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Thresholding Algorithm Applied
to Chest X-Ray Images with Pneumonia
Jesus Murillo-Olmos, Erick Rodríguez-Esparza, Marco Pérez-Cisneros,
Daniel Zaldivar, Erik Cuevas, Gerardo Trejo-Caballero, and Angel A. Juan
1 Introduction
Respiratory diseases are the main reasons of death worldwide [44]. According to the
World Health Org a n i z a t i o n ( W H O ) , i n 2 0 0 8 , t h e r e w e r e 9 . 5 m i l l i o n d e a t h s world-
wide due to lung diseases such as tuberculosis, pneumonia, lung cancer, and chronic
obstructive pulmonary disease [41]. Furthermore, the WHO announced a list of the
top ten causes of death in the world in 2018. Within this list are lower respiratory
J. Murillo-Olmos (B)·E. Rodríguez-Esparza ·M. Pérez-Cisneros ·D. Zaldivar ·E. Cuevas
Universidad de Guadalajara, CUCEI, Blv. Gral. Marcelino García Barragán 1421, Olímpica,
44430 Guadalajara, Jal., Mexico
e-mail: jesus.murilloO@alumno.udg.mx
E. Rodríguez-Esparza
e-mail: erick.rodriguez@deusto.es
M. Pérez-Cisneros
e-mail: marco.perez@cucei.udg.mx
D. Zaldivar
e-mail: daniel.zaldivar@cucei.udg.mx
E. Cuevas
e-mail: erik.cuevas@cucei.udg.mx
E. Rodríguez-Esparza
DeustoTech, Faculty of Engineering, University of Deusto, Av. Universidades,
24, 48007 Bilbao, Spain
G. Trejo-Caballero
Instituto Tecnológico Superior de Irapuato, Carr. Irapuato-Silao km. 12.5, Irapuato, Gto., Mexico
e-mail: getrejo@itesi.edu.mx
A. A. Juan
IIN3—Computer Science Department, Universitat Oberta de Catalunya, Castelldefels, Spain
e-mail: ajuanp@uoc.edu
©TheAuthor(s),underexclusivelicensetoSpringerNatureSwitzerlandAG2021
D. Oliva et al. (eds.), Metaheuristics in Machine Learning: Theory and Applications,
Studies in Computational Intelligence 967,
https://doi.org/10.1007/978-3-030-70542- 8_16
359
360 J. Murillo-Olmos et al.
tract infections that remain the deadliest infectious disease, causing 3 million deaths
worldwide in 2016 [64]. These statistics confirm that lung diseases have continued
to be the leading causes of death and disability worldwide for the past decades.
Pneumonia is a disease of the lower respiratory tract, usually caused by an infec-
tious agent that causes inflammation of the alveoli in one or both lungs. The alveoli
in healthy people fill with air when breathing; while the alveoli in sick patients fill
with pus (purulent matter) or liquid, which makes breathing painful and limits the
absorption of oxygen. This disease can range in severity from mild to life-threatening.
Pneumonia kills millions of people each year, making it a leading cause of death for
babies and young children, people over 65, and people with health problems or with
weakened immune systems [47]. To detect this disease, the doctor first evaluates
symptoms such as cough, fever, sputum production, chest pain, and abnormal lung
auscultation. If the doctor suspects with this physical evaluation the presence of
pneumonia, diagnostic tests are performed, such as a chest X-ray, blood tests, among
others. Chest radiography is one of the most widely used non-invasive diagnostic test
because it helps to diagnose pneumonia and determine the extent visually, location
of the infection, and added complications [80]. In an X-ray, the alveoli that are filled
with fluid or inflammatory tissue due to pneumonia are seen in white, while healthy
alveoli, which are filled with air, are black [56].
The chest X-ray contains a wealth of information about a patient’s health. How-
ever, correctly detecting information on chest radiography is a challenging, tedious,
and subjective task that depends on the experience and professional training of expert
doctors [72]. Furthermore, this interpretation also depends on momentary factors
such as fatigue, distraction, and concentration [53]. Because of this, computer-aided
diagnostic (CADx) tools have begun to be developed and applied to improve the
quality and productivity of radiologists’ tasks, by maximizing the accuracy and con-
sistency of diagnostics, and by minimizing the time of reading the images [69].
CADx tools include multiple elements such as artificial intelligence concepts,
computer vision, and medical image processing [25]. However, digital image pro-
cessing techniques have become an elementary process to improve medical images,
since they are commonly affected by noise or phenomena that difficult their correct
interpretation. Those artifacts that affect medical images, such as the physiological
system, can reduce contrast and detail visibility [79].
The image segmentation (IS) is a fundamental technique in image processing [1,
45]. It is considered as a process of partitioning a digital image into several segments,
or pixels [34,59,66]. Segmentation is the stage where a significant commitment is
made during automated analysis by delineating structures of interest and discrimi-
nating them from background tissue. These algorithms operate on the intensity or
texture variations of the image using techniques that include thresholding, region
growing, deformable templates, and pattern recognition [9,30].
The thresholding (TH) technique of images is one of the most popular methods
for image segmentation due to its simplicity in the implementation [28,62,88].
This method works by taking the histogram information to find a unique threshold
value to divide the pixels into two classes. Over the past decade, the TH method
Thresholding Algorithm Applied to Chest X-Ray Images … 361
has been reformulated to efficiently record multiple threshold values for multilevel
thresholding (MTH) technique [58,63].
In recent years, MTH techniques have been used in the medical applications
domain to segment images due to their simplicity, high precision, and robustness
compared to other methods [2,73]. As in the case of the work of Chavarin et al., in
which brain injuries are detected using magnetic resonance imaging (MRI) through
a multilevel segmentation [11]. Likewise, also in the works of Oliva et al. and Itzel et
al., MTH are applied to MRI images of the brain to assist in the diagnosis of different
brain diseases [6,7,61]. Other examples are in the detection of abnormal masses
in mammography images as in the works of Rodriguez et al. [74–76]. Furthermore,
Hinojosa et al. segmented images from histological samples of the breast to detect
cancer tissue [31]andDíazetal.todetectareaswithcancerthroughthermalimages
of the breast [16]. Additionally, Ibrahim et al. segmented lesions in skin cancer
efficiently [35]. Finally, Primitivo et al. used this technique for the segmentation of
vascular vessels in retinographies [68].
There are two types of approaches to find the optimal threshold values, parametric
and non-parametric [57,60]. The parametric approach estimates the parameters of the
probability density functions. In contrast, the non-parametric method uses a discrim-
inatory criterion (entropy, class variance, and error rate) to separate pixels into homo-
geneous regions [3,5]. Still, this criterion must be optimized to determine the opti-
mal threshold values [13,55]. In recent years, optimizations have been used, through
metaheuristic algorithms, of different entropy criteria, such as Kapur’s entropy, Tsal-
lis entropy, and cross-entropy for multilevel thresholding segmentation [20].
In the literature, there are various proposals and approaches to metaheuristic
algorithms that are divided according to their inspiration in evolutionary algorithms,
swarm intelligence, physical laws, and human behavior [15]. In Table1,someopti-
mizers are listed classified according to their inspiration. As noted, many metaheuris-
tic algorithms present good results in tests performed using benchmarks. However,
according to the “No Free Lunch” theorem [84], not all algorithms can solve a spe-
cific problem with precision. This is because there is no universal algorithm that
efficiently solves any type of problem.
This article presents the multilevel segmentation of X-ray images for the detection
of pneumonia through the Whale Optimization Algorithm (WOA) [51]. This meta-
heuristic algorithm mimics the social behavior of humpback whales. In this work,
acomparisonismadeusingasobjectivefunctionthemaximizationofthestatisti-
cal criteria of the variance of Otsu and the Kapur’s entropy, to find the statistical
criterion that works best for these images. Besides, different threshold numbers are
tested to obtain the best settings based on the metrics used to assess the quality of the
results. The experiments are performed using a database of chest radiography images,
publicly available online, to evaluate the performance of the proposed methodology.
The next sections of the chapter are as follows. In Sect.2, the WOA algorithm is
introduced. Section3provides the basics of image segmentation and introduces the
Otsu’s variance and Kapur’s entropy method. Then, in Sect.4presents the proposed
methodology. The results and the discussions are provided in Sect.5.Finally,Sect.6
includes some conclusions and future work.
362 J. Murillo-Olmos et al.
Table 1 List of main optimizers based on their classification
Category Algorithm Authors Year
Evolutionary Genetic algorithm (GA) Holland [32]1992
Genetic programming (GP) Koza and Koza [42]1992
Evolutionary strategies (ES) Michalewicz [49]1994
Differential evolution (DE) Storn and Price [81]1997
Swarm intelligence Particle swarm optimization
(PSO)
Eberhart and Kennedy [18]1995
Ant colony optimization
(ACO)
Dorigo and Di Caro [17]1999
Artificial bee colony (ABC) Karaboga and Basturk [37]2007
Firefly optimization (FFO) Yang [85]2010
Social spider optimization
(SSO)
Cuevas et al. [12]2013
Grey wolf optimizer (GWO) Mirjalili et al. [52]2014
Grasshopper optimization
algorithm (GOA)
Saremi et al. [77]2017
Selfish herd optimizer
(SHO)
Fausto et al. [21]2017
Yellow saddle goatfish
algorithm (YSGA)
Zaldivar et al. [86]2018
Harris hawks optimization
(HHO)
Heidari et al. [29]2019
Side-blotched lizard
algorithm (SBLA)
Maciel et al. [46]2020
Physical laws Central force optimization
(CFO)
Formato [22]2007
Gravitational search
algorithm (GSA)
Rashedi et al. [71]2009
Ray optimization Kaveh and Khayatazad [38]2012
Black hole algorithm (BHA) Hatamlou [27]2013
Sine-cosine algorithm
(SCA)
Mirjalili [50]2016
Human behavior Harmony search algorithm
(HS)
Geem et al. [23]2001
Imperialist competitive
algorithm (ICA)
Atashpaz-Gargari and Lucas
[8]
2007
Tea che r-l ear nin g-ba sed
optimization (TLBO)
Rao et al. [70]2010
Gaining-sharing knowledge
based algorithm (GSK)
Mohamed et al. [54]2019
Thresholding Algorithm Applied to Chest X-Ray Images … 363
2 The Whale Optimization Algorithm
The Whale Optimization Algorithm (WOA) [51] is a metaheuristic optimization algo-
rithm that mimics the hunting behavior of humpback whales, this algorithm uses a
spiral to simulate the bubble-net attacking mechanism of humpback whales. Since
the position of the optimal design in the search space is not previously known, the
WOA algorithm assumes that the current best candidate solution is the target prey
or is close to the optimum. After the best agent is defined, the other search agents
will hence try to update their position towards the best search agent. This behavior
is represented by:
!
D=!!!
!
C·!
X∗(t)−!
X(t)!!!(1)
!
X(t+1)=!
X∗(t)−!
A·!
D(2)
where tindicates the current iteration, !
Aand !
Care coefficient vectors, !
X∗is the
position vector of the best solution obtained o far, !
Xis the position vector, $$ is the
absolute value, and ·is an element-by-element multiplication. It is worth mentioning
here that !
X∗should be updated in each iteration if there is a better solution. The
vectors !
Aand !
Care calculated as follow:
!
A=2a·!r−a(3)
!
C=2·!r(4)
where ais a linearly decreased from 2 to 0 over the course of iterations, and !ris a
random vector with values [0,1].
2.1 Exploitation Phase
In order to mathematically model the bubble-net behavior of humpback whales, two
approaches are designed as follow:
•Shrinking encircling mechanism:Thisbehaviorisarchivedbydecreasingvalue
of ain Eq.3.Figure1ashowsthepossiblepositionfrom(X,Y)towards (X∗,Y∗)
that can be achieved by 0 ≤A≤1ina2Dspace.
•Spiral updating position:AscanbeseeninFig.1baspiralequationiscreated
between the position of whale and prey to mimic the helix-shaped movement of
humpback whales as follow:
!
X(t+1)=!
D&·ebl ·cos(2πl)+!
X∗(t)(5)
364 J. Murillo-Olmos et al.
Fig. 1 Bubble-net search mechanism implemented in WOA [51]
where !
D&=!!!
!
X∗(t)−!
X(t)!!!and indicate the distance of the ith whale to the prey
(best solution obtained so far), bis a constant for defining the shape of the loga-
rithmic spiral and lis a random number between [−1,1].
2.2 Exploration Phase
The same approach based on the variation of the !
Avector can be utilized to search
for prey (exploration). The mathematical model is as follow:
!
D=!!!
!
C·−−→
Xrand −!
X!!!(6)
!
X(t+1)=−−→
Xrand −!
A·!
D(7)
where −−→
Xrand is a random position vector chosen from the current population.
3 Image Multilevel Thresholding
Thresholding is a process in which the pixels of a grayscale image are divided into
sets depending on their intensity levels of the pixels (L).Forthisclassificationofthe
pixels is necessary to select a threshold value (th)and apply the simple next rule:
C1←pif 0≤p<th
C2←pif th≤p<L−1(8)
Thresholding Algorithm Applied to Chest X-Ray Images … 365
where pis one of the m×npixels of the grayscale image (Ig)that can be represented
in Llevels. The rule in Eq.8correspond to a bilevel thresholding and can be extended
for multiple sets:
C1←pif 0≤p<th1
C2←pif th
1≤p<th2
Ci+1←pif th
i≤p<thi+1
Cn−1←pif th
n≤p<L−1
(9)
where the different th represent the different thresholds. The problem in bilevel and
multilevel thresholding is to select the th values that correctly identify the classes.
Otsu’s and Kapur’s methods propose a different objective function that must be
maximized in order to find the optimal values.
3.1 Otsu’s Method Based in Between-Class Variance
This method is a non-parametric technique for thresholding proposed by Otsu [65]
that employs the maximum variance value of the different classes as a criterion to
segment the image. Taking the Lintensity levels and the histogram information. The
probability of the intensity values is defined by:
Phc
i=hc
i
NP
NP
"
i=1
Phc
i=1(10)
where iis a specific intensity level (0≤i≤L−1),cis the component of the image,
NP is the total number of the pixels in the image. hc
iis the histogram and represents
the number of pixels that corresponds to the iintensity level in c.Thehistogramis
normalized to a probability distribution Phc
i.Forthesimplesegmentation(bilevel),
two classes are defined by:
c1=Phc
i
ωc
0(th),..., Phc
th
ωc
0(th)and c2=Phc
th+1
ωc
1(th),..., Phc
L
ωc
1(th)(11)
where ωc
0and ωc
1(th)are probabilities for C1and C2,asitishownby:
ωC
0(th)=
th
"
i=1
PhC
i,ω
C
1(th)=
L
"
i=th+1
PhC
i(12)
366 J. Murillo-Olmos et al.
It is necessary to compute the mean levels µC
0and µC
1that defined the classes
using Eq.13.
µC
0=
th
"
i=1
iPhC
i
µC
0(th),µ
C
1=
L
"
i=th+1
iPhC
i
µC
1(th)(13)
In Eq.13,Cdepends on the objective function. Therefore, the optimization prob-
lem is reduced to find the intensity level that maximized the equation.
fOtsu(th)=max(σ2C
B(th)), 0≤th ≤L−1(14)
where σ2C
B(th)is the Otsu’s variance for given th value. Therefore, the optimization
problem is reduce to find the intensity level that maximized Eq.14.Theobjective
function fOtsu(th)can thus be rewritten for multiple thresholds as follow:
fOtsu(TH )=max(σ2C
B(TH )), 0≤thi≤L−1,i=1,2,3,...,k(15)
where TH =[th1,th2,...,thk−1],isavectorcontainingmultiplethresholdsandtheir
variance is computed through Eq.16.
σ2C
B=
K
"
i=1
σC
i=
K
"
i=1
ωC
i(µC
i−µC
T)2(16)
where irepresents and specifics class. ωC
iand µC
jare the probability of occurrence
and the mean of class, respectively. For multilevel thresholding, such values are
obtained using Eq.17.
ωC
0(th)=
th1
"
i=1
PhC
i
ωC
1(th)=
th2
"
i=th1+1
PhC
i
.
.
..
.
.
ωC
k−1(th)=
L
"
i=thk
PhC
i
(17)
Thresholding Algorithm Applied to Chest X-Ray Images … 367
and for the mean values using Eq.18.
µC
0=
th1
"
i=1
iPhC
i
ωC
0(th1)
µC
1=
th2
"
i=th1+1
iPhC
i
ωC
0(th2)
.
.
..
.
.
µC
k−1=
L
"
i=thk+1
iPhC
i
ωC
1(thk)
(18)
where Ccorresponds to the image component.
3.2 Kapur’s Method Based in Entropy
Another non-parametric method used to determine the optimal threshold values has
been proposed by Kapur [36]. It is based on the entropy and the probability distribu-
tion of the image histogram. The method aims to find the optimal th that maximizes
the overall entropy. The entropy of an image measures the compactness and separa-
bility among classes. In this sense, when the optimal th value appropriately separates
the classes, the entropy has the maximum value. For the bilevel example, the objective
function of the Kapur’s problem can be defined as:
fKapur (th)=HC
1+HC
2,C=#1,2,4ifRGBimage
1ifgrayscaleimage (19)
where the entropies H1and H2are computed by the following model:
HC
1=
th
"
i=1
PhC
i
ωC
0
ln $PhC
i
ωC
0%,HC
2=
L
"
i=th+1
PhC
i
ωC
1
ln $PhC
i
ωC
1%(20)
where ω0(th)and ω1(th)are probabilities distributions for C1and C2.Similartothe
Otsu’s method, the entropy based approach can be extended for multiple threshold
values, for such a case, it is necessary to divide the image into kclasses using a
similar number of thresholds. Under such conditions, the new objective function is
defined by:
fKapur (th)=
k
"
i=1
HC
i,C=#1,2,4ifRGBimage
1ifgrayscaleimage (21)
368 J. Murillo-Olmos et al.
where TH =[th1,th2,...,thk−1]is a vector that contains multiple thresholds. Each
entropy is computed separately with it is respective th,soEq.20 is expanded for k
entropies.
HC
1=
L
"
i=1
PhC
i
ωC
0
ln $PhC
i
ωC
0%,
HC
2=
L
"
i=th1+1
PhC
i
ωC
1
ln $PhC
i
ωC
1%,
.
.
..
.
.
HC
1=
L
"
i=1
PhC
i
ωC
0
ln $PhC
i
ωC
0%
(22)
The values of the probability occurrence (ωC
0,ω
C
1,...,ω
C
k−1)of the kclasses are
obtained by:
ωC
0(th)=
th
"
i=1
PhC
i
ωC
1(th)=
th2
"
i=th1+1
PhC
i
.
.
..
.
.
ωC
k+1(th)=
th
"
i=thk+1
PhC
i
(23)
and the probability distribution PhC
iis obtained using Eq.20.Finally,toseparatethe
pixels in the respective classes, it is necessary to use Eq.9.
C1←pif 0 ≤p<th1
C2←pif th1≤p<th2
Ci←pif thi≤p<thi+1
Cn←pif thn≤p<L−1
where {th1,th2,...,thi,thi+1,thk}represent the different thresholds. The problem
for bilevel and multilevel thresholding is to select the optimal values that correctly
identify the classes. Otsu’s and Kapur’s methods propose a different objective func-
tion that must be maximized in order to find optimal threshold values.
Thresholding Algorithm Applied to Chest X-Ray Images … 369
4 Automatic Detection of Thresholds Values Using WOA
with Kapur and Otsu as Objective Functions
Initially, manual preprocessing is performed to remove artifacts and cut edges that
appear in the X-ray image as noise. Then, a WOA-based multilevel threshold seg-
mentation is applied with Kapur and Otsu as objective functions, followed by the
selection of the best number of regions for segmentation compared to a healthy chest.
Finally, the results of the previous steps are compared among other algorithms. Below
are the actions of Algorithm 1 application for multilevel segmentation.
Algorithm 1: Application algorithm
Read Image IGr;
Calculated the hGr of the IGr;
Initialize the WOA parameters itermax,nt,Agents;
Initialize the location of a population of WOA with Agents in nt dimensions.;
Calculate the fitness of each search agent;
X∗=the best search agent;
t<itermax;
Update parameters;
Update the position of the current search agent by Eq. 5or Eq. 7;
Select a random search agent;
Evaluate the objective function using Otsu Eq. 15,orKapurEq.21;
Update X∗if there is a better solution;
t=t+1
where IGr represents the grayscale image, hGr the image histogram, nt the threshold
number, and Agents the algorithm population. All experiments were performed using
Matlab on an Intel i5 2.30GHz CPU with 8 GB of RAM.
4.1 Dataset Description
The digital images used for this proposed method are X-ray images of the chest
(anteroposterior) selected from retrospective cohorts of pediatric patients aged one to
five years from the Guangzhou Women’s and Children’s Medical Center, Guangzhou.
All chest X-ray images were performed as part of routine clinical care for patients
[39].
370 J. Murillo-Olmos et al.
4.2 Experiments Details
The present work has been carried out on a set of eight samples, four images of
patients with pneumonia and four healthy patients. All images have the same size
(512 ×512 pixels) and are in JPEG format [33,78].
The WOA algorithm applied in multilevel segmentation is compared against the
Firefly Optimization (FFO) [85], Sine-Cosine Algorithm (SCA) [50], Differential
Evolution (DE) [81] and Particle Swarm Optimization (PSO) [18]. All of these algo-
rithms are stochastic, so it is necessary to use adequate statistics to compare the
efficiency of the algorithm. Therefore, all algorithms are run 35 times per image,
and according to related literature, the number of thresholds for testing is set to
th =2,3,4,5,6,7[4,24,26].
In each experiment, the stop criteria is set to 150 iterations. This is because
increasing this value does not affect WOA performance in terms of the quality of
the solution. Therefore, this value has been selected to maintain compatibility with
similar works reported in the literature [14,33,78].
The internal parameters of each algorithm were adjusted according to the refer-
ences proposed [18,50,81,85].
4.3 Metrics
Image quality evaluation methods are divided into objective and subjective methods
[43]. Subjective methods are based on human judgment and operate without any
reference [40]. While on the other hand, objective methods are based on comparisons
[10] that use explicit numerical criteria through references, such as ground truth or
prior knowledge in terms of statistical parameters [19,48]. The metrics used in this
work belong to the classification of objective methods.
4.3.1 Peak Signal-to-Noise Ratio
The peak-to-signal ratio (PSNR) is used to compare the similarity of an image (image
segmented) against a reference image (original image) based on the mean square error
(RMSE) of each pixel [4,33,67]. PSNR and RMSE are defined in Eq.24.
PSNR =log10
255
RMSE ,(dB)
RMSE =&'ro
i=1'co
j=1[IC
0(i,j)−IC
th (i,j)]
ro ×co
(24)
Thresholding Algorithm Applied to Chest X-Ray Images … 371
where Ic
0is the original image, IC
th is the segmented image, Cdepends on the image
(RGB or grayscale) and ro,co are the total number of rows and columns of the image,
respectively.
4.3.2 Structural Similarity
Structural similarity index (SSIM) is a method for measuring the internal structures
between two images. This metric compares local patterns of pixel intensities [82].
SSIM (x,y)=[l(x,y)]α·[c(x,y)]β·[s(x,y)]γ(25)
where α>0,β>0andγ>0, simplify the expression, α=β=σ=1andC3=
C2/2. Where lis for luminance comparison, cis the contrast comparison, sis for the
structure comparison [82].
SSIM (x,y)=(2µxµy+C1)(2σxy +C2)
*µ2
x+µ2
y+C1+*σ2
x+σ2
y+C2+(26)
4.3.3 Feature Similarity
The feature similarity index (FSIM) maps features and measures the similarities
between two images [87]. The calculation of the FSIM index consists of two stages.
First, the local similarity map is calculated. Then, the similarity map is grouped into a
single similarity score. The FSIM index between two components f1and f2is defined
in Eq.27.
FSIM ='x'( SL(x)PCm(x)
'x'( PCm(x)(27)
where (means the entire spatial domain of the image. SLis the similarity of the
components. PC is a phase congruence that postulates that the characteristics are
perceived at points, where the Fourier components are maxima in phase.
5 Experimental Results
The set of eight images, four of healthy patients and four of patients with pneumonia,
used as a point of reference for the development of this work are presented in Figs.2
and 3,respectively.Furthermore,ontherightsideoftheimages,theircorresponding
histograms are presented, where it is possible to observe the heterogeneity in the
intensities of the gray levels of each image, which makes it possible to test the
behavior of the proposed approach with different data to verify the robustness.
372 J. Murillo-Olmos et al.
(a) Person 1 bacteria 2
050100150200250
Gray Level
0
2000
4000
6000
8000
10000
12000
14000
Frequency
(b)
(c) Person 3 bacteria 10
0 50 100 150 200 250
Gray Level
0
0.5
1
1.5
2
2.5
3
3.5
Frequency
10
4
(d)
(e) Person 7 bacteria 25
050100150200250
Gray Level
0
2000
4000
6000
8000
10000
12000
14000
16000
Frequency
(f)
(g) Person 7 bacteria 28
0 50 100 150 200 250
Gray Level
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Frequency
(h)
Fig. 2 a, c, e, g are pneumonia images dataset, b, d, f, h are histograms of the images
Thresholding Algorithm Applied to Chest X-Ray Images … 373
(a) IM-0145
0 50 100 150 200 250
Gray Level
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18
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10
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(b)
(c) IM-0211
0 50 100 150 200 250
Gray Level
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(d)
(e) IM-0224
0 50 100 150 200 250
Gray Level
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(f)
(g) IM-0225
0 50 100 150 200 250
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(h)
Fig. 3 a, c, e, h are healthy images dataset, b, d, f, h are histograms of the images
374 J. Murillo-Olmos et al.
5.1 Results of Otsu’s Objective Function
The results with the best average value, concerning the metrics, are marked in bold
for a better appreciation. In Table2,presentsthePSNRvaluesobtainedforeach
of the algorithms. In general, the highest PSNR values are obtained using the WOA
algorithm, and it can be observed that in the images corresponding to person 7 bacteria
25 and person 7 bacteria 28, the proposed algorithm presents more favorable results
in five thresholds of the seven possible. However, in the remaining two thresholds,
the performance of the algorithm is not so far from the values obtained by the DE and
PSO algorithms. In cases where the algorithm presents the least amount of optimal
values with two thresholds, it occurs in healthy images corresponding to IM-0224
and IM-0225. While for the remaining five thresholds, it presents the same trend
since it is not that far from the results with the algorithms with the highest average
PSNR. The PSO and DE algorithms also present the averages of the highest values
in at least two thresholds. This reflects that although the algorithm does not present
the most favorable result in all segmentation cases, it does present significant results
in most cases compared to the other algorithms compared in this work. Based on
the PSNR evaluated in this table, it can also be observed that the standard deviation
of the algorithm does not present the lowest values in any case, but in general, it is
close to the best values obtained by the PSO algorithm.
Table3presents the comparison of the average SSIM values obtained for the Otsu
maximization approach. The possible values of the metric are in the intervals of [0,
1]. The WOA algorithm does not present the best results except in the case of the
healthy image IM-0145, in which the highest values of this metric are presented in
four of the seven thresholds tested. In the other cases, it is close to the highest average
values obtained by the SCA and DE algorithms. Regarding the standard deviation
that represents the stability of the algorithm in the 35 executions, the algorithm with
the lowest values is the DE.
In Table4,theaverageresultsoftheFSIMmetricappliedtothedifferentalgo-
rithms are observed. The best values, similar to the previous tables, are presented
in bold, the highest values with the most significant performance when segmenting
the images. Similar to the PSNR metric, the most optimal mean values are obtained
through the WOA algorithm, in which the corresponding healthy images IM-0145,
IM-0211 and IM-0224 present the most favorable results in six or more of the thresh-
olds tested. However, in the case of pneumonia images, significant results are only
presented in Person 1 bacteria 2 and Person 3 bacteria 12. While for the images
Person 7 bacteria 25 and Person 7 bacteria 28 the best values are obtained by the
DE algorithm. In addition, the PSO and DE algorithms are the ones that present the
lowest standard deviation values, representing the highest stability.
In general, it is shown that in most cases, the WOA algorithm presents the best
results when evaluating the three metrics (PSNR, SSIM, and FSIM) used to measure
the quality of the segmentation with respect to the algorithms mentioned to make
the comparisons. However, in cases where significant results are not presented, the
results are not far from the average of the optimal values.
Thresholding Algorithm Applied to Chest X-Ray Images … 375
Table 2 Comparison of the Otsu results of the PSNR values obtained by WOA, FFO, SCA, DE and PSO
Image nTh WOA FFO SCA DE PSO
PSNR STD PSNR STD PSNR STD PSNR STD PSNR STD
Person 1
bacteria 2
212.2999 5.289E−01 11.8334 1.659E−01 11.7998 9.008E−15 11.7998 9.008E−15 11.7998 9.008E−15
316.6040 4.979E−01 15.8855 2.325E−01 16.1793 3.217E−02 16.1724 4.919E−02 16.1663 5.194E−02
419.2838 5.157E−01 18.1041 7.205E−01 18.8722 2.491E−01 18.8859 1.943E−01 18.9405 1.485E−01
521.2304 6.338E−01 19.6552 8.494E−01 20.7602 3.984E−01 21.1319 1.498E−01 21.1248 1.537E−01
622.8456 6.012E−01 20.8944 9.442E−01 21.8228 6.029E−01 22.8481 1.590E−01 22.8766 2.018E−01
723.8127 6.097E−01 21.9780 7.019E−01 22.9918 6.317E−01 23.9101 2.973E−01 23.9025 2.740E−01
824.7188 5.667E−01 22.8859 9.507E−01 23.6906 8.027E−01 25.1740 3.043E−01 25.2231 2.802E−01
Person 3
bacteria 12
212.9665 1.017E+00 11.7265 3.804E−02 11.7229 4.130E−02 11.7334 3.752E−02 11.7315 3.685E−02
316.1680 7.138E−01 15.0379 7.555E−01 15.3539 1.686E−01 15.3393 2.048E−02 15.3289 2.361E−02
418.4325 7.836E−01 17.6130 7.534E−01 17.9652 3.328E−01 18.0898 2.071E−01 18.1595 2.770E−01
520.5745 5.509E−01 19.2200 8.841E−01 19.9306 5.392E−01 20.1932 2.408E−01 20.1829 2.666E−01
621.8708 3.372E−01 20.7765 7.480E−01 21.2693 4.948E−01 21.8608 2.623E−01 21.9288 3.100E−01
722.9412 5.550E−01 21.5261 8.946E−01 22.3569 6.718E−01 23.2217 3.030E−01 23.2423 3.375E−01
823.9023 6.611E−01 22.2433 8.112E−01 22.9944 6.971E−01 24.1976 4.371E−01 24.1788 4.420E−01
Person 7
bacteria 25
212.5911 5.575E−01 12.3193 6.432E−02 12.3200 1.533E−02 12.3205 1.757E−02 12.3130 1.576E−02
316.6192 3.342E−01 16.1942 3.471E−01 16.5075 2.160E−02 16.5100 2.125E−02 16.5118 2.458E−02
419.0023 2.798E−01 18.3375 5.345E−01 18.7777 1.085E−01 18.8258 5.273E−02 18.8261 4.440E−02
521.6581 2.574E−01 19.9531 6.482E−01 21.1536 5.545E−01 21.6261 2.977E−02 21.6172 3.290E−02
623.3708 3.877E−01 21.2480 7.654E−01 22.4489 5.400E−01 23.3091 6.029E−02 23.3253 6.785E−02
724.6061 4.991E−01 22.3525 8.141E−01 23.4900 6.961E−01 24.7016 9.182E−02 24.7257 1.004E−01
825.7457 3.840E−01 23.4233 8.313E−01 24.2428 7.474E−01 25.9659 1.032E−01 25.9958 1.110E−01
(continued)
376 J. Murillo-Olmos et al.
Table 2 (continued)
Image nTh WOA FFO SCA DE PSO
PSNR STD PSNR STD PSNR STD PSNR STD PSNR STD
Person 7
bacteria 28
212.1593 4.362E−01 11.8419 1.536E−01 11.8338 9.008E−15 11.8338 9.008E−15 11.8338 9.008E−15
316.8274 4.700E−01 15.9799 5.468E−01 16.4698 4.337E−02 16.4761 1.869E−02 16.4756 1.791E−02
418.9568 2.974E−01 18.1277 5.415E−01 18.7307 8.029E−02 18.8095 2.978E−02 18.7998 3.178E−02
521.4010 6.282E−01 19.8752 7.302E−01 20.8220 5.196E−01 21.3877 3.500E−02 21.3694 9.056E−02
623.0807 5.295E−01 20.9970 7.916E−01 21.9493 7.254E−01 23.0149 7.034E−02 23.0412 8.755E−02
724.1102 5.886E−01 22.4315 9.189E−01 22.9219 8.844E−01 24.3211 2.074E−01 24.3596 2.009E−01
825.1435 6.043E−01 22.7508 9.846E−01 23.6934 8.816E−01 25.2575 1.892E−01 25.3678 2.343E−01
IM−0145 213.3077 1.066E+00 12.2721 4.948E−02 12.2722 3.961E−02 12.2809 3.878E−02 12.2728 4.008E−02
316.5396 6.720E−01 15.3799 7.109E−01 15.6968 1.679E−01 15.7248 7.639E−02 15.7023 6.000E−02
418.7285 5.329E−01 17.5817 7.966E−01 18.2705 2.548E−01 18.2888 2.499E−01 18.3177 2.241E−01
520.5660 5.569E−01 19.2078 9.779E−01 20.1059 4.385E−01 20.3898 2.567E−01 20.3830 2.372E−01
621.9873 4.346E−01 20.6971 7.626E−01 21.3160 5.113E−01 21.9362 2.420E−01 21.9018 2.221E−01
723.1335 4.437E−01 21.6586 7.744E−01 22.3905 4.690E−01 23.2328 2.796E−01 23.1942 2.636E−01
823.9742 5.717E−01 22.8182 8.293E−01 23.2828 5.795E−01 24.2761 3.277E−01 24.3226 3.094E−01
IM−0211 213.1157 8.080E−01 12.0886 4.703E−02 12.1010 1.673E−02 12.1030 1.710E−02 12.1059 1.405E−02
316.6426 6.101E−01 15.7754 4.439E−01 15.9762 1.099E−01 15.9557 1.045E−01 16.0009 9.209E−02
418.5793 4.188E−01 17.8337 7.236E−01 18.3292 2.561E−01 18.3744 1.832E−01 18.3752 1.956E−01
520.5375 4.273E−01 19.4555 8.866E−01 20.2144 3.072E−01 20.5986 1.245E−01 20.6121 9.440E−02
621.9512 4.931E−01 20.5433 8.376E−01 21.5547 4.823E−01 22.0293 1.905E−01 21.9799 2.181E−01
722.8830 5.142E−01 21.7674 8.088E−01 22.5129 5.062E−01 23.0913 1.801E−01 23.0384 2.787E−01
823.6592 4.088E−01 22.5349 6.440E−01 23.1277 6.586E−01 23.9839 3.109E−01 23.9991 3.343E−01
(continued)
Thresholding Algorithm Applied to Chest X-Ray Images … 377
Table 2 (continued)
Image nTh WOA FFO SCA DE PSO
PSNR STD PSNR STD PSNR STD PSNR STD PSNR STD
IM−0224 210.5842 4.599E−01 10.4698 4.666E−01 10.6027 3.143E−01 10.5160 3.062E−01 10.4677 2.804E−01
315.3641 5.955E−01 15.0556 7.713E−01 15.0472 4.108E−01 15.3059 7.206E−15 15.3059 7.206E−15
418.5185 4.266E−01 17.2953 8.884E−01 18.0730 3.156E−01 18.4260 1.117E−01 18.3818 1.301E−01
520.0450 6.809E−01 19.0665 7.764E−01 19.9189 5.346E−01 20.2669 2.443E−01 20.2341 2.377E−01
621.2687 7.409E−01 20.1864 9.586E−01 20.8796 7.195E−01 21.7731 3.373E−01 21.7253 4.297E−01
722.5141 7.902E−01 21.2963 1.070E+00 21.9134 7.392E−01 22.7059 4.032E−01 22.8867 3.333E−01
823.4369 8.832E−01 22.1699 8.640E−01 22.8727 7.678E−01 23.8280 5.248E−01 23.8357 5.800E−01
IM−0225 212.3125 6.820E−01 11.6028 1.221E−01 11.5157 5.405E−15 11.5157 5.405E−15 11.5157 5.405E−15
316.2275 7.313E−01 15.1013 7.435E−01 15.5739 2.618E−01 15.5193 3.199E−01 15.6248 2.411E−01
417.8274 8.512E−01 17.1953 7.783E−01 17.7114 5.664E−01 18.0259 3.046E−01 18.0441 3.015E−01
519.9000 8.025E−01 19.0592 6.532E−01 19.9717 3.989E−01 20.0805 4.320E−01 19.9690 4.339E−01
620.9757 7.825E−01 20.3371 8.357E−01 20.5697 7.132E−01 21.4292 5.324E−01 21.4301 5.233E−01
722.0365 1.050E+00 21.1230 9.119E−01 21.6201 8.950E−01 22.4315 5.519E−01 22.0964 6.189E−01
822.8044 8.835E−01 21.9180 1.078E+00 22.3468 7.680E−01 22.9111 6.138E−01 23.2017 4.772E−01
378 J. Murillo-Olmos et al.
Table 3 Comparison of the Otsu results of the SSIM values obtained by WOA, FFO, SCA, DE and PSO
Image nTh WOA FFO SCA DE PSO
SSIM STD SSIM STD SSIM STD SSIM STD SSIM STD
Person 1
bacteria 2
20.50324 2.141E−02 0.51514 1.949E−02 0.50869 1.126E−16 0.50869 1.126E−16 0.50869 1.126E−16
30.64344 1.663E−02 0.64870 1.944E−02 0.65212 4.993E−03 0.65237 6.116E−03 0.65337 7.091E−03
40.70234 1.653E−02 0.70080 2.315E−02 0.71040 4.720E−03 0.71333 4.967E−03 0.71258 4.706E−03
50.72578 1.113E−02 0.71554 2.169E−02 0.72945 8.957E−03 0.73343 3.472E−03 0.73380 3.091E−03
60.74012 8.597E−03 0.72884 2.405E−02 0.73729 1.699E−02 0.74781 2.586E−03 0.74674 3.760E−03
70.74467 7.356E−03 0.74401 2.194E−02 0.75149 1.339E−02 0.74768 4.953E−03 0.75135 7.538E−03
80.76359 6.608E−03 0.75802 1.945E−02 0.76044 1.871E−02 0.76543 3.657E−03 0.76710 3.179E−03
Person 3
bacteria 12
20.51544 2.642E−02 0.52373 9.370E−03 0.52558 8.163E−03 0.52322 7.808E−03 0.52385 7.602E−03
30.66418 1.799E−02 0.66633 1.425E−02 0.67237 3.466E−03 0.67317 2.811E−03 0.67175 3.241E−03
40.68100 1.303E−02 0.68219 1.761E−02 0.68868 8.875E−03 0.68851 6.221E−03 0.68839 5.410E−03
50.70664 8.025E−03 0.69927 1.750E−02 0.70480 1.198E−02 0.70634 6.830E−03 0.70773 7.776E−03
60.72044 8.276E−03 0.72091 1.850E−02 0.72296 1.495E−02 0.71987 9.895E−03 0.72070 1.042E−02
70.74075 8.648E−03 0.72999 1.951E−02 0.73790 1.472E−02 0.74248 6.970E−03 0.74137 7.684E−03
80.75445 1.432E−02 0.74847 1.406E−02 0.75305 1.474E−02 0.75633 8.333E−03 0.75946 1.068E−02
Person 7
bacteria 25
20.57960 2.292E−02 0.59070 1.303E−02 0.58664 2.526E−03 0.58673 2.894E−03 0.58548 2.592E−03
30.67584 1.313E−02 0.68004 2.195E−02 0.68099 4.249E−03 0.68027 4.789E−03 0.67981 4.778E−03
40.69294 1.270E−02 0.70852 2.542E−02 0.69782 5.711E−03 0.69920 1.758E−03 0.69922 1.593E−03
50.76581 9.125E−03 0.75496 2.446E−02 0.76890 1.489E−02 0.76789 1.302E−03 0.76858 1.474E−03
60.78364 1.170E−02 0.77393 2.288E−02 0.78990 1.034E−02 0.79237 3.259E−03 0.79122 3.025E−03
70.79919 7.246E−03 0.78674 2.698E−02 0.79948 1.301E−02 0.80595 6.262E−03 0.80497 6.128E−03
80.81012 5.525E−03 0.80015 1.765E−02 0.81110 1.287E−02 0.81412 2.584E−03 0.81515 2.960E−03
(continued)
Thresholding Algorithm Applied to Chest X-Ray Images … 379
Table 3 (continued)
Image nTh WOA FFO SCA DE PSO
SSIM STD SSIM STD SSIM STD SSIM STD SSIM STD
Person 7
bacteria 28
20.45255 1.711E−02 0.46020 1.378E−02 0.45933 1.689E−16 0.45933 1.689E−16 0.45933 1.689E−16
30.61610 1.591E−02 0.61174 3.586E−02 0.62591 6.424E−03 0.62522 5.030E−03 0.62473 5.060E−03
40.65346 1.163E−02 0.67116 4.001E−02 0.65661 7.730E−03 0.66196 1.329E−03 0.66139 1.640E−03
50.73117 1.276E−02 0.72063 2.833E−02 0.73695 1.806E−02 0.74202 2.657E−03 0.74015 4.979E−03
60.74960 8.397E−03 0.72956 2.989E−02 0.74004 1.865E−02 0.75885 3.093E−03 0.75879 3.320E−03
70.76808 8.505E−03 0.75461 2.128E−02 0.75658 1.620E−02 0.77634 2.844E−03 0.77499 4.491E−03
80.78188 7.525E−03 0.75289 2.167E−02 0.77054 1.705E−02 0.78355 4.676E−03 0.78610 5.537E−03
IM−0145 20.46925 1.628E−02 0.46858 1.118E−02 0.47260 6.511E−03 0.47061 6.664E−03 0.47236 6.688E−03
30.58463 1.049E−02 0.57731 1.758E−02 0.58697 5.212E−03 0.58847 1.269E−03 0.58823 1.418E−03
40.61875 9.462E−03 0.60502 1.812E−02 0.61604 5.653E−03 0.61551 5.055E−03 0.61523 5.080E−03
50.64947 8.394E−03 0.63797 1.920E−02 0.64399 1.008E−02 0.64763 6.162E−03 0.64861 4.593E−03
60.67621 8.556E−03 0.66256 1.927E−02 0.66364 1.121E−02 0.67407 4.911E−03 0.67430 5.805E−03
70.70581 1.026E−02 0.68685 1.592E−02 0.69572 1.433E−02 0.70557 4.482E−03 0.70451 3.773E−03
80.72853 1.117E−02 0.70958 1.628E−02 0.71586 1.283E−02 0.73369 6.690E−03 0.73244 6.754E−03
IM−0211 20.40035 1.703E−02 0.41722 1.197E−02 0.41785 5.238E−03 0.41854 5.401E−03 0.41927 4.546E−03
30.52922 1.081E−02 0.55233 1.542E−02 0.55593 3.503E−03 0.55645 3.624E−03 0.55409 4.145E−03
40.55331 4.772E−03 0.57453 1.905E−02 0.57830 5.661E−03 0.57602 3.638E−03 0.57567 2.071E−03
50.58097 7.711E−03 0.59095 1.796E−02 0.59713 9.359E−03 0.60099 5.181E−03 0.59949 5.828E−03
60.61285 1.492E−02 0.61399 2.042E−02 0.62192 9.001E−03 0.62203 7.414E−03 0.62010 7.494E−03
70.63336 1.468E−02 0.64216 2.882E−02 0.65435 2.468E−02 0.63934 4.804E−03 0.64403 1.593E−02
80.65562 2.358E−02 0.65964 2.777E−02 0.66913 2.548E−02 0.66801 1.777E−02 0.66861 2.077E−02
(continued)
380 J. Murillo-Olmos et al.
Table 3 (continued)
Image nTh WOA FFO SCA DE PSO
SSIM STD SSIM STD SSIM STD SSIM STD SSIM STD
IM−0224 20.40169 2.325E−02 0.45933 3.247E−02 0.46806 2.196E−02 0.46190 2.104E−02 0.45841 1.899E−02
30.54936 2.464E−02 0.60124 4.064E−02 0.58111 1.692E−02 0.58860 1.126E−16 0.58860 1.126E−16
40.61712 1.347E−02 0.63938 2.184E−02 0.64538 9.346E−03 0.65450 5.863E−03 0.64960 6.500E−03
50.64461 8.516E−03 0.66918 1.878E−02 0.67272 9.532E−03 0.67307 5.100E−03 0.67199 5.582E−03
60.67024 1.232E−02 0.68772 1.812E−02 0.69069 1.397E−02 0.69643 6.283E−03 0.69586 6.760E−03
70.69882 1.126E−02 0.70115 1.777E−02 0.71118 1.575E−02 0.72071 8.708E−03 0.72046 9.361E−03
80.71871 1.730E−02 0.71596 1.708E−02 0.72469 1.523E−02 0.73932 1.285E−02 0.73843 1.454E−02
IM−0225 20.35728 1.201E−02 0.37682 2.433E−02 0.35799 1.126E−16 0.35799 1.126E−16 0.35799 1.126E−16
30.56602 1.534E−02 0.57893 2.121E−02 0.58838 1.183E−02 0.58951 1.048E−02 0.58769 1.024E−02
40.57494 1.463E−02 0.59375 2.070E−02 0.60036 1.148E−02 0.60454 2.330E−03 0.60419 2.266E−03
50.59523 1.286E−02 0.62086 2.352E−02 0.62315 9.148E−03 0.62281 8.051E−03 0.62018 1.028E−02
60.61261 2.425E−02 0.63721 3.238E−02 0.63486 2.129E−02 0.62956 7.584E−03 0.63118 9.457E−03
70.62851 2.305E−02 0.65009 2.548E−02 0.65207 2.670E−02 0.64137 1.190E−02 0.64212 2.013E−02
80.65338 3.615E−02 0.67483 5.017E−02 0.67895 3.569E−02 0.65539 2.456E−02 0.66021 2.317E−02
Thresholding Algorithm Applied to Chest X-Ray Images … 381
Table 4 Comparison of the Otsu results of the FSIM values obtained by WOA, FFO, SCA, DE and PSO
Image nTh WOA FFO SCA DE PSO
FSIM STD FSIM STD FSIM STD FSIM STD FSIM STD
Person 1
bacteria 2
20.70092 1.90E−02 0.70344 4.37E−03 0.70115 2.25E−16 0.70115 2.25E−16 0.70115 2.25E−16
30.72606 8.99E−03 0.72354 7.94E−03 0.72351 2.39E−03 0.72275 2.11E−03 0.72326 1.44E−03
40.76836 6.07E−03 0.76029 1.15E−02 0.76555 3.80E−03 0.76711 3.12E−03 0.76690 2.56E−03
50.81008 7.53E−03 0.77976 1.69E−02 0.80520 6.09E−03 0.80966 2.92E−03 0.81002 2.97E−03
60.84507 5.87E−03 0.80573 1.94E−02 0.82919 1.63E−02 0.84805 2.92E−03 0.84755 2.50E−03
70.86244 7.02E−03 0.82832 1.94E−02 0.84922 1.35E−02 0.86751 4.86E−03 0.86862 5.81E−03
80.87807 1.05E−02 0.84933 1.68E−02 0.86131 1.89E−02 0.88791 4.78E−03 0.89010 3.33E−03
Person 3
bacteria 12
20.65365 2.11E−02 0.63958 3.73E−04 0.63955 2.78E−04 0.63959 3.00E−04 0.63955 2.93E−04
30.68425 1.40E−02 0.67080 1.06E−02 0.66880 2.90E−03 0.66869 1.28E−03 0.66804 1.47E−03
40.73168 1.45E−02 0.71778 1.34E−02 0.72168 6.23E−03 0.72228 3.68E−03 0.72236 3.80E−03
50.78498 1.01E−02 0.75456 1.89E−02 0.76820 1.01E−02 0.77513 4.51E−03 0.77481 5.88E−03
60.81717 7.61E−03 0.79073 1.73E−02 0.80223 1.39E−02 0.81683 5.06E−03 0.81830 4.98E−03
70.84456 1.53E−02 0.81247 1.82E−02 0.82873 1.69E−02 0.84817 6.48E−03 0.84875 6.27E−03
80.86517 1.35E−02 0.82765 1.73E−02 0.84767 1.67E−02 0.87193 8.34E−03 0.87186 8.44E−03
Person 7
bacteria 25
20.72805 1.21E−02 0.72663 1.84E−03 0.72762 3.97E−04 0.72754 4.22E−04 0.72775 3.51E−04
30.76751 8.38E−03 0.76801 1.09E−02 0.76987 2.39E−03 0.76991 2.82E−03 0.76957 2.73E−03
40.77891 5.78E−03 0.77650 1.27E−02 0.78020 3.58E−03 0.78079 1.71E−03 0.78063 1.57E−03
50.79423 3.43E−03 0.79192 1.48E−02 0.79686 6.31E−03 0.79471 8.38E−04 0.79486 7.25E−04
60.81957 5.12E−03 0.80662 1.63E−02 0.81764 9.58E−03 0.82290 2.43E−03 0.82192 2.60E−03
70.84095 4.96E−03 0.82141 2.17E−02 0.83055 9.36E−03 0.84467 3.12E−03 0.84319 2.73E−03
80.85789 6.86E−03 0.83281 1.29E−02 0.84175 1.42E−02 0.86169 2.70E−03 0.86296 2.65E−03
(continued)
382 J. Murillo-Olmos et al.
Table 4 (continued)
Image nTh WOA FFO SCA DE PSO
FSIM STD FSIM STD FSIM STD FSIM STD FSIM STD
Person 7
bacteria 28
20.71594 9.19E−03 0.71602 6.01E−03 0.71582 5.63E−16 0.71582 5.63E−16 0.71582 5.63E−16
30.74580 8.38E−03 0.74800 1.46E−02 0.75046 2.36E−03 0.75034 2.59E−03 0.75004 2.68E−03
40.78260 3.64E−03 0.77828 1.73E−02 0.78330 6.53E−03 0.78543 2.09E−03 0.78573 1.87E−03
50.81086 5.46E−03 0.80012 1.62E−02 0.81100 1.13E−02 0.81338 2.02E−03 0.81220 3.81E−03
60.84333 3.82E−03 0.81838 2.05E−02 0.83586 1.37E−02 0.84799 3.48E−03 0.84731 3.73E−03
70.87335 7.75E−03 0.84077 1.83E−02 0.85310 1.40E−02 0.87915 2.05E−03 0.87821 2.44E−03
80.89042 5.79E−03 0.84733 1.57E−02 0.86796 1.41E−02 0.89858 2.14E−03 0.89711 4.28E−03
IM−0145 20.63478 2.91E−02 0.60666 7.17E−04 0.60697 3.19E−04 0.60698 2.80E−04 0.60697 3.18E−04
30.69589 2.90E−02 0.65578 1.27E−02 0.65881 3.39E−03 0.65955 2.00E−03 0.65894 1.63E−03
40.76140 1.98E−02 0.72986 1.23E−02 0.74219 3.49E−03 0.74260 3.14E−03 0.74273 2.86E−03
50.82439 1.74E−02 0.78011 2.46E−02 0.80334 1.12E−02 0.81044 3.22E−03 0.81010 2.91E−03
60.86124 9.49E−03 0.82107 1.81E−02 0.83820 1.63E−02 0.85491 2.91E−03 0.85416 3.08E−03
70.89040 1.10E−02 0.84503 2.05E−02 0.86284 1.44E−02 0.88946 5.78E−03 0.88897 6.59E−03
80.90422 1.43E−02 0.87157 1.95E−02 0.88577 1.48E−02 0.91127 7.20E−03 0.91217 7.05E−03
IM−0211 20.63807 2.05E−02 0.61108 1.44E−03 0.61196 1.20E−04 0.61195 1.21E−04 0.61192 9.69E−05
30.68296 2.40E−02 0.65305 6.47E−03 0.64959 2.57E−03 0.64906 2.67E−03 0.65080 2.92E−03
40.75179 1.41E−02 0.71886 1.09E−02 0.72851 1.97E−03 0.72866 1.71E−03 0.72795 1.47E−03
50.80827 1.15E−02 0.77270 1.42E−02 0.78747 3.54E−03 0.79222 2.10E−03 0.79151 2.26E−03
60.84926 1.19E−02 0.79988 1.93E−02 0.82497 1.42E−02 0.84035 2.52E−03 0.83980 2.94E−03
70.87440 1.16E−02 0.83516 2.14E−02 0.85458 1.13E−02 0.87159 6.43E−03 0.87199 7.11E−03
80.89496 1.19E−02 0.85431 1.58E−02 0.87348 1.38E−02 0.89661 6.98E−03 0.89784 5.29E−03
(continued)
Thresholding Algorithm Applied to Chest X-Ray Images … 383
Table 4 (continued)
Image nTh WOA FFO SCA DE PSO
FSIM STD FSIM STD FSIM STD FSIM STD FSIM STD
IM−0224 20.64286 2.01E−02 0.62103 5.53E−03 0.62220 3.92E−03 0.62104 3.45E−03 0.62034 2.85E−03
30.69762 1.75E−02 0.66925 9.01E−03 0.67466 4.91E−03 0.67143 3.38E−16 0.67143 3.38E−16
40.76260 1.40E−02 0.72517 1.26E−02 0.73300 5.33E−03 0.73866 3.94E−03 0.73666 3.86E−03
50.81261 1.56E−02 0.76685 1.54E−02 0.78649 1.23E−02 0.79649 5.81E−03 0.79609 5.03E−03
60.83835 1.83E−02 0.79454 2.09E−02 0.81274 1.61E−02 0.83223 7.50E−03 0.83323 8.26E−03
70.86783 1.59E−02 0.82512 2.29E−02 0.83702 1.42E−02 0.85507 8.42E−03 0.85939 8.23E−03
80.88411 1.65E−02 0.83915 1.92E−02 0.85928 1.64E−02 0.88050 1.08E−02 0.88182 1.15E−02
IM−0225 20.60607 2.11E−02 0.58598 2.75E−03 0.58932 0.00E+00 0.58932 0.00E+00 0.58932 0.00E+00
30.65243 1.83E−02 0.62846 6.10E−03 0.62878 4.01E−03 0.62868 4.56E−03 0.62943 3.89E−03
40.70933 1.37E−02 0.69306 8.70E−03 0.69532 5.16E−03 0.69671 2.01E−03 0.69731 2.32E−03
50.77262 1.74E−02 0.74352 1.89E−02 0.76512 6.85E−03 0.76642 5.95E−03 0.76327 6.05E−03
60.80743 1.65E−02 0.78142 2.36E−02 0.78830 1.95E−02 0.80747 1.09E−02 0.80995 1.07E−02
70.83762 2.38E−02 0.80409 2.26E−02 0.82120 1.84E−02 0.84106 1.35E−02 0.83056 1.61E−02
80.85590 1.89E−02 0.82736 2.44E−02 0.83471 2.19E−02 0.85552 1.45E−02 0.86376 1.54E−02
384 J. Murillo-Olmos et al.
Table 5 Results after applying segmentation using the WOA metaheuristic algorithm for the max-
imization of the Otsu’s variance
2345
0 50 100 150 200 250 300
0
2000
4000
6000
8000
10000
12000
14000
0 50 100 150 200 250 300
0
2000
4000
6000
8000
10000
12000
14000
050100150200250300
0
2000
4000
6000
8000
10000
12000
14000
050100150200250300
0
2000
4000
6000
8000
10000
12000
14000
678
Person 1 bacteria 2
0 50 100 150 200 250 300
0
2000
4000
6000
8000
10000
12000
14000
0 50 100 150 200 250 300
0
2000
4000
6000
8000
10000
12000
14000
050100150200250300
0
2000
4000
6000
8000
10000
12000
14000
Tables 5and 6show some visual results of the segmented images using the seven
thresholds together with their corresponding histogram through the WOA algorithm
to maximize the Otsu’s objective function, where the different thresholds selected
by the algorithm are marked with a red vertical line. As it is possible to determine
in both tables, with a higher number of thresholds, the features and details of the
X-ray images can be better appreciated for the detection of pneumonia in patients in
asimplerandfasterway.
5.2 Results of Kapur’s Objective Function
The results obtained when applying the PSNR, SSIM and FSIM metrics to evaluate
the quality of the segmentation using Kapur maximization for all algorithms are
exposed in the three tables below. Similar to the results shown with Otsu’s objective
function, the best results are presented in bold.
In Table7,thePSNRvaluesobtainedforeachofthealgorithmsareshown.This
metric allows evaluating the affinity between the original image and the segmented
Thresholding Algorithm Applied to Chest X-Ray Images … 385
Table 6 Results after applying segmentation using the WOA metaheuristic algorithm for the max-
imization of the Otsu’s variance
2345
05010015020025030
0
0
0.5
1
1.5
2
2.5 105
05010015020025030
0
0
0.5
1
1.5
2
2.5 105
0 50 100 150 200 250 30
0
0
0.5
1
1.5
2
2.5 105
0 50 100 150 200 250 30
0
0
0.5
1
1.5
2
2.5 105
567
Person 3 bacteria 12
05010015020025030
0
0
0.5
1
1.5
2
2.5 105
05010015020025030
0
0
0.5
1
1.5
2
2.5 105
0 50 100 150 200 250 30
0
0
0.5
1
1.5
2
2.5 105
image, with a higher value representing better quality. The highest values are obtained
through the PSO algorithm, and in the other cases, the highest values are distributed
in the WOA, FFO, SCA and DE algorithms. Similarly, measuring the stability with
the standard deviation of the 35 runs, the PSO algorithm presents the smallest values
at most of the thresholds in the eight images.
Table8presents a comparison with the mean SSIM metric values obtained using
the Kapur’s method as an objective function. The PSO algorithm presents the best
results in five or six thresholds for the cases of pneumonia images. While for the
healthy images, the best values are distributed among the five compared algorithms.
Table9shows a trend similar to the average results of the PSNR metric revealed in
Table7. Therefore, the highest values are obtained using the PSO and DE algorithm,
and for the other cases, the optimal values are distributed between the WOA, FFO
and SCA algorithms. And in the same way, the algorithms that presented the best
stability in the 35 runs are the PSO and the DE.
386 J. Murillo-Olmos et al.
Table 7 Comparison of the Kapur results of the PSNR values obtained by WOA, FFO, SCA, DE and PSO
Image nTh WOA FFO SCA DE PSO
PSNR STD PSNR STD PSNR STD PSNR STD PSNR STD
Person 1
bacteria 2
211.8482 3.60E−15 11.8345 2.37E−01 11.8482 3.60E−15 11.8482 3.60E−15 11.8482 3.60E−15
315.6694 1.26E−14 15.4054 7.52E−01 15.7041 5.67E−02 15.6694 1.26E−14 15.6694 1.26E−14
418.5988 1.12E+00 17.7136 1.07E+00 18.8035 7.06E−01 18.5751 1.18E+00 18.9462 5.61E−01
519.0139 9.77E−02 18.2991 1.58E+00 18.7118 1.35E+00 19.5135 9.76E−01 21.2012 7.74E−01
620.7474 9.31E−01 20.2595 1.27E+00 19.4659 1.38E+00 21.2215 6.01E−01 21.6529 1.19E−01
722.1361 5.10E−01 21.0263 1.58E+00 20.7620 1.31E+00 21.7349 5.54E−03 22.8052 9.25E−01
823.5189 4.74E−01 21.3375 1.71E+00 21.1708 1.64E+00 23.6457 1.99E−03 23.9651 5.20E−01
Person 3
bacteria 12
211.4112 9.01E−15 11.3355 3.54E−01 11.4112 9.01E−15 11.4112 9.01E−15 11.4112 9.01E−15
314.6246 3.60E−15 14.1884 1.33E+00 14.6401 1.17E−01 14.6246 3.60E−15 14.6246 3.60E−15
414.7258 1.08E−14 16.1456 1.50E+00 14.8091 4.91E−01 14.9961 7.75E−01 15.3340 1.07E+00
517.1886 1.94E−03 17.7411 1.77E+00 17.5086 1.01E+00 17.1882 0.00E+00 17.1882 0.00E+00
619.6195 2.81E−02 19.5368 1.61E+00 19.7731 1.07E+00 19.6325 3.86E−02 19.6232 2.56E−02
721.8931 4.21E−01 19.6359 1.31E+00 20.9804 9.92E−01 22.1495 2.96E−01 21.6622 1.04E−01
823.7633 4.23E−01 21.0581 1.77E+00 21.3894 1.01E+00 23.8466 6.37E−02 23.7324 5.79E−01
Person 7
bacteria 25
212.0278 0.00E+00 11.8649 3.90E−01 12.0278 0.00E+00 12.0278 0.00E+00 12.0278 0.00E+00
312.0525 7.73E−02 14.5483 1.67E+00 11.9330 3.54E−01 12.5248 1.13E+00 14.4297 1.20E+00
415.2842 4.20E−01 16.2841 2.21E+00 14.9431 8.40E−01 15.1156 6.37E−01 16.8132 1.93E+00
518.7517 1.67E−01 17.8088 2.04E+00 17.5756 8.43E−01 18.8292 1.44E−14 19.1227 5.16E−01
620.3725 3.98E−01 19.4024 2.21E+00 19.4174 1.19E+00 20.0034 1.08E−14 20.2427 7.31E−01
722.4290 7.48E−01 19.3266 2.35E+00 20.5432 1.54E+00 22.6281 1.80E−14 22.6729 2.54E−01
823.2230 9.47E−01 21.0587 1.86E+00 20.8153 1.30E+00 23.7706 7.76E−01 23.9228 6.51E−01
(continued)
Thresholding Algorithm Applied to Chest X-Ray Images … 387
Table 7 (continued)
Image nTh WOA FFO SCA DE PSO
PSNR STD PSNR STD PSNR STD PSNR STD PSNR STD
Person 7
bacteria 28
25.5921 3.60E−15 12.2034 2.39E−01 5.5921 3.60E−15 11.9122 1.55E+00 12.0980 1.12E+00
312.2512 1.38E−01 13.9578 2.28E+00 12.1929 1.67E−01 12.8678 1.46E+00 14.7280 1.54E+00
416.0199 4.06E−01 16.0276 2.21E+00 15.3591 4.88E−01 15.6680 1.80E−15 16.8742 1.73E+00
519.1369 1.83E−01 17.5419 2.03E+00 18.2427 6.48E−01 19.2640 6.76E−02 19.6196 8.51E−01
621.2804 3.93E−01 18.6022 2.14E+00 19.8878 7.64E−01 21.4936 1.08E−14 21.5333 3.08E−01
722.2265 9.73E−01 19.6603 1.75E+00 20.7727 1.30E+00 23.3189 2.55E−02 23.0968 5.98E−01
823.2773 9.10E−01 20.7504 1.70E+00 20.9407 1.73E+00 23.1309 5.91E−01 24.0791 4.65E−01
IM−0145 211.1639 7.21E−15 11.1014 7.70E−01 11.1639 7.21E−15 11.1639 7.21E−15 11.1639 7.21E−15
314.4589 1.08E−14 13.7873 1.27E+00 14.4900 1.91E−01 14.4589 1.08E−14 14.4589 1.08E−14
414.6863 4.27E−02 15.6310 1.57E+00 14.7664 4.99E−01 14.7124 1.80E−15 14.7124 1.80E−15
516.9685 2.62E−02 17.2745 2.00E+00 16.8310 8.93E−01 16.9638 5.17E−03 16.9623 7.21E−15
618.4685 6.20E−02 18.7011 2.01E+00 19.2282 1.11E+00 18.5555 8.53E−03 18.5509 3.22E−03
719.4969 7.82E−02 19.4845 1.89E+00 20.6854 9.68E−01 20.4026 3.28E−01 19.4672 6.61E−02
821.1276 3.22E−01 21.0283 1.32E+00 21.3733 9.80E−01 22.3260 6.45E−01 21.0716 8.13E−02
IM−0211 212.0689 3.60E−15 11.9852 1.95E−01 12.0485 1.80E−15 12.0485 1.80E−15 12.0485 1.80E−15
316.2654 0.00E+00 15.3712 6.95E−01 16.2515 2.90E−02 16.2683 7.21E−15 16.2683 7.21E−15
416.5498 7.21E−15 16.9205 1.31E+00 16.3991 1.42E−01 16.6166 3.50E−01 16.6166 3.50E−01
519.1006 2.30E−02 17.8834 1.22E+00 18.4193 5.09E−01 19.1081 1.41E−02 19.1107 0.00E+00
620.2925 2.26E−01 19.1997 1.14E+00 19.6172 6.57E−01 20.1964 9.40E−03 20.1980 0.00E+00
721.8327 1.49E−02 20.3832 1.46E+00 20.8773 8.08E−01 21.8697 1.80E−14 21.8697 1.80E−14
822.9210 7.17E−01 21.4162 1.25E+00 21.2227 9.28E−01 23.4605 1.39E−02 23.4006 2.50E−01
(continued)
388 J. Murillo-Olmos et al.
Table 7 (continued)
Image nTh WOA FFO SCA DE PSO
PSNR STD PSNR STD PSNR STD PSNR STD PSNR STD
IM−0224 210.3273 3.60E−15 10.7090 6.25E−01 10.3245 3.60E−15 10.3245 3.60E−15 10.3245 3.60E−15
315.6773 3.60E−15 14.6500 8.36E−01 15.6782 5.54E−02 15.6727 1.80E−15 15.6727 1.80E−15
418.3297 3.60E−15 16.9321 1.03E+00 18.1651 2.72E−01 18.3949 1.44E−14 18.3949 1.44E−14
519.7359 1.83E−03 18.5024 1.13E+00 19.6624 5.05E−01 19.7248 0.00E+00 19.7248 0.00E+00
621.8317 7.21E−15 19.6219 1.46E+00 20.7485 7.34E−01 21.8827 1.80E−14 21.7681 4.80E−01
721.8991 4.45E−02 20.2612 1.28E+00 21.3748 1.10E+00 21.7474 3.44E−01 22.2432 4.74E−01
823.2258 3.70E−02 21.4318 1.52E+00 21.8446 1.57E+00 23.2004 1.60E−01 23.2698 3.22E−02
IM−0225 211.5085 7.21E−15 11.5143 2.02E−01 11.5023 7.21E−15 11.5023 7.21E−15 11.5023 7.21E−15
315.6921 5.40E−15 15.0226 7.33E−01 15.6925 7.30E−02 15.6846 1.80E−15 15.6846 1.80E−15
418.4596 8.72E−03 17.2198 9.20E−01 18.3705 1.27E−01 18.4530 0.00E+00 18.4530 0.00E+00
518.5975 9.66E−02 17.8417 1.56E+00 18.3429 5.72E−01 18.5855 7.29E−02 18.9474 7.95E−01
619.9769 8.64E−01 19.2052 1.11E+00 19.4016 7.93E−01 19.1200 3.20E−03 19.9770 8.99E−01
721.5098 1.11E−02 20.2321 1.39E+00 20.5036 9.11E−01 21.5426 1.08E−14 21.5419 3.86E−03
823.0300 8.00E−03 21.1671 1.59E+00 21.4078 8.54E−01 23.0296 3.60E−15 23.0315 8.34E−03
Thresholding Algorithm Applied to Chest X-Ray Images … 389
Table 8 Comparison of the Kapur results of the SSIM values obtained by WOA, FFO, SCA, DE and PSO
Image nTh WOA FFO SCA DE PSO
SSIM STD SSIM STD SSIM STD SSIM STD SSIM STD
Person 1
bacteria 2
20.5889 1.126E−16 0.5803 1.9670E−02 0.5889 1.126E−16 0.5889 1.126E−16 0.5889 1.126E−16
30.6778 2.252E−16 0.6668 2.4632E−02 0.6776 1.875E−03 0.6778 2.252E−16 0.6778 2.252E−16
40.7063 1.547E−02 0.6997 3.1366E−02 0.7082 1.667E−02 0.7070 1.482E−02 0.7112 5.709E−03
50.7102 7.835E−03 0.6972 3.5053E−02 0.7178 1.684E−02 0.7162 7.985E−03 0.7299 6.341E−03
60.7351 5.291E−03 0.7298 2.5939E−02 0.7353 1.805E−02 0.7344 4.178E−03 0.7459 9.237E−03
70.7504 4.069E−03 0.7500 2.9168E−02 0.7515 2.183E−02 0.7520 1.712E−04 0.7586 7.053E−03
80.7625 5.385E−03 0.7414 2.8010E−02 0.7646 2.003E−02 0.7655 6.549E−04 0.7670 2.934E−03
Person 3
bacteria 12
20.4654 2.252E−16 0.4669 3.2098E−02 0.4654 2.252E−16 0.4654 2.252E−16 0.4654 2.252E−16
30.5491 0.000E+00 0.5502 6.1788E−02 0.5503 5.138E−03 0.5491 0.000E+00 0.5491 0.000E+00
40.5549 1.126E−16 0.6041 4.9215E−02 0.5584 2.128E−02 0.5599 1.436E−02 0.5661 1.978E−02
50.6052 2.231E−04 0.6541 6.4805E−02 0.6245 3.539E−02 0.6052 1.126E−16 0.6052 1.126E−16
60.6555 6.781E−04 0.6764 4.0966E−02 0.6784 3.844E−02 0.6559 1.289E−03 0.6555 8.430E−04
70.6998 1.324E−02 0.7035 3.5554E−02 0.7242 1.656E−02 0.7052 7.912E−03 0.6927 2.177E−03
80.7401 8.425E−03 0.7278 3.2443E−02 0.7378 1.597E−02 0.7426 9.477E−04 0.7379 1.278E−02
Person 7
bacteria 25
20.6302 5.630E−16 0.6255 1.2133E−02 0.6302 5.630E−16 0.6302 5.630E−16 0.6302 5.630E−16
30.6292 3.780E−03 0.6861 6.3711E−02 0.6275 5.565E−03 0.6465 3.694E−02 0.7089 3.923E−02
40.7193 1.340E−02 0.7385 4.1976E−02 0.7177 1.568E−02 0.7289 5.844E−03 0.7445 1.775E−02
50.7590 1.180E−02 0.7477 3.8302E−02 0.7647 1.762E−02 0.7630 3.378E−16 0.7700 1.229E−02
60.7843 5.273E−03 0.7657 3.8356E−02 0.7816 1.652E−02 0.7910 3.378E−16 0.7911 3.097E−03
70.7977 5.796E−03 0.7703 4.3060E−02 0.7943 1.587E−02 0.8001 5.630E−16 0.8005 2.397E−03
80.8044 1.046E−02 0.7849 3.4776E−02 0.8044 2.407E−02 0.8118 5.501E−03 0.8115 5.648E−03
(continued)
390 J. Murillo-Olmos et al.
Table 8 (continued)
Image nTh WOA FFO SCA DE PSO
SSIM STD SSIM STD SSIM STD SSIM STD SSIM STD
Person 7
bacteria 28
20.0065 4.398E−18 0.5278 1.6240E−02 0.0065 4.398E−18 0.4937 1.198E−01 0.5080 8.597E−02
30.5210 1.581E−02 0.5917 1.0076E−01 0.5245 2.122E−02 0.5552 6.599E−02 0.6415 7.494E−02
40.6637 2.621E−02 0.6233 9.7840E−02 0.6819 1.808E−02 0.6873 2.252E−16 0.6971 1.399E−02
50.7204 5.539E−03 0.6663 6.7075E−02 0.7201 2.077E−02 0.7175 2.672E−03 0.7218 8.893E−03
60.7378 5.596E−03 0.7104 4.8023E−02 0.7381 2.464E−02 0.7391 6.756E−16 0.7409 3.589E−03
70.7489 9.549E−03 0.7217 3.3304E−02 0.7550 1.864E−02 0.7585 1.457E−03 0.7560 5.681E−03
80.7631 9.309E−03 0.7412 3.2691E−02 0.7626 2.915E−02 0.7634 8.056E−03 0.7677 5.801E−03
IM−0145 20.3585 1.126E−16 0.3604 4.6412E−02 0.3585 1.126E−16 0.3585 1.126E−16 0.3585 1.126E−16
30.4545 0.000E+00 0.4361 4.8799E−02 0.4559 7.949E−03 0.4545 0.000E+00 0.4545 0.000E+00
40.4635 1.418E−03 0.4970 5.7737E−02 0.4675 2.051E−02 0.4644 3.378E−16 0.4644 3.378E−16
50.5230 8.235E−04 0.5543 6.0898E−02 0.5240 2.708E−02 0.5230 4.959E−04 0.5228 3.378E−16
60.5709 1.020E−03 0.6034 5.8655E−02 0.5962 2.904E−02 0.5724 2.393E−04 0.5722 9.029E−05
70.5984 1.460E−03 0.6285 4.5832E−02 0.6467 2.482E−02 0.6223 1.002E−02 0.5978 1.149E−03
80.6497 4.814E−03 0.6753 2.3725E−02 0.6744 1.894E−02 0.6706 1.104E−02 0.6489 1.403E−03
IM−0211 20.3876 1.689E−16 0.4176 3.7168E−02 0.4053 0.000E+00 0.4053 0.000E+00 0.4053 0.000E+00
30.5006 2.252E−16 0.5030 5.0735E−02 0.5235 5.609E−03 0.5243 2.252E−16 0.5243 2.252E−16
40.5042 1.126E−16 0.5477 3.8432E−02 0.5283 1.485E−02 0.5287 5.285E−03 0.5287 5.285E−03
50.5501 1.527E−03 0.5755 3.4730E−02 0.5840 1.403E−02 0.5703 1.677E−03 0.5698 3.378E−16
60.5891 5.033E−04 0.6012 2.4331E−02 0.6073 1.052E−02 0.6089 5.514E−05 0.6089 0.000E+00
70.6086 3.766E−04 0.6190 2.5590E−02 0.6276 1.835E−02 0.6262 0.000E+00 0.6262 0.000E+00
80.6263 1.151E−02 0.6623 2.6656E−02 0.6663 2.924E−02 0.6476 1.125E−04 0.6469 3.460E−03
(continued)
Thresholding Algorithm Applied to Chest X-Ray Images … 391
Table 8 (continued)
Image nTh WOA FFO SCA DE PSO
SSIM STD SSIM STD SSIM STD SSIM STD SSIM STD
IM−0224 20.5907 1.126E−16 0.6076 3.1357E−02 0.6210 2.252E−16 0.6210 2.252E−16 0.6210 2.252E−16
30.6167 2.252E−16 0.6447 3.1831E−02 0.6490 4.332E−03 0.6521 4.504E−16 0.6521 4.504E−16
40.6216 1.126E−16 0.6561 2.8207E−02 0.6526 6.501E−03 0.6515 5.630E−16 0.6515 5.630E−16
50.6445 1.000E−04 0.6683 1.8229E−02 0.6736 6.049E−03 0.6739 5.630E−16 0.6739 5.630E−16
60.6670 1.126E−16 0.6814 2.6033E−02 0.6862 1.191E−02 0.6915 4.504E−16 0.6905 4.096E−03
70.6699 4.295E−04 0.7036 2.3034E−02 0.6969 1.632E−02 0.6975 3.289E−03 0.6962 3.408E−03
80.6868 7.515E−04 0.7137 2.2509E−02 0.7132 1.501E−02 0.7094 2.741E−03 0.7064 5.625E−04
IM−0225 20.3413 2.815E−16 0.3740 4.3267E−02 0.3554 1.689E−16 0.3554 1.689E−16 0.3554 1.689E−16
30.4904 4.504E−16 0.5143 6.4015E−02 0.5096 7.192E−03 0.5079 1.126E−16 0.5079 1.126E−16
40.5612 9.846E−04 0.5718 5.0850E−02 0.5777 1.182E−02 0.5793 1.126E−16 0.5793 1.126E−16
50.5648 1.357E−02 0.5838 6.1699E−02 0.5897 2.303E−02 0.5802 1.035E−02 0.5858 1.368E−02
60.6076 9.829E−03 0.6118 3.6607E−02 0.6226 1.788E−02 0.6347 2.158E−04 0.6256 1.035E−02
70.6269 6.637E−04 0.6239 4.0711E−02 0.6362 1.413E−02 0.6449 3.378E−16 0.6449 1.316E−04
80.6384 1.957E−04 0.6546 3.5947E−02 0.6584 3.303E−02 0.6544 3.378E−16 0.6544 1.174E−05
392 J. Murillo-Olmos et al.
Table 9 Comparison of the Kapur results of the FSIM values obtained by WOA, FFO, SCA, DE and PSO
Image nTh WOA FFO SCA DE PSO
FSIM STD FSIM STD FSIM STD FSIM STD FSIM STD
Person 1
bacteria 2
20.7180 3.378E−16 0.7169 3.959E−03 0.7180 3.378E−16 0.7180 3.378E−16 0.7180 3.378E−16
30.7237 2.252E−16 0.7272 9.647E−03 0.7233 9.412E−04 0.7237 2.252E−16 0.7237 2.252E−16
40.7582 1.389E−02 0.7516 1.854E−02 0.7615 8.260E−03 0.7585 1.311E−02 0.7626 6.667E−03
50.7636 3.561E−03 0.7669 2.635E−02 0.7707 1.652E−02 0.7719 1.670E−02 0.8008 1.324E−02
60.8001 9.940E−03 0.7959 2.825E−02 0.7890 2.221E−02 0.8045 7.000E−03 0.8162 7.238E−03
70.8281 8.355E−03 0.8176 2.633E−02 0.8130 2.173E−02 0.8211 2.421E−04 0.8418 1.826E−02
80.8555 9.790E−03 0.8203 3.081E−02 0.8232 2.380E−02 0.8589 4.297E−04 0.8647 9.621E−03
Person 3
bacteria 12
20.6364 1.126E−16 0.6352 3.065E−03 0.6364 1.126E−16 0.6364 1.126E−16 0.6364 1.126E−16
30.6897 3.378E−16 0.6818 1.592E−02 0.6901 1.659E−03 0.6897 3.378E−16 0.6897 3.378E−16
40.7001 2.252E−16 0.7132 2.359E−02 0.6957 8.375E−03 0.7042 1.165E−02 0.7093 1.606E−02
50.7477 4.641E−05 0.7349 2.905E−02 0.7415 1.253E−02 0.7477 3.378E−16 0.7477 3.378E−16
60.7965 4.172E−04 0.7726 3.132E−02 0.7840 1.103E−02 0.7964 4.004E−04 0.7963 2.268E−04
70.8330 3.219E−03 0.7800 2.787E−02 0.8027 1.931E−02 0.8354 2.703E−03 0.8315 7.726E−04
80.8655 7.701E−03 0.8120 2.915E−02 0.8188 2.022E−02 0.8674 8.684E−04 0.8650 9.316E−03
Person 7
bacteria 25
20.7193 5.630E−16 0.7182 3.709E−03 0.7193 5.630E−16 0.7193 5.630E−16 0.7193 5.630E−16
30.7195 8.512E−04 0.7535 1.926E−02 0.7184 2.854E−03 0.7258 1.485E−02 0.7509 1.577E−02
40.7628 7.120E−03 0.7704 2.732E−02 0.7574 1.159E−02 0.7592 3.948E−03 0.7697 1.199E−02
50.7830 4.847E−03 0.7800 2.402E−02 0.7851 1.617E−02 0.7822 3.378E−16 0.7868 8.091E−03
60.7989 3.664E−03 0.7961 2.797E−02 0.7960 1.434E−02 0.8007 2.252E−16 0.8020 6.092E−03
70.8175 7.187E−03 0.7981 2.812E−02 0.8086 1.611E−02 0.8217 7.882E−16 0.8220 2.182E−03
80.8275 1.095E−02 0.8092 2.924E−02 0.8168 1.856E−02 0.8324 5.363E−03 0.8333 5.958E−03
(continued)
Thresholding Algorithm Applied to Chest X-Ray Images … 393
Table 9 (continued)
Image nTh WOA FFO SCA DE PSO
FSIM STD FSIM STD FSIM STD FSIM STD FSIM STD
Person 7
bacteria 28
20.7178 0.011E+00 0.7352 5.043E−03 0.7187 0.012E+00 0.7360 0.000E+00 0.7360 0.000E+00
30.7350 4.931E−03 0.7309 2.963E−02 0.7342 2.994E−03 0.7372 1.062E−02 0.7456 6.027E−03
40.7509 6.446E−03 0.7565 3.264E−02 0.7579 1.897E−02 0.7493 0.000E+00 0.7589 1.381E−02
50.7791 2.318E−03 0.7674 3.347E−02 0.7768 1.762E−02 0.7785 9.368E−04 0.7840 1.191E−02
60.8091 6.017E−03 0.7916 3.704E−02 0.8068 2.245E−02 0.8094 3.378E−16 0.8115 6.493E−03
70.8278 1.733E−02 0.8008 3.391E−02 0.8206 2.145E−02 0.8479 7.316E−04 0.8434 1.207E−02
80.8486 1.863E−02 0.8185 2.375E−02 0.8398 2.976E−02 0.8500 9.649E−03 0.8621 8.907E−03
IM−0145 20.5965 4.504E−16 0.5931 1.083E−02 0.5965 4.504E−16 0.5965 4.504E−16 0.5965 4.504E−16
30.6819 5.630E−16 0.6647 2.258E−02 0.6822 1.646E−03 0.6819 5.630E−16 0.6819 5.630E−16
40.6960 3.408E−04 0.7088 3.104E−02 0.6969 5.886E−03 0.6962 5.630E−16 0.6962 5.630E−16
50.7648 1.851E−04 0.7469 3.343E−02 0.7543 1.099E−02 0.7647 6.987E−05 0.7647 4.504E−16
60.8061 3.713E−04 0.7799 3.348E−02 0.8005 1.645E−02 0.8064 8.597E−05 0.8064 1.039E−05
70.8238 8.845E−04 0.8034 3.927E−02 0.8322 1.841E−02 0.8405 7.580E−03 0.8234 6.373E−04
80.8601 4.519E−03 0.8363 3.407E−02 0.8509 2.056E−02 0.8744 1.025E−02 0.8593 1.147E−03
IM−0211 20.6134 1.126E−16 0.6078 3.222E−03 0.6112 0.000E+00 0.6112 0.000E+00 0.6112 0.000E+00
30.6689 1.126E−16 0.6547 8.793E−03 0.6651 1.182E−03 0.6656 5.630E−16 0.6656 5.630E−16
40.6903 2.252E−16 0.7027 2.273E−02 0.6822 5.823E−03 0.6872 7.114E−03 0.6872 7.114E−03
50.7580 7.334E−04 0.7433 2.297E−02 0.7451 6.832E−03 0.7512 7.374E−04 0.7513 1.126E−16
60.8159 4.617E−03 0.7774 2.654E−02 0.7927 1.425E−02 0.8070 2.890E−04 0.8071 2.252E−16
70.8570 3.138E−04 0.8074 2.909E−02 0.8285 1.820E−02 0.8508 4.504E−16 0.8508 4.504E−16
80.8865 1.795E−02 0.8326 3.136E−02 0.8404 2.022E−02 0.8916 2.253E−04 0.8903 6.029E−03
(continued)
394 J. Murillo-Olmos et al.
Table 9 (continued)
Image nTh WOA FFO SCA DE PSO
FSIM STD FSIM STD FSIM STD FSIM STD FSIM STD
IM−0224 20.6387 2.252E−16 0.6409 5.491E−03 0.6404 2.252E−16 0.6404 2.252E−16 0.6404 2.252E−16
30.6706 5.630E−16 0.6675 1.687E−02 0.6647 2.075E−03 0.6660 2.252E−16 0.6660 2.252E−16
40.7432 3.378E−16 0.7120 1.933E−02 0.7322 5.551E−03 0.7341 5.630E−16 0.7341 5.630E−16
50.7777 4.701E−05 0.7523 2.308E−02 0.7690 1.278E−02 0.7665 5.630E−16 0.7665 5.630E−16
60.8378 3.378E−16 0.7850 2.884E−02 0.8042 1.651E−02 0.8268 2.252E−16 0.8239 1.214E−02
70.8453 8.299E−04 0.8012 2.710E−02 0.8261 2.327E−02 0.8316 7.860E−03 0.8418 1.217E−02
80.8823 9.779E−04 0.8286 3.195E−02 0.8413 2.904E−02 0.8682 3.823E−03 0.8703 8.394E−04
IM−0225 20.5894 1.126E−16 0.5866 2.690E−03 0.5894 0.000E+00 0.5894 0.000E+00 0.5894 0.000E+00
30.6424 0.000E+00 0.6345 7.715E−03 0.6407 9.280E−04 0.6409 3.378E−16 0.6409 3.378E−16
40.7112 1.046E−04 0.6914 1.290E−02 0.7066 1.709E−03 0.7082 2.252E−16 0.7082 2.252E−16
50.7243 7.524E−03 0.7249 2.472E−02 0.7172 1.518E−02 0.7211 5.183E−03 0.7287 1.770E−02
60.7755 7.734E−03 0.7637 2.403E−02 0.7679 1.428E−02 0.7642 2.439E−05 0.7730 1.028E−02
70.8294 4.572E−04 0.7864 3.034E−02 0.8046 1.972E−02 0.8261 4.504E−16 0.8260 1.704E−04
80.8770 3.051E−04 0.8204 3.303E−02 0.8279 2.262E−02 0.8732 4.504E−16 0.8731 1.862E−04
Thresholding Algorithm Applied to Chest X-Ray Images … 395
Table 1 0 Results after applying segmentation using the WOA metaheuristic algorithm for the
maximization of the Kapur’s entropy
2345
05010015020025030
0
0
2000
4000
6000
8000
10000
12000
14000
0 50 100 150 200 250 30
0
0
2000
4000
6000
8000
10000
12000
14000
0 50 100 150 200 250 30
0
0
2000
4000
6000
8000
10000
12000
14000
05010015020025030
0
0
2000
4000
6000
8000
10000
12000
14000
567
Person 1 bacteria 2
05010015020025030
0
0
2000
4000
6000
8000
10000
12000
14000
0 50 100 150 200 250 30
0
0
2000
4000
6000
8000
10000
12000
14000
0 50 100 150 200 250 30
0
0
2000
4000
6000
8000
10000
12000
14000
It can be observed in Tables7,9and 8that even though it does not present the
best results based on the PSNR and the SSIM, it does present the values with a lower
standard deviation in most cases, therefore, we can infer that the proposed combina-
tion of WOA and Kapur as an objective function offers a more robust combination
concerning the algorithms against which it competes.
Tables 10 and 11 show the visual results when maximizing the Kapur’s entropy of
the same two images with which the results using the Otsu’s objective function were
previously compared. The images are shown in the same way together with their
corresponding histogram and their thresholds marked with a red vertical line. As can
be seen in both images, only in one of them by increasing the number of thresholds
can be detected the details and features of pneumonia through X-ray images.
Tables 13 and 12 show the p-values obtained through the Wilcoxon test. This
non-parametric statistical test is used to statistically validate the numerical results
to indicate the significant differences between the behavior of one algorithm and
another [83]. These results are calculated by comparing the PSNR and FSIM values
between the WOA algorithm and each of the algorithms used in the comparison.
Four different pairs are presented which are WOA versus FFO, WOA versus SCA,
396 J. Murillo-Olmos et al.
Table 1 1 Results after applying segmentation using the WOA metaheuristic algorithm for the
maximization of the Kapur’s entropy
2345
05010015020025030
0
0
0.5
1
1.5
2
2.5 105
05010015020025030
0
0
0.5
1
1.5
2
2.5 105
0 50 100 150 200 250 30
0
0
0.5
1
1.5
2
2.5 105
0 50 100 150 200 250 30
0
0
0.5
1
1.5
2
2.5 105
567
Person 3 bacteria 12
05010015020025030
0
0
0.5
1
1.5
2
2.5 105
05010015020025030
0
0
0.5
1
1.5
2
2.5 105
0 50 100 150 200 250 30
0
0
0.5
1
1.5
2
2.5 105
WOA versus DE and WOA versus PSO. When these p-values are less than 0.05,
it represents that they are statistically significant and present differences between
them. The values lower than the p-value criterion are highlighted to simplify the
interpretation of these results since they reject the null hypothesis, which would
mean that they present differences between one and the other.
Specifically, Table 12 presents the values obtained through the Wilcoxon test based
on PSNR and FSIM using Otsu variance maximization as an objective function. It is
possible to see that the amount of values that are marked in bold is more significant
compared to the amount of data. These differences occur especially in images of
healthy patients, whereas for images of patients with pneumonia, the differences
arise for five or more number of thresholds. It is essential to mention that the results
with a NaN value represent that there is no difference between the results of the
algorithms.
On the other hand, in Table13 the values are presented in the same way using
Wilcoxon’s non-parametric test but using the Kapur entropy maximization function
Thresholding Algorithm Applied to Chest X-Ray Images … 397
Table 1 2 Comparison of the p-values obtained through the Wilcoxon signed-rank test between the pairs of WOA versus FFO, WOA versus SCA, WOA versus
DE and WOA versus PSO, for PSNR and FSIM using Otsu’s objective function
Image nTh FFO SCA DE PSO
PSNR FSIM PSNR FSIM PSNR FSIM PSNR FSIM
Person 1
bacteria 2
25.308E−04 9.730E−01 3.564E−12 4.398E−02 3.564E−12 4.398E−02 3.564E−12 4.398E−02
35.698E−12 1.783E−01 1.030E−05 2.173E−01 1.002E−05 4.993E−02 2.697E−06 1.970E−01
46.733E−11 3.113E−03 1.508E−04 4.322E−02 9.744E−05 5.888E−01 6.436E−04 4.850E−01
58.431E−11 2.322E−11 1.651E−04 6.990E−03 3.244E−01 9.596E−01 3.646E−01 6.893E−01
66.679E−12 2.187E−12 3.105E−08 2.123E−05 4.014E−01 4.619E−03 6.402E−01 1.261E−02
76.679E−12 9.788E−11 1.560E−06 5.224E−06 4.272E−01 7.434E−04 4.078E−01 1.889E−04
81.318E−10 3.414E−10 9.094E−08 2.865E−05 1.806E−04 1.093E−05 8.419E−06 3.530E−08
Person 3
bacteria 12
23.629E−12 1.185E−05 2.258E−12 1.114E−05 2.849E−12 1.365E−05 2.849E−12 1.231E−05
33.901E−07 1.441E−04 1.749E−09 2.921E−08 2.228E−11 2.556E−09 1.134E−11 7.405E−10
43.010E−05 3.067E−04 2.358E−04 2.148E−03 9.667E−04 8.919E−04 1.521E−02 2.146E−03
53.252E−09 1.461E−11 6.466E−06 8.068E−10 4.696E−04 5.482E−08 3.968E−04 1.472E−06
65.992E−09 1.322E−09 1.489E−07 6.616E−07 6.646E−01 7.397E−01 1.298E−01 2.133E−01
72.152E−09 3.729E−09 2.359E−04 1.315E−04 1.386E−02 4.956E−01 5.501E−03 3.135E−01
89.085E−11 5.371E−11 6.131E−06 1.920E−05 5.924E−02 4.207E−02 1.270E−01 6.893E−02
Person 7
bacteria 25
2 1.705E−01 5.415E−03 4.281E−02 1.157E−01 5.570E−02 9.539E−02 1.559E−03 6.028E−01
31.011E−10 1.228E−01 3.915E−02 2.998E−01 1.132E−01 2.256E−01 2.193E−01 4.708E−01
46.399E−09 2.051E−01 2.517E−04 7.783E−01 1.576E−02 4.102E−01 9.378E−03 5.924E−01
53.045E−13 3.952E−01 1.974E−08 3.772E−02 1.817E−01 7.226E−01 4.467E−01 3.582E−01
65.453E−13 9.978E−05 4.240E−10 4.676E−01 5.468E−01 3.470E−03 9.775E−01 5.923E−02
75.020E−13 7.578E−06 3.945E−10 1.030E−07 5.394E−01 2.691E−04 2.217E−01 1.146E−02
85.020E−13 1.579E−11 9.893E−12 8.834E−07 2.404E−03 2.687E−03 1.651E−04 5.667E−05
(continued)
398 J. Murillo-Olmos et al.
Table 1 2 (continued)
Image nTh FFO SCA DE PSO
PSNR FSIM PSNR FSIM PSNR FSIM PSNR FSIM
Person 7
bacteria 28
21.516E−03 6.997E−01 2.924E−07 3.078E−01 2.924E−07 3.078E−01 2.924E−07 3.078E−01
34.142E−09 5.924E−01 2.520E−04 3.856E−02 9.718E−05 2.161E−02 9.456E−05 4.178E−02
41.204E−10 5.764E−02 4.349E−07 2.820E−01 4.511E−02 2.578E−04 1.056E−02 2.612E−05
59.085E−11 2.893E−03 1.212E−05 9.955E−01 1.146E−01 5.241E−02 1.392E−01 3.665E−01
61.240E−12 4.275E−08 7.837E−09 3.599E−03 7.468E−03 3.766E−06 3.014E−02 9.077E−05
79.788E−11 1.644E−10 7.543E−08 4.854E−08 1.747E−01 7.577E−06 5.070E−02 6.572E−04
83.016E−12 3.046E−13 1.322E−09 2.306E−09 8.526E−01 2.008E−09 1.575E−01 1.394E−06
IM−0145 25.316E−10 2.396E−10 1.747E−10 1.068E−09 5.500E−10 NaN 2.125E−10 1.042E−09
32.246E−08 2.727E−08 1.330E−09 5.651E−09 7.676E−10 NaN 9.167E−11 2.713E−09
48.029E−08 1.149E−09 6.855E−05 1.317E−06 1.146E−04 7.392E−04 1.766E−04 2.243E−06
53.991E−09 1.991E−11 7.136E−04 7.012E−07 1.162E−01 7.109E−01 1.136E−01 1.917E−03
61.223E−10 1.716E−12 8.339E−07 9.296E−10 5.173E−01 2.709E−05 2.260E−01 3.849E−05
79.788E−11 1.070E−11 8.545E−08 2.745E−10 2.975E−01 5.940E−13 4.404E−01 5.246E−01
82.559E−08 1.520E−09 1.414E−05 3.389E−06 1.430E−02 5.335E−10 9.747E−03 2.127E−02
IM−0211 28.555E−13 2.910E−13 5.712E−13 2.084E−13 7.061E−13 2.005E−13 5.897E−13 1.811E−13
31.489E−07 1.788E−07 6.445E−07 8.938E−10 4.550E−07 1.471E−10 2.361E−06 1.452E−08
41.746E−06 3.312E−13 3.348E−03 3.045E−13 1.109E−02 3.042E−13 1.221E−02 3.038E−13
51.030E−07 3.046E−13 1.846E−03 3.913E−13 3.413E−01 8.924E−13 2.175E−01 5.913E−13
61.055E−10 8.939E−13 2.068E−03 1.770E−10 3.244E−01 6.233E−05 7.312E−01 3.849E−05
71.168E−08 3.676E−11 3.599E−03 1.093E−08 6.233E−02 3.706E−01 1.712E−01 4.815E−01
82.953E−10 2.187E−12 6.572E−04 2.248E−08 4.324E−04 5.100E−01 6.050E−04 2.217E−01
(continued)
Thresholding Algorithm Applied to Chest X-Ray Images … 399
Table 1 2 (continued)
Image nTh FFO SCA DE PSO
PSNR FSIM PSNR FSIM PSNR FSIM PSNR FSIM
IM−0224 24.467E−01 1.804E−06 6.227E−01 3.395E−05 7.386E−01 2.083E−06 4.582E−01 4.258E−07
33.706E−01 1.578E−11 4.550E−02 1.497E−10 1.000E+00 6.415E−15 1.000E+00 6.415E−15
41.417E−09 1.345E−12 1.846E−06 1.053E−12 8.565E−02 9.541E−12 2.118E−02 2.475E−12
53.902E−07 1.860E−12 2.577E−01 4.893E−09 2.483E−01 1.746E−06 3.135E−01 1.317E−06
63.389E−06 9.788E−11 3.772E−02 5.239E−07 2.316E−03 3.669E−02 6.531E−03 7.609E−02
72.064E−06 4.616E−11 2.893E−03 4.896E−10 2.175E−01 3.345E−04 9.128E−03 1.887E−02
82.145E−07 8.457E−12 2.789E−03 2.570E−07 6.233E−02 1.609E−01 5.924E−02 3.889E−01
IM−0225 23.323E−07 2.054E−07 6.411E−15 9.472E−03 6.411E−15 9.472E−03 6.411E−15 9.472E−03
32.570E−07 2.306E−09 5.937E−05 5.634E−10 2.346E−05 8.647E−10 2.254E−04 1.317E−09
45.120E−04 3.466E−07 2.052E−01 1.176E−06 4.604E−01 4.870E−06 4.012E−01 1.805E−05
53.849E−05 5.509E−08 6.242E−01 1.887E−02 2.624E−01 3.876E−02 6.083E−01 5.499E−03
62.148E−03 7.189E−06 1.830E−02 1.315E−04 6.531E−03 9.059E−01 6.100E−03 4.539E−01
77.189E−05 1.583E−07 3.376E−02 9.870E−04 1.242E−01 4.956E−01 8.880E−01 6.557E−02
85.804E−04 4.212E−06 1.040E−02 8.676E−05 6.976E−01 7.740E−01 2.394E−02 4.207E−02
400 J. Murillo-Olmos et al.
Table 1 3 Comparison of the p-values obtained through the Wilcoxon signed-rank test between the pairs of WOA versus FFO, WOA versus SCA, WOA versus
DE and WOA versus PSO, for PSNR and FSIM using Kapur’s objective function
Image nTh DE FFO PSO SCA
PSNR FSIM PSNR FSIM PSNR FSIM PSNR FSIM
Person 1
bacteria 2
2 3.832E−01 8.008E−02 NaN NaN NaN NaN NaN NaN
3 1.956E−01 3.069E−02 7.927E−05 4.525E−04 NaN NaN NaN NaN
41.216E−07 8.670E−02 5.897E−02 5.088E−01 7.257E−01 8.927E−01 2.591E−01 2.324E−01
54.559E−02 5.468E−01 1.725E−04 1.430E−02 8.396E−02 6.703E−02 8.255E−12 5.934E−12
6 1.386E−01 6.402E−01 6.231E−05 5.499E−03 1.716E−02 9.206E−02 1.123E−10 6.050E−09
74.144E−04 1.542E−01 7.012E−07 9.107E−04 1.594E−05 7.231E−12 1.137E−02 1.534E−01
84.272E−09 3.530E−08 7.515E−10 3.037E−09 1.940E−01 4.330E−01 2.469E−03 1.094E−02
Person 3
bacteria 12
2 6.651E−01 3.832E−01 NaN NaN NaN NaN NaN NaN
3 3.893E−01 3.893E−01 8.298E−01 4.730E−02 NaN NaN NaN NaN
41.504E−05 5.375E−04 3.893E−01 3.069E−02 4.241E−02 4.241E−02 1.499E−03 1.499E−03
53.166E−02 1.982E−01 5.786E−04 3.361E−02 3.309E−01 3.309E−01 3.309E−01 3.309E−01
6 6.842E−01 7.113E−04 4.109E−03 4.440E−10 3.614E−01 7.150E−01 5.985E−02 1.544E−02
72.026E−10 5.625E−12 4.432E−05 1.126E−12 4.943E−03 1.109E−03 1.512E−01 2.228E−01
83.244E−12 1.335E−12 1.448E−12 1.134E−12 2.131E−01 5.618E−01 1.215E−01 2.222E−01
Person 7
bacteria 25
2 2.782E−01 2.782E−01 NaN NaN NaN NaN NaN NaN
34.622E−08 1.999E−10 2.433E−01 2.433E−01 3.732E−01 3.732E−01 8.649E−11 8.649E−11
41.452E−03 7.511E−03 6.345E−02 6.332E−03 5.406E−03 7.757E−02 1.940E−02 5.085E−03
52.611E−02 1.747E−01 3.977E−09 9.220E−02 1.094E−03 2.146E−04 2.334E−05 4.362E−01
64.809E−02 9.059E−01 2.257E−04 2.052E−01 1.444E−11 4.676E−03 1.436E−06 2.282E−02
76.730E−11 1.157E−03 7.835E−09 1.252E−03 6.651E−01 1.194E−08 9.000E−01 4.340E−08
82.145E−07 1.112E−03 1.770E−10 1.261E−02 4.643E−02 1.635E−01 2.119E−03 5.594E−02
(continued)
Thresholding Algorithm Applied to Chest X-Ray Images … 401
Table 1 3 (continued)
Image nTh DE FFO PSO SCA
PSNR FSIM PSNR FSIM PSNR FSIM PSNR FSIM
Person 7
bacteria 28
26.033E−15 8.120E−11 NaN 6.757E−03 1.668E−15 3.321E−13 2.640E−16 2.483E−13
36.329E−02 5.205E−01 1.239E−03 8.201E−02 6.188E−02 4.514E−03 1.350E−09 2.606E−10
47.383E−01 2.599E−01 4.659E−08 3.812E−03 6.872E−05 4.973E−04 7.734E−01 5.606E−01
52.549E−05 2.299E−01 3.024E−11 6.209E−02 2.848E−03 1.542E−02 1.225E−03 9.291E−01
64.010E−08 1.944E−02 2.150E−11 5.695E−01 2.047E−07 3.893E−01 7.411E−05 4.882E−01
76.853E−09 7.135E−04 1.276E−05 2.304E−01 5.849E−08 7.556E−11 1.995E−06 4.128E−08
81.644E−10 7.430E−07 1.520E−09 1.416E−01 3.528E−01 9.059E−01 5.694E−06 9.477E−04
IM−0145 23.891E−01 3.891E−01 NaN NaN NaN NaN NaN NaN
39.472E−03 2.047E−07 8.298E−01 5.111E−01 NaN NaN NaN NaN
41.860E−04 1.279E−02 4.502E−02 1.279E−02 7.392E−04 7.392E−04 7.392E−04 7.392E−04
53.457E−02 1.029E−02 8.112E−02 2.491E−06 7.109E−01 7.109E−01 1.602E−01 1.602E−01
62.182E−02 4.666E−05 1.476E−05 1.466E−02 7.960E−10 2.709E−05 2.085E−09 4.222E−05
72.878E−01 1.082E−03 9.933E−10 1.833E−02 3.303E−13 5.940E−13 2.493E−02 1.148E−02
86.000E−01 1.409E−04 1.671E−01 4.777E−02 2.534E−11 5.335E−10 3.279E−01 3.164E−01
IM−0211 23.892E−01 6.332E−15 3.776E−17 3.776E−17 3.776E−17 3.776E−17 3.776E−17 3.776E−17
31.811E−13 6.415E−15 8.400E−02 6.357E−15 3.776E−17 3.776E−17 3.776E−17 3.776E−17
43.069E−02 5.375E−04 8.289E−11 1.811E−13 6.095E−17 2.825E−15 6.095E−17 2.825E−15
51.375E−07 4.827E−02 5.698E−12 3.261E−13 1.643E−10 2.128E−14 4.518E−15 4.518E−15
61.144E−05 9.863E−10 1.464E−06 1.141E−11 2.308E−03 8.947E−15 2.454E−03 6.282E−15
72.110E−04 2.921E−12 7.425E−10 4.339E−11 1.895E−15 1.895E−15 1.895E−15 1.895E−15
81.774E−07 1.965E−11 5.202E−10 1.883E−10 8.273E−10 1.027E−02 3.827E−05 9.362E−03
(continued)
402 J. Murillo-Olmos et al.
Table 1 3 (continued)
Image nTh DE FFO PSO SCA
PSNR FSIM PSNR FSIM PSNR FSIM PSNR FSIM
IM−0224 25.363E−04 2.037E−07 3.776E−17 3.776E−17 3.776E−17 3.776E−17 3.776E−17 3.776E−17
31.346E−09 6.691E−01 8.392E−02 6.250E−15 3.776E−17 3.776E−17 3.776E−17 3.776E−17
48.289E−11 1.811E−13 3.069E−02 6.415E−15 3.776E−17 3.776E−17 3.776E−17 3.776E−17
53.675E−10 5.369E−07 4.062E−01 1.167E−03 6.593E−16 6.593E−16 6.593E−16 6.593E−16
64.248E−12 6.415E−15 4.248E−12 6.415E−15 3.776E−17 3.776E−17 1.501E−13 9.470E−17
71.198E−09 8.803E−11 5.609E−02 3.036E−04 1.019E−03 5.504E−12 1.968E−10 2.397E−04
88.338E−06 1.424E−12 7.918E−08 8.904E−11 3.526E−01 2.970E−13 2.032E−06 1.336E−13
IM−0225 23.067E−02 4.223E−12 3.776E−17 3.776E−17 3.776E−17 3.776E−17 3.776E−17 3.776E−17
32.047E−07 2.047E−07 1.000E+00 6.343E−15 3.776E−17 3.776E−17 3.776E−17 3.776E−17
42.251E−14 1.707E−14 2.574E−04 1.707E−14 5.777E−12 1.417E−16 5.777E−12 1.417E−16
59.633E−03 7.468E−01 3.375E−07 2.712E−08 1.455E−04 2.538E−13 8.278E−13 1.285E−06
63.781E−03 8.384E−03 3.647E−03 1.081E−03 3.499E−02 1.453E−14 1.366E−02 4.723E−04
73.686E−05 5.928E−10 7.509E−09 3.772E−09 1.629E−15 1.629E−15 4.747E−15 2.393E−15
84.725E−13 1.266E−14 3.323E−13 1.389E−14 1.501E−13 9.470E−17 3.945E−06 8.811E−16
Thresholding Algorithm Applied to Chest X-Ray Images 403
as an objective function. In the same way as the previous table, the results behave
similarly and the most remarkable difference between algorithms occurs for the
four images of healthy patients. However, signi cant differences in the images of
pneumonia patients occur with a threshold number of four or more.
6Conclusions
The WOA presented as a metaheuristic algorithm to nd the thresholds to ef ciently
segment the images is a good and viable option that offers results with good perfor-
mance for the proposed application based on the metrics used to measure the quality
of the segmentation. According to the results obtained, when using the Otsuís objec-
tive function, it presents better results compared to the Kapurís objective function.
The WOA algorithm shows good performance when using Otsuís maximization
of variance in the eight test images for the three metrics and in the results to verify
robustness through the standard deviation of the 35 runs. Although the results of the
maximization of the Kapur entropy present greater robustness and stability when
comparing the standard deviation, it did not offer the best values in the evaluated
metrics. In addition to the visual results, when using the Kapurís objective function, it
does not present enough details and features in the images of patients with pneumonia
to be able to detect lung lesions more easily and quickly.
In the case of the application presented in this work, it will be used for future
work given the results obtained as a step in the processing of the images for the
CADx tools used to correctly detect the information in the chest X-ray images, and
from this maximize accuracy and consistency in diagnoses and reduce radiologistsí
reading times.
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