. The other one is the spiral up-

ating position, Eq. (12) is used to mimic the helix-shaped move-

ent of the humpback whales around

� X ∗ ( Mirjalili & Lewis, 2016 ):

�

i (ν + 1) =

� D

′ � e bl

� cos (2 π l) +

� X

∗(ν) (12)

here →

D

′ = | →

X ∗(v ) − →

X i (ν) | , b is a constant for defining the shape

f the logarithmic spiral and l ∈ [ −1 , 1] is a random variable.

These whales can swim around the � X ∗ simultaneously through

shrinking circle and along a spiral-shaped path; therefore,

qs. (8) , (9) and (12) are combined in the following equation

Mirjalili & Lewis, 2016 ):

→

X i ( ν + 1 ) =

{ →

X

∗( ν) −

→

A

�→

D

if p < 0 . 5

→

D

′ � e bl

� cos ( 2 π l ) +

→

X

∗( ν) if p ≥ 0 . 5

(13)

here p ∈ [0, 1] represents the probability of choosing either the

piral model or shrinking encircling mechanism to update � X i .

As well as the humpback whales search randomly for � X ∗, the

ocation of a whale is updated by choosing a random search agent

nstead of the best search agent as follows ( Mirjalili & Lewis, 2016 ):

�

= | � B � � X rand − �

X i (ν) | (14)

�

i (ν + 1) =

� X rand − �

A � � D (15)

here � X rand is a random position vector chosen from the current

opulation.

Finally, based on the value of � a (decreases from 2 to 0), � A ,�

and the probability p , the position of i th whale is updated. If

> 0.5 then use Eq. (12) otherwise use either Eqs. (8) and (9)

r Eqs. (14) and (15) based on the value of | � A | . This process is

epeated until the stopping criterion is satisfied, then the output

s the � X ∗ that represents the optimal threshold. Fig. 1 illustrates

he entire structure of WOA that is used in this paper for multi-

evel thresholding, where E 1 is given in Eq. (12) , E 2 performs Eqs.

8) and (9) , and E 3 calculates Eqs. (14) and (15) .

.2. Moth-Flame Optimization (MFO)

The authors of Mirjalili (2015) modeled the natural behavior of

oths in a mathematical form to provide the MFO algorithm as

new metaheuristic algorithm. In this paper, the MFO algorithm


Fig. 1. The structure of the first proposed algorithm based on WOA.

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Fig. 2. The structure of the second proposed algorithm based on MFO.

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as been applied to determine the multilevel thresholding as fol-

ows; a population of N individual moth is created. Each individual

oth or solution

� X i (i = 1 , . . . , N) is encoded as shown in Eq. (6) .

ach

� X i uses K decision variables that each one represents a differ-

nt threshold point x i, j ( j = 1 , . . . , K) that is used for the multilevel

mage thresholding. The position of each individual moth in the

opulation is initialized using Eq. (7) and evaluated using Eq. (2) ,

hen the optimal position of moths is saved in flames .

The input to MFO algorithm is the image histogram and the

ain steps of MFO can be defined as follows ( Mirjalili, 2015 ):

F O = (R, V, T ) (16)

here R is used to produce and initialize the population of moths

andomly and also the fitness values of them; V is a main function

hat makes the moths move around the search space, and T is a

ermination criterion flag.

In V function, the flames are used to update the position of

oths by the following equation ( Mirjalili, 2015 ):

�

i = S( � X i , � F u ) , (17)

here S is the spiral function, � X i is the i th moth, and

� F u is the u th

ame. Whereas, S( � X i , � F u ) is calculated using the following equa-

ions ( Mirjalili, 2015 ):

( � X i , � F u ) =

� D i · e bl · cos (2 π l) +

� F u (18)

�

i = | � F u − � X i | (19)

here b is a constant to define the shape of the logarithmic spi-

al, and l ∈ [ −1 , 1] is a random number (similar to Eq. (12) ). � D
i
efines the distance between the i th moth

� X i and the u th flame

�

u . The exploitation of the best solutions may degrade because of

he updating of moths’ position regarding to N different locations

n the search space. To resolve this problem, there is an adaptive

echanism used for overcoming this issue by proposing a number

f flames ( Fno ), the following equation is applied to perform that

Mirjalili, 2015 ):

no = round

(N − ν × N − 1

T

)(20)

here ν is the current number of iterations, N is the maximum

umber of flames, and T indicates the maximum number of itera-

ions (termination criterion). Fig. 2 illustrates the whole operations

f MFO, where E 1 is calculated by Eq. (20) , E 2 is given by Eq. (19) ,

nd E 3 is performed by Eq. (18) .

. Experiments and results

In this section, we introduce the environment of the experi-

ents for the proposed algorithms. The description of benchmark

mages is introduced firstly, then the parameters setting for each

lgorithm are illustrated briefly and a set of quality metrics are

sed to evaluate the quality of the segmentation process.

.1. Benchmark images

In this paper, the proposed algorithms are tested on eight com-

on grayscale images from the database of Berkeley University

Martin, Fowlkes, Tal, & Malik, 2001 ). These images are called,

estE4, TestE1, Test1, Test6, Test5, Test11, Test3, and Test9 as illus-

rated in Fig. 3 .

.2. Experimental settings

The results of the proposed algorithms are compared with

ther five evolutionary algorithms, namely, SCA ( Mirjalili, 2016 ),

S ( Oliva et al., 2013 ), SSO ( Ouadfel & Taleb-Ahmed, 2016 ), FASSO

Abd El-Aziz et al., 2016 ), and FA; these algorithms were applied in

revious works and proved good results. For a fair comparison, all

lgorithms used in this paper have the same stopping conditions


Fig. 3. Samples of the tested images.

formance.

(maximum number of iterations was set to 100), with a total of 30

runs per algorithm, and the size of the population (set to 25). The

parameters of each algorithm are illustrated in Table 1 .

All experiments are evaluated on the test images with the fol-

lowing number of thresholds: 2, 3, 4, and 5 as in Bhandari et al.

(2014) , Akay (2013) , and Ouadfel and Taleb-Ahmed (2016) . The rea-

son for selecting such thresholds was to show the performance of

the proposed algorithms compared to the traditional swarm-based

segmentation algorithms.

All the algorithms are programmed in “Matlab2014” and imple-

mented on “Windows 7 - 64bit” environment on a computer hav-

ing Intel Core2Duo (1.66 GHz) processor and ”2GB” memory.

4.3. Segmented image quality metrics

Four measures are applied to evaluate the performance of the

segmented image by the proposed algorithms, as follows:

1. The time-consuming. 2) The fitness function value by Eq. (3) .

2. The Peak Signal-to-Noise Ratio (PSNR) measure ( Yin, 2007 ): it is

used to measure the difference between the segmented image

and the reference image and it depends on the intensity val-

ues in the image, and refers to the quality of the reconstructed

image. The PSNR is defined as:

P SNR = 20 log 10

(255

RMSE

), (in dB ) (21)

where the RMSE is the root mean-squared error, defined as:

RMSE =

√ ∑ M

i =1

∑ Q j=1

(I(i, j) − Seg(i, j)) 2

M × Q

(22)

where I and Seg are the original and segmented images of size

M × Q , respectively. The high value of PSNR refers to the high

performance of the segmentation algorithm.

3. The SSIM ( Wang, Bovik, Sheikh, & Simoncelli, 2004 ): it is de-

fined as in Eq. (23) and is used to assess the similarity between

I and Seg .

SSI M(I , Seg) =

(2 μI μSeg + c 1 )(2 σI,Seg + c 2 )

(μ2 I

+ μ2 Seg

+ c 1 )(σ 1 I

+ σ 2 Seg

+ c 2 ) (23)

where μI and μSeg are the mean intensity of the image I and

Seg respectively; σ I and σ Seg represent the standard deviation

of I and Seg respectively; σ I, Seg is the covariance of I and Seg .

Following ( Wang et al., 2004 ), c 1 and c 2 are two constants,

such that c 1 = 6 . 5025 and c 2 = 58 . 52252 ( Mlakar, Poto ̌cnik, &

Brest, 2016 ). The highest value of SSIM indicates a better per-


Table 1

The parameters of all algorithms and their values.

Algorithm Parameters Value

SCA a 2

HS HMCR 0.7

pitch adjusting rate for each generation ( PAR ) 0.3

minimum pitch adjusting rate ( PAR min ) 0.3

maximum pitch adjusting rate ( PAR max ) 0.9

minimum bandwidth ( bw min ) 0.2

maximum bandwidth 0.5

WOA a [0, 2]

b 1

l [ −1, 1]

MFO b 1

l [ −1, 1]

SSO Probabilities of attraction or repulsion ( pm ) 0.7

Lower Female Percent 65

Upper Female Percent 90

FASSO γ FA 0.7

βFA 1.0

αFA 0.8

Probabilities of attraction or repulsion ( pm ) 0.7

Lower Female Percent 65

Upper Female Percent 90

FA γ FA 0.7

βFA 1.0

αFA 0.8

4

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.4. The results and discussions

The results of the proposed algorithms compared to other algo-

ithms are illustrated in Tables 2–6 and Figs. 4–7 . Tables 2 and 3

how the fitness values and the optimal threshold values ob-

ained by the algorithms over 30 runs, respectively. The results in

able 2

he best fitness values obtained from the algorithms.

Images K Fitness values

SCA HS WOA

Test E4 2 5064.5391 5039.9047 5070.6206

3 5165.9159 5157.9705 5230.4810

4 5299.4234 5252.2572 5312.4881

5 5319.7711 5294.0391 5338.2348

Test E1 2 3414.7717 3388.7484 3471.8841

3 3586.8042 3498.7638 3613.4802

4 3574.7764 3651.7961 3708.4724

5 3690.1246 3650.8226 3734.1223

Test 1 2 3515.8433 3576.7970 3649.3678

3 3680.5642 3676.9657 3690.1193

4 3749.1817 3733.8854 3760.5080

5 3718.1888 3775.6881 3795.8628

Test 6 2 2324.5930 2420.2291 2433.3641

3 2550.4775 2574.0580 2493.1884

4 2537.9873 2578.9291 2632.9086

5 2603.8331 2631.0178 2682.0104

Test 5 2 1901.7366 1923.8044 1942.8450

3 1983.7344 2004.9483 2022.5890

4 1998.3009 2022.2556 2054.8458

5 2069.7045 2037.5637 2074.8249

Test 11 2 3969.7370 3900.9384 3968.9561

3 3979.0300 4047.7959 4040.3573

4 4095.5692 4100.8283 4154.3274

5 4121.8177 4128.5393 4136.5779

Test 3 2 1455.2294 1537.2237 1545.9279

3 1527.80 0 0 1606.6116 1635.7034

4 1663.4374 1652.8367 1669.8319

5 1628.2841 1604.0117 16 82.4 839

Test 9 2 2483.2066 2507.2149 2526.9324

3 2782.3159 2672.5653 2856.89

4 2682.8583 2781.1644 2718.6392

5 2746.6330 2804.5901 2808.0800

he bold value indicates the best result

able 2 and Fig. 4 indicate that all the algorithms performed nearly

qually whenever K = 2 , however, the WOA algorithm is the high-

st fitness function and the FA algorithm comes at the second rank

ollowed by MFO. When K = 3 , the SSO, FA and FASSO have nearly

he same fitness function, however, the WOA and MFO are bet-

er than the rest algorithms. Also, from Fig. 4 , the MFO algorithm

s better than the WOA algorithm at a higher value of threshold,

hich indicates that the WOA algorithm is more sensitive to the

ncreasing of the threshold level than the MFO algorithm.

Tables 4 and 5 and Figs. 5 and 6 give the SSIM and PSNR values,

espectively, whereas the number of the threshold increases, the

SIM and the PSNR values are increased for all algorithms. These

alues indicate that the performance of the proposed method is

etter than other algorithms, also, the MFO is better than WOA

t all thresholds except at K = 3 , the WOA has a better perfor-

ance (with a small difference). However, it can be seen from

ables 4 and 5 that, the proposed algorithms have better results

n most cases. This occurred because each image is considered as

different optimization problem; and due to the randomness of

he swarm approaches the results can vary in some cases; also,

ased on the No-Free Lunch Theorem (NFL) ( Wolpert & Macready,

997 ) which illustrates that it is difficult to find a single algorithm

uitable for several optimization problems. In addition, each image

as a different gray level histogram and the segmentation becomes

difficult process due to the multimodality of the histograms; as

ell as, the segmented image is built by specifying each class a

rey level value determined from the average of the members in

he class. So, for each image, the proposed algorithms achieve good

esults in the fitness, PSNR, and SSIM values when the thresholds’

umber is close to the number of gray levels; whereas, when the

hresholds’ number is greater than the number of gray levels or

he image’s histogram has several spikes, the fitness, PSNR, and

MFO SSO FASSO FA

5048.1828 5051.3459 5070.7344 5067.0938

5231.6618 5229.5149 5218.8900 5219.7479

5305.1061 5295.8144 5288.4145 5288.3079

6083.6214 5333.6823 5338.2206 5323.7090

3470.7866 3458.2832 3470.1153 3458.8482

3592.7662 3615.4737 3623.573 3606.4336

4234.6624 3681.5660 3691.5305 3698.4993

5256.7775 3727.7242 3716.1480 3707.1112

3643.3199 3643.3813 3634.6238 3641.3059

3720.2506 3719.5956 3715.9656 3713.0343

3748.7521 3762.9716 3770.4375 3743.4140

3758.7248 3789.3692 3795.9645 3792.6467

2435.5069 2429.4 4 43 2429.5964 2436.7088

2574.7041 2580.0456 2513.5387 2542.0552

2647.6704 2620.4375 2641.8972 2624.0218

2669.4779 2663.1375 2639.6097 2646.3557

1945.1633 1949.2131 1937.4039 1942.9876

1996.8834 2016.1655 2016.9118 2023.2169

2061.949 2058.5454 2059.6235 2047.6726

2080.1690 2068.4019 2096.8914 2058.1369

3970.0579 3975.8412 3971.7841 3976.6612

4095.6016 4094.5830 4085.0319 4110.1048

4176.697 4169.4633 4156.2061 4123.1617

4178.6363 4188.7660 4981.247 4162.1601

1538.8138 1539.7624 1547.8407 1545.1063

1592.9889 1630.4651 1634.0543 1628.9734

1647.9387 1644.1720 1655.8984 1674.267

1705.9335 1678.6309 1808.2887 1680.8519

2530.9172 2523.9278 2492.6657 2530.2152

2695.2402 2839.5165 2848.9213 2832.9652

2815.9829 2720.5544 2656.5920 2682.3690

2848.0778 2818.3497 2766.7178 2790.5508


Table 3

The best threshold values obtained from the algorithms for all test images.

Images K MFO WOA SCA HS SSO FASSO FA

Test E4 2 105 231 102 197 117 217 111 201 111 188 103 200 108 203

3 93 137 231 104 138 211 85 135 232 109 190 241 81 118 205 84 129 213 95 152 204

4 24 60 94 229 67 135 185 235 83 122 158 205 87 135 199 199 34 70 123 198 65 96 152 205 85 129 163 205

5 13 78 90 90 215 51 114 138 185 203 33 80 107 155 222 52 107 142 181 240 12 86 119 128 182 56 103 140 162 221 66 81 111 155 208

Test E1 2 87 142 46 97 75 157 87 141 73 137 81 146 63 138

3 48 120 173 75 138 191 44 80 145 66 87 151 37 78 153 49 93 138 43 97 151

4 10 12 54 90 61 106 142 237 41 71 120 166 49 103 137 228 105 123 123 223 45 93 110 167 59 105 139 173

5 16 45 70 130 219 44 59 117 155 226 39 82 102 164 213 11 48 76 101 150 113 116 143 143 223 43 76 95 130 182 39 64 105 131 170

Test 1 2 96 167 94 146 86 158 96 168 97 167 86 150 87 161

3 65 155 197 59 143 208 73 151 196 74 142 175 81 142 186 74 144 201 68 143 188

4 59 117 133 203 77 135 200 222 76 126 166 188 62 124 160 198 0 0 95 134 66 119 169 210 65 115 159 184

5 47 85 110 173 210 3 53 111 166 184 80 126 171 202 207 52 95 99 137 202 15 24 83 92 252 2 45 93 93 172 78 112 148 182 206

Test 6 2 100 182 56 152 66 143 51 143 65 127 75 145 75 139

3 92 124 161 72 119 165 59 127 163 53 140 214 77 131 176 71 104 153 70 118 165

4 41 139 157 187 47 74 132 155 68 94 136 167 71 94 119 152 6 16 111 120 65 110 141 188 44 99 152 180

5 59 81 121 165 207 29 85 97 133 157 38 81 125 181 183 77 91 110 141 174 42 82 105 119 220 43 78 133 178 205 58 80 128 147 190

Test 5 2 103 166 111 181 111 174 116 167 97 165 117 173 113 175

3 96 119 178 104 121 178 92 141 195 99 135 187 112 152 189 101 150 187 94 140 177

4 141 161 190 205 34 78 145 198 57 107 147 195 93 125 145 161 2 12 121 159 78 78 107 140 66 90 159 201

5 17 72 115 162 180 39 118 149 167 188 58 81 120 173 201 36 46 116 176 195 4 24 126 169 235 28 28 31 139 194 95 112 150 174 200

Test 11 2 96 167 94 146 86 158 96 168 97 167 86 150 87 161

3 65 155 197 59 143 208 73 151 196 74 142 175 81 142 186 74 144 201 68 143 188

4 59 117 133 203 77 135 200 222 76 126 166 188 62 124 160 198 3 10 95 134 66 119 169 210 65 115 159 184

5 47 85 110 173 210 4 53 111 166 184 80 126 171 202 207 52 95 99 137 202 15 25 83 92 252 2 12 93 93 172 78 112 148 182 206

Test 3 2 111 133 83 151 103 150 77 156 92 134 96 144 87 150

3 74 137 168 27 83 144 81 112 145 36 99 148 86 115 149 53 106 161 99 128 166

4 44 84 133 173 96 109 134 152 61 82 128 164 30 81 112 159 0 0 121 127 66 103 138 164 62 89 144 163

5 46 94 158 189 219 32 77 101 148 207 75 99 140 159 188 60 117 130 138 158 26 26 81 107 155 36 36 71 123 123 71 108 136 169 194

Test 9 2 123 213 87 190 91 162 87 165 79 158 89 151 100 152

3 81 110 175 93 161 217 76 120 170 80 140 187 61 101 158 57 97 167 64 113 152

4 81 124 148 213 17 90 126 192 68 109 142 184 42 98 144 183 126 154 154 223 64 113 142 186 50 101 154 199

5 71 94 128 141 193 62 112 167 185 221 62 86 128 171 222 62 67 98 152 193 12 34 85 100 147 62 94 135 190 220 42 112 118 164 209

Table 4

The average of the SSIM measure of all algorithms.

Images K SSIM measure

SCA HS WOA MFO SSO FASSO FA

Test E4 2 0.6195 0.4922 0.6203 0.6047 0.5852 0.5439 0.5487

3 0.7276 0.7562 0.7324 0.7391 0.6819 0.6012 0.6348

4 0.7547 0.7268 0.80 0 0 0.7929 0.7613 0.7749 0.7846

5 0.5985 0.7487 0.8053 0.8251 0.8035 0.7696 0.7876

Test E1 2 0.3739 0.3812 0.4901 0.5045 0.4251 0.4509 0.4564

3 0.5814 0.4403 0.6349 0.6596 0.5938 0.6221 0.5723

4 0.5321 0.5685 0.724 0.6815 0.6428 0.7283 0.7097

5 0.6 86 8 0.6739 0.7516 0.7469 0.6259 0.7554 0.7645

Test 1 2 0.6088 0.6236 0.6455 0.6554 0.618 0.6048 0.6323

3 0.6804 0.7005 0.6935 0.6709 0.7007 0.6294 0.6168

4 0.6692 0.6917 0.7384 0.7087 0.6253 0.6919 0.6569

5 0.6221 0.6493 0.7668 0.6824 0.6635 0.663 0.6806

Test 6 2 0.4846 0.6287 0.6478 0.6399 0.6173 0.6381 0.6261

3 0.6078 0.667 0.6581 0.7017 0.6759 0.658 0.6493

4 0.6077 0.7002 0.715 0.7175 0.6728 0.6837 0.6495

5 0.6632 0.6742 0.7511 0.734 0.7065 0.6859 0.7627

Test 5 2 0.7521 0.6782 0.7333 0.7523 0.7015 0.7068 0.7242

3 0.7529 0.6796 0.8023 0.7843 0.7822 0.7424 0.8004

4 0.8053 0.8085 0.8216 0.8032 0.7624 0.7676 0.8174

5 0.8235 0.8125 0.7974 0.8420 0.8102 0.7314 0.7127

Test 11 2 0.4414 0.3723 0.5524 0.48 0.5044 0.5189 0.4906

3 0.4857 0.4529 0.6484 0.6213 0.5203 0.5472 0.4859

4 0.6553 0.7396 0.6816 0.7082 0.5892 0.5312 0.5531

5 0.5045 0.6806 0.7048 0.7108 0.5415 0.6204 0.7235

Test 3 2 0.6103 0.5844 0.6449 0.6388 0.6102 0.6227 0.6364

3 0.6448 0.6859 0.7206 0.7409 0.7267 0.6858 0.6842

4 0.7156 0.69 0.7950 0.787 0.7438 0.7287 0.7747

5 0.6802 0.6682 0.7812 0.8498 0.821 0.6295 0.7529

Test 9 2 0.4987 0.4926 0.4709 0.5903 0.442 0.3885 0.4257

3 0.5792 0.467 0.6422 0.5526 0.5196 0.4974 0.5776

4 0.6482 0.7238 0.6769 0.6676 0.6732 0.7151 0.6723

5 0.6965 0.7348 0.7652 0.7334 0.7266 0.7586 0.6688

The bold value indicates the best result

Table 5

The average of the PSNR measure of all algorithms.

Images K PSNR Values


Test E4 2 13.0045 12.2166 13.653 13.8395 12.9733 12.5911 12.387

3 17.2053 15.7524 18.059 17.1193 16.8979 13.9514 14.7777

4 19.2715 17.9618 19.0711 19.9507 19.2601 18.2197 18.124

5 14.2107 18.337 20.0892 20.6621 17.857 19.2864 16.7468

Test E1 2 14.4233 14.7626 15.7292 15.7546 15.376 15.7217 15.763

3 16.3755 15.8382 18.1021 18.5076 18.1777 18.4039 17.9375

4 17.4391 18.2664 20.0853 19.1225 19.5899 19.9914 19.7929

5 20.5316 19.4005 20.731 20.3132 19.5003 20.5745 20.7466

Test 1 2 15.8362 15.8607 18.2862 17.3744 16.5656 18.0274 16.9873

3 18.0557 19.0232 19.9084 20.0161 19.5581 19.0713 19.4861

4 20.219 18.8846 21.1897 21.9564 19.2004 21.5815 21.1582

5 18.6505 20.6799 22.1592 21.6302 19.9675 21.2913 21.1184

Test 6 2 14.2092 15.7202 16.2716 16.6278 16.3635 16.1094 15.978

3 16.4665 17.8253 18.0953 18.1623 17.4433 18.1653 18.2383

4 16.9392 18.5928 19.7982 20.6309 20.0213 19.8527 19.3548

5 19.5709 19.9212 21.6086 21.4056 20.1802 19.8086 21.0645

Test 5 2 14.7758 13.9101 12.9643 16.2863 14.5212 14.0105 14.9586

3 16.6242 18.1719 18.9844 17.5732 19.3025 19.368 18.8623

4 18.1081 18.674 21.2975 21.4182 20.5376 20.9627 20.7689

5 17.9419 19.9499 21.9104 21.617 21.6164 15.7763 19.8828

Test 11 2 13.8044 13.594 15.0451 14.73 14.7411 14.6021 14.6212

3 15.4964 14.9382 17.1398 17.1414 15.565 16.3517 15.1539

4 17.6467 19.5433 18.3906 17.9965 17.2343 16.3003 16.6301

5 15.8154 19.0958 17.7304 20.0647 16.6175 11.6553 19.9204

Test 3 2 15.2642 14.6551 16.0311 15.8636 15.1832 15.4887 15.8376

3 16.6058 17.6512 18.3643 18.5521 18.6601 16.9365 16.8615

4 17.5951 17.1198 20.4056 20.0673 18.9211 18.4171 19.625

5 18.0885 17.4659 20.2745 22.6505 21.6425 15.8491 19.0558

Test 9 2 14.9772 14.7914 14.3004 14.3439 13.9318 13.2174 13.6242

3 16.5885 14.3528 17.3002 16.825 15.5837 14.8871 16.5448

4 17.0656 19.1206 18.2904 18.4916 18.1812 18.8855 18.5408

5 18.9307 19.1787 20.7993 19.52 19.7274 20.4243 18.4551



Table 6

The average of the execution time of all algorithms.

Images K Execution time (in second)


Test E4 2 5.97 4.36 5.98 3.36 5.01 5.75 3.52

3 5.85 18.75 4.53 3.78 4.06 7.89 4.77

4 4.86 6.49 3.92 4.43 3.28 3.46 2.63

5 5.06 7.63 4.98 5.01 3.76 3.79 2.95

Test E1 2 3.86 6.62 3.88 3.19 3.09 2.73 2.04

3 5.43 8.13 4.97 3.8 4.11 3.78 3.07

4 6.41 6.7 4.31 4.39 4.7 4.41 3.42

5 7.25 8.74 5.16 5.52 5.5 5.24 3.93

Test 1 2 4.33 4.13 2.71 2.7 2.68 3.56 2.4

3 5.96 6.54 3.02 3.24 3.14 4.98 2.4

4 5.28 6.28 2.14 3.73 2.83 2.97 2.33

5 7.04 7.02 4.35 4.2 4.21 4.11 3.01

Test 6 2 4 8.79 3.98 4.43 3.36 4.37 2.78

3 5.47 10.31 3.17 4.51 3.54 3.75 2.93

4 6.02 9.25 4.36 5.26 4.43 4.7 3.63

5 7.47 9.02 4.2 5.94 5.26 6.33 4.84

Test 5 2 4.45 6.21 3.8 3.74 3.27 3.42 2.74

3 5.43 6.65 4.82 4.48 3.99 3.94 3.26

4 5.2 7.61 5.4 5.32 4.02 4.04 3.33

5 6.53 11.25 6 5.95 4.81 6.12 4.24

Test 11 2 4.99 26.42 2.23 3.71 3.89 5.08 3.49

3 5.97 21.7 3.81 4.43 3.85 7.58 3.98

4 6.53 7.78 4.55 5.23 5.45 5.15 4.06

5 7.76 14.1 5.28 5.97 5.86 6.29 4.98

Test 3 2 3.92 5.79 3.56 3.74 2.82 2.84 2.32

3 4.89 6.68 3.84 4.6 3.38 3.58 2.77

4 6.48 10.48 4.11 5.25 4.26 4.83 4.18

5 6.03 8.89 4.25 6.09 4.68 4.82 4.01

Test 9 2 3.66 5.39 3.79 3.72 2.67 2.73 2.18

3 4.4 7.43 4.52 4.94 3.3 3.35 2.71

4 6.53 7.95 3.83 5.55 4.86 6 4.63

5 5.9 9.61 4.03 6.14 4.59 4.65 3.82


Fig. 4. The best fitness values of the algorithms over all images.

Fig. 5. The average of the SSIM measure of algorithms over all images.

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Fig. 6. The average of the PSNR measure of algorithms over all images.

Fig. 7. The average of the execution time of the algorithms over all images.

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SIM values become low and both proposed algorithms may fail

o segment the image. For these reasons, we used the statistical

omparisons to determine the best algorithm for a large number

f images.

The best results of the elapsed time by each algorithm have

een illustrated in Table 6 and Fig. 7 . They show that, the FA al-

orithm is the best one, and that, the proposed methods are better

han FASSO, HS and SCA algorithms; whereas, the WOA is better

han MFO.

Figs. 8–15 show the segmentation results of the proposed al-

orithms and the other algorithms with different threshold levels.

e can conclude from these figures that, the images with higher

evel contain more details than the others.

The MFO accuracy can be viewed as a result of the fact that,

his algorithm used many operators to explore and exploit the

earch domain during the evolution process. Using these operators

lso make the distribution of agents better in the search domain

hich increases the probability to determine the global optima.

he ability to avoid the problem of getting stuck in local optima

s high because the MFO uses a moth population to perform op-

imization. The WOA limitations are probably due to determining

he optimal starting value for the parameter a . In fact, the conver-

ence of WOA depends on this value (e.g. if this value is not se-

ected in optimal form then the convergence of WOA may be pre-

ature).

Based on the experiments’ execution time the fastest algorithm

as FA, although it could not achieve the best mean fitness values

n most cases because it got stuck in local optima; since the pro-

osed algorithms obtained the best fitness value in most of the ex-

eriments, despite not being the fastest. These results, in general,

ue to the proposed algorithms have the good ability to switch be-

ween exploration and exploitation phases than other algorithms

nd they have low complexity and high performance, as well as,

hey have small control parameters compared to others algorithms

hich make them suitable for adapting to most of the optimiza-

ion problems because tuning the algorithm’s parameters might be

ore complex than the problem itself.

.5. ANOVA test

A parametric statistical test known as “the analysis of variance”

ANOVA) test has been conducted with a 5% significance level to

est the significant difference between algorithms. In the experi-

ents, the proposed algorithms were chosen as the control group

nd were compared with the SCA, HS, FASSO and FA algorithms in

erms of the mean value of the four measures (which are normally

istributed). The null hypothesis assumes that there is no signif-

cant difference between the mean values of the four algorithms;

hereas, the alternative hypothesis considers a significant differ-

nce between them.

Table 7 reports, the p -value was produced by the ANOVA test

or the fitness function, execution time, SSIM and PSNR measures


Fig. 8. The thresholded images of “Test E4” obtained by all algorithms.

Fig. 9. The thresholded images of “Test e1” obtained by all algorithms.

t

a

0

a

(Note: the ( ∗) indicates that there exists a significant difference).

Based on the fitness function, the p -value is greater than 0.05,

therefore, the null hypothesis is accepted and this indicates that

there is no difference between the proposed algorithms and the

other algorithms. However, the MFO has the highest fitness func-

ion, and the WOA is better than all other algorithms except SSO

nd FASSO.

The p -value for SSIM, PSNR, and execution time is less than

.05, therefore, we accept the alternative hypothesis that refers to

significant difference between the proposed algorithms and other


Fig. 10. The thresholded images of “Test1” obtained by all algorithms.


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lgorithms. In general, there are existent significant differences be-

ween the proposed algorithms and both of SCA and HS in terms of

ll measures. There is also a significant difference between FASSO

nd the proposed algorithms in terms of SSIM and PSNR. It can be

bserved that, the MFO is better than WOA in all measures except

he execution time.

It can be concluded from Table 7 that, there is no significant

ifference between the proposed algorithms and the SSO and FA

lgorithms overall threshold values and along all images. However,

n order to investigate the difference between them (SSO, FA, MFO,

nd WOA), we compare between them at each threshold level (at

ach image) as in Tables 8–10 for fitness function, SSIM and PSNR,

espectively. Based on this tables it can be seen that, there is a

ignificant difference between the SSO, FA and the proposed algo-

ithms since the p -value (which has value less than 0.05) for all

easures. For example, in term of fitness values, the WOA algo-

ithm is better than the SSO and FA in 20 cases and 22 cases, re-

pectively; whereas, the MFO has better values in 19 cases and 21

ases than SSO and FA respectively. In terms of SSIM the WOA and

FO are better than the SSO and FA in 27 cases and 29 cases for

OA, as well as, 29 cases and 23 cases for MFO, respectively. How-

ver, the SSO and FA have better PSNR values than WOA and MFO




s

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time.

only in 8 cases and 6 cases for WOA, as well as 4 cases and 7 cases

for MFO, respectively.

Moreover, by comparing the results of MFO and WOA it can be

seen that, the MFO gives the best fitness values and SSIM values in

19 cases from 32; as well as, the both algorithms have nearly the

same performance in terms of PSNR.

To sum up, the results of our experiments illustrated that us-

ing the MFO for image multilevel thresholding is the most ef-

fective and most powerful; whilst the WOA, compared to MFO,

howed good results for a small number of thresholds, whereas

ts performance degraded for higher numbers. This can be due

o, the MFO has a good ability to switch between exploration

nd exploitation, while, the WOA traps early in local optima dur-

ng the optimization process. The FA algorithm has the fast ex-

cution time (in our study), although it could not achieve the

est values in the other measures (in most cases); however,

he both proposed algorithms are have an acceptable execution




5

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. Conclusion and future work

In this paper, the problem of determining the optimal thresh-

lding in a case of multilevel thresholding for image segmentation

as been considered as an optimization problem where the Otsu’s

ethod has been used as a fitness function. Therefore, two new

warm algorithms, namely, the WOA and MFO have been proposed

o solve this problem. The aim of each algorithm is to determine

he best thresholds value that maximizes the Otsu’s function. The

xperimental results of the proposed algorithms have been com-

ared to SCA, HS, SSO, FASSO, and FA algorithms. The performance

f each algorithm has been assessed based on four measures, the

est fitness values, PSNR, SSIM, and execution time. We used eight

enchmark images in all experiments. The obtained results showed

hat all the algorithms achieved the same fitness function value

t a threshold level equal two; this is because the segmentation

roblem becomes easy at this level of threshold. At the three-level

hresholding, the WOA and MFO algorithms are better than other

lgorithms on almost all images, in terms of PSNR and SSIM, how-

ver, WOA is better than MFO. For a higher number of thresholds,


Table 7

The ANOVA test results.

Dependent

variable

Proposed

algorithm

Algorithms Mean

difference

p -value Dependent

variable

Proposed

algorithms

Algorithms Mean

difference

p -value

Fitness values WOA SCA 49.08546 0.865 PSNR WOA SCA 1.69776( ∗) 0.004

HS 38.19250 0.895 HS 1.27529( ∗) 0.030

MFO −88.94053 0.758 MFO −0.12966 0.824

SSO −1.91314 0.995 SSO 0.66146 0.258

FASSO −25.57542 0.929 FASSO 1.13391 0.053

FA 4.31972 0.988 FA 0.72067 0.218

MFO SCA 138.02599 0.632 MFO SCA 1.82742( ∗) 0.002

HS 127.13303 0.659 HS 1.40495( ∗) 0.017

WOA 88.94053 0.758 WOA 0.12966 0.824

SSO 87.02739 0.763 SSO 0.79112 0.176

FASSO 63.36512 0.826 FASSO 1.26357( ∗) 0.031

FA 93.26025 0.746 FA 0.85033 0.146

SSIM WOA SCA 0.07191( ∗) 0.005 Execution time WOA SCA −1.42028( ∗) 0.006

HS 0.06311( ∗) 0.013 HS −4.97567( ∗) 0.0 0 0

MFO 0.00269 0.915 MFO −0.40223 0.435

SSO 0.04810 0.059 SSO 0.15035 0.770

FASSO 0.05376( ∗) 0.035 FASSO −0.39842 0.439

FA 0.04313 0.090 FA 0.81713 0.113

MFO SCA 0.06921( ∗) 0.007 MFO SCA −1.01805( ∗) 0.049

HS 0.06042( ∗) 0.018 HS −4.57344( ∗) 0.0 0 0

WOA −0.00269 0.915 WOA 0.40223 0.435

SSO 0.04541 0.074 SSO 0.55258 0.283

FASSO 0.05106( ∗) 0.045 FASSO 0.00382 0.994

FA 0.04044 0.112 FA 1.21937( ∗) 0.019

( ∗) Indicates a significant difference at level p -value < 0.005

Table 8

The ANOVA test results of SSO, FA, and the proposed algorithms for fitness values.

Mean difference

WOA MFO

K MFO SSO FA SSO FA

Test E4 2 22.437( ∗) 19.274( ∗) 3.526( ∗) −3.163( ∗) −18.911( ∗)

3 −1.180( ∗) 0.966( ∗) 10.733( ∗) 2.146( ∗) 11.913( ∗)

4 7.382( ∗) 16.673( ∗) 24.180( ∗) 9.291( ∗) 16.798( ∗)

5 −745.386( ∗) 4.552( ∗) 14.525( ∗) 749.939( ∗) 759.912( ∗)

Test E1 2 1.097( ∗) 13.600( ∗) 13.035( ∗) 12.503( ∗) 11.938( ∗)

3 20.7140( ∗) −1.993( ∗) 7.046( ∗) −22.707( ∗) −13.667( ∗)

4 −526.190( ∗) 26.906( ∗) 9.973( ∗) 553.096( ∗) 536.163( ∗)

5 −1522.65( ∗) 6.398( ∗) 27.011( ∗) 1529.053( ∗) 1549.666( ∗)

Test 1 2 6.047( ∗) 5.986( ∗) 8.061( ∗) −0.061( ∗) 2.0140( ∗)

3 −30.131( ∗) −29.476( ∗) −22.915( ∗) 0.655( ∗) 7.216( ∗)

4 11.755( ∗) −2.463( ∗) 17.094( ∗) −14.219( ∗) 5.338( ∗)

5 37.138( ∗) 6.49360( ∗) 3.21610( ∗) 30.644( ∗) −33.921( ∗)

Test 6 2 −2.14280( ∗) 3.91980( ∗) −3.34470( ∗) 6.06260( ∗) −1.20190( ∗)

3 −81.51570( ∗) −86.85720( ∗) −4 8.866 80( ∗) −5.34150( ∗) 32.64890( ∗)

4 −14.76180( ∗) 12.47110( ∗) 8.88680( ∗) 27.23290( ∗) 23.64860( ∗)

5 12.53250( ∗) 18.87290( ∗) 35.65470( ∗) 6.34040( ∗) 23.12220( ∗)

Test 5 2 −2.31830( ∗) −6.36810( ∗) −0.14260( ∗) −4.04980( ∗) 2.17570( ∗)

3 25.70560( ∗) 6.42350( ∗) −0.62790( ∗) −19.28210( ∗) −26.33350( ∗)

4 −7.10320( ∗) −3.69960( ∗) 7.17320( ∗) 3.40360( ∗) 14.27640( ∗)

5 −5.34410( ∗) 6.42300( ∗) 16.68800( ∗) 11.76710( ∗) 22.03210( ∗)

Test 11 2 −1.101( ∗) −6.885( ∗) −7.705( ∗) −5.783( ∗) −6.603( ∗)

3 −55.244( ∗) −54.225( ∗) −69.747( ∗) 1.018( ∗) −14.503( ∗)

4 −22.369( ∗) −15.135( ∗) 31.165( ∗) 7.233( ∗) 53.535( ∗)

5 −42.058( ∗) −52.188( ∗) −25.582( ∗) −10.129( ∗) 16.476( ∗)

Test 3 2 7.11410( ∗) 6.16550( ∗) 0.82160( ∗) −0.94860( ∗) −6.29250( ∗)

3 42.71450( ∗) 5.23830( ∗) 6.730 0 0( ∗) −37.47620( ∗) −35.98450( ∗)

4 21.89320( ∗) 25.65990( ∗) −4.43510( ∗) 3.76670( ∗) −26.32830( ∗)

5 −23.44960( ∗) 3.85300( ∗) 1.63200( ∗) 27.30260( ∗) 25.08160( ∗)

Test 9 2 −3.98480( ∗) 3.00460( ∗) −3.28280( ∗) 6.98940( ∗) 0.70200( ∗)

3 161.64980( ∗) 17.37350( ∗) 23.92480( ∗) −144.27630( ∗) −137.72500( ∗)

4 −97.34370( ∗) −1.91520( ∗) 36.27020( ∗) 95.42850( ∗) 133.61390( ∗)

5 −39.99780( ∗) −10.26970( ∗) 17.52920( ∗) 29.72810( ∗) 57.52700( ∗)


h

o

m

i

the MFO algorithm is better than WOA algorithm in all images, and

in terms of the fitness value, PSNR, and SSIM. However, in terms of

time complexity, analysis of recorded execution time required by

each algorithm has shown that the MFO algorithm exhibits higher

execution time than FA, WOA, and SSO.

In future, we will study the performance of both algorithms for

igher numbers of thresholds, we will also apply them in other

ptimization problems and will try to utilize them in the dynamic

ultilevel thresholding problem, as well as multi-objective issues

n order to attain better segmentation results.


Table 9

The ANOVA test results of SSO, FA, and the proposed algorithms for SSIM.

Mean difference

WOA MFO

K MFO SSO FA SSO FA

Test E4 2 0.015( ∗) 0.035( ∗) 0.071( ∗) 0.019( ∗) 0.056( ∗)

3 −0.006( ∗) 0.050( ∗) 0.097( ∗) 0.057( ∗) 0.104( ∗)

4 0.007( ∗) 0.038( ∗) 0.015( ∗) 0.031( ∗) 0.008( ∗)

5 −0.019( ∗) 0.001( ∗) 0.017( ∗) 0.021( ∗) 0.037( ∗)

Test E1 2 −0.014( ∗) 0.065( ∗) 0.033( ∗) 0.079( ∗) 0.048( ∗)

3 −0.024( ∗) 0.041( ∗) 0.062( ∗) 0.065( ∗) 0.087( ∗)

4 0.042( ∗) 0.081( ∗) 0.014( ∗) 0.038( ∗) −0.028( ∗)

5 0.004( ∗) 0.125( ∗) −0.012( ∗) 0.121( ∗) −0.017( ∗)

Test 1 2 −0.009( ∗) 0.027( ∗) 0.013( ∗) 0.037( ∗) 0.023( ∗)

3 0.022( ∗) −0.007( ∗) 0.076( ∗) −0.029( ∗) 0.054( ∗)

4 0.029( ∗) 0.113( ∗) 0.081( ∗) 0.083( ∗) 0.051( ∗)

5 0.084( ∗) 0.103( ∗) 0.086( ∗) 0.018( ∗) 0.001( ∗)

Test 6 2 0.007( ∗) 0.030( ∗) 0.021( ∗) 0.022( ∗) 0.013( ∗)

3 −0.043( ∗) −0.017( ∗) 0.008( ∗) 0.025( ∗) 0.052( ∗)

4 −0.002( ∗) 0.042( ∗) 0.065( ∗) 0.044( ∗) 0.068( ∗)

5 0.017( ∗) 0.044( ∗) −0.011( ∗) 0.027( ∗) −0.028( ∗)

Test 5 2 −0.019( ∗) 0.031( ∗) 0.009( ∗) 0.050( ∗) 0.028( ∗)

3 0.018( ∗) 0.020( ∗) 0.001( ∗) 0.002( ∗) −0.016( ∗)

4 0.018( ∗) 0.059( ∗) 0.004( ∗) 0.040( ∗) −0.014( ∗)

5 −0.044( ∗) −0.012( ∗) 0.084( ∗) 0.031( ∗) 0.129( ∗)

Test 11 2 0.072( ∗) 0.048( ∗) 0.061( ∗) −0.024( ∗) −0.010( ∗)

3 0.027( ∗) 0.128( ∗) 0.162( ∗) 0.101( ∗) 0.135( ∗)

4 −0.026( ∗) 0.092( ∗) 0.128( ∗) 0.119( ∗) 0.155( ∗)

5 −0.006( ∗) 0.163( ∗) −0.018( ∗) 0.169( ∗) −0.012( ∗)

Test 3 2 0.006( ∗) 0.034( ∗) 0.008( ∗) 0.028( ∗) 0.002( ∗)

3 −0.020( ∗) −0.006( ∗) 0.036( ∗) 0.014( ∗) 0.056( ∗)

4 0.008( ∗) 0.051( ∗) 0.020( ∗) 0.043( ∗) 0.012( ∗)

5 −0.068( ∗) −0.039( ∗) 0.028( ∗) 0.028( ∗) 0.096( ∗)

Test 9 2 −0.119( ∗) 0.028( ∗) 0.045( ∗) 0.148( ∗) 0.164( ∗)

3 0.089( ∗) 0.122( ∗) 0.064( ∗) 0.033( ∗) −0.025( ∗)

4 0.009( ∗) 0.003( ∗) 0.004( ∗) −0.005( ∗) −0.004( ∗)

5 0.031( ∗) 0.038( ∗) 0.096( ∗) 0.006( ∗) 0.064( ∗)


Table 10

The ANOVA test results of SSO, FA, and the proposed algorithms for PSNR.

Mean difference

WOA MFO

K MFO SSO FA SSO FA

Test E4 2 −0.186( ∗) 0.679( ∗) 1.266( ∗) 0.866( ∗) 1.452( ∗)

3 −0.939( ∗) 1.161( ∗) 3.281( ∗) 0.221( ∗) 2.341( ∗)

4 −0.879( ∗) −0.189( ∗) 0.947( ∗) 0.690( ∗) 1.826( ∗)

5 −0.572( ∗) 2.232( ∗) 3.342( ∗) 2.805( ∗) 3.915( ∗)

Test E1 2 −0.025( ∗) 0.35320( ∗) −0.033( ∗) 0.37860( ∗) −0.008( ∗)

3 −0.405( ∗) −0.075( ∗) 0.164( ∗) 0.329( ∗) 0.570( ∗)

4 0.962( ∗) 0.495( ∗) 0.292( ∗) −0.467( ∗) −0.670( ∗)

5 0.417( ∗) 1.230( ∗) −0.015( ∗) 0.812( ∗) −0.433( ∗)

Test 1 2 0.911( ∗) 1.720( ∗) 1.298( ∗) 0.808( ∗) 0.387( ∗)

3 −0.107( ∗) 0.350( ∗) 0.422( ∗) 0.458( ∗) 0.530( ∗)

4 −0.766( ∗) 1.989( ∗) 0.031( ∗) 2.756( ∗) 0.798( ∗)

5 0.529( ∗) 2.191( ∗) 1.040( ∗) 1.662( ∗) 0.511( ∗)

Test 6 2 −0.356( ∗) −0.091( ∗) 0.293( ∗) 0.264( ∗) 0.649( ∗)

3 −0.067( ∗) 0.652( ∗) −0.143( ∗) 0.719( ∗) −0.076( ∗)

4 −0.832( ∗) −0.223( ∗) 0.443( ∗) 0.609( ∗) 1.276( ∗)

5 0.203( ∗) 1.428( ∗) 0.544( ∗) 1.225( ∗) 0.341( ∗)

Test 5 2 −3.322( ∗) −1.556( ∗) −1.994( ∗) 1.765( ∗) 1.327( ∗)

3 1.411( ∗) −0.318( ∗) 0.122( ∗) −1.729( ∗) −1.289( ∗)

4 −0.12( ∗) 0.759( ∗) 0.528( ∗) 0.880( ∗) 0.649( ∗)

5 0.293( ∗) 0.294( ∗) 2.027( ∗) 0.0 0 0( ∗) 1.734( ∗)

Test 11 2 0.315( ∗) 0.304( ∗) 0.423( ∗) −0.011( ∗) 0.108( ∗)

3 −0.001( ∗) 1.574( ∗) 1.985( ∗) 1.574( ∗) 1.985( ∗)

4 0.394( ∗) 1.156( ∗) 1.760( ∗) 0.762( ∗) 1.366( ∗)

5 −2.334( ∗) 1.112( ∗) −2.190( ∗) 3.447( ∗) 0.144( ∗)

Test 3 2 0.167( ∗) 0.847( ∗) 0.193( ∗) 0.680( ∗) 0.026( ∗)

3 −0.187( ∗) −0.295( ∗) 1.502( ∗) 0.187( ∗) −0.108( ∗)

4 0.338( ∗) 1.484( ∗) 0.780( ∗) 1.146( ∗) 0.442( ∗)

5 −2.376( ∗) −1.368( ∗) 1.218( ∗) 1.008( ∗) 3.594( ∗)

Test 9 2 −0.043( ∗) 0.368( ∗) 0.676( ∗) 0.412( ∗) 0.719( ∗)

3 0.475( ∗) 1.716( ∗) 0.755( ∗) 1.241( ∗) 0.280( ∗)

4 −0.201( ∗) 0.109( ∗) −0.250( ∗) 0.310( ∗) −0.049( ∗)

5 1.279( ∗) 1.071( ∗) 2.344( ∗) −0.207( ∗) 1.064( ∗)



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Acknowledgment

This work was in part supported by National High-tech R&D

Program of China (863 Program)(Grant No. 2015AA015403) and Na-

ture Science Foundation of Hubei Province (Grant No. 2015CFA059).

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