Hindawi
Contrast Media & Molecular Imaging
Volume 2022, Article ID 4736113, 12 pages
https://doi.org/10.1155/2022/4736113
Research Article
Design of Metaheuristic Optimization-Based Vascular
Segmentation Techniques for Photoacoustic Images
Thavavel Vaiyapuri ,1 Ashit Kumar Dutta ,2 Mohamed Yacin Sikkandar ,3
Deepak Gupta ,4 Bader Alouffi ,5 Abdullah Alharbi,6 Hafiz Tayyab Rauf ,7
and Seifedine Kadry 8
1
College of Computer Engineering and Sciences, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
Department of Computer Science and Information Systems, College of Applied Sciences, AlMaarefa University, Ad Diriyah,
Riyadh 13713, Saudi Arabia
3
Department of Medical Equipment Technology, College of Applied Medical Sciences, Majmaah University,
Al Majmaah 11952, Saudi Arabia
4
Department of Computer Science & Engineering, Maharaja Agrasen Institute of Technology, Delhi, India
5
Department of Computer Science, College of Computers and Information Technology, Taif University, P.O. Box 11099,
Taif 21944, Saudi Arabia
6
Department of Information Technology, College of Computers and Information Technology, Taif University, P.O. Box 11099,
Taif 21944, Saudi Arabia
7
Department of Computer Science, Faculty of Engineering & Informatics, University of Bradford, Bradford, UK
8
Faculty of Applied Computing and Technology, Noroff University College, Kristiansand, Norway
2
Correspondence should be addressed to Thavavel Vaiyapuri; t.thangam@psau.edu.sa
Received 4 October 2021; Revised 5 January 2022; Accepted 10 January 2022; Published 30 January 2022
Academic Editor: Yuvaraja Teekaraman
Copyright © 2022 Thavavel Vaiyapuri et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
Biomedical imaging technologies are designed to offer functional, anatomical, and molecular details related to the internal organs.
Photoacoustic imaging (PAI) is becoming familiar among researchers and industrialists. The PAI is found useful in several
applications of brain and cancer imaging such as prostate cancer, breast cancer, and ovarian cancer. At the same time, the vessel
images hold important medical details which offer strategies for a qualified diagnosis. Recently developed image processing
techniques can be employed to segment vessels. Since vessel segmentation on PAI is a difficult process, this paper employs
metaheuristic optimization-based vascular segmentation techniques for PAI. The proposed model involves two distinct kinds of
vessel segmentation approaches such as Shannon’s entropy function (SEF) and multilevel Otsu thresholding (MLOT). Moreover,
the threshold value and entropy function in the segmentation process are optimized using three metaheuristics such as the cuckoo
search (CS), equilibrium optimizer (EO), and harmony search (HS) algorithms. A detailed experimental analysis is made on
benchmark PAI dataset, and the results are inspected under varying aspects. The obtained results pointed out the supremacy of the
presented model with a higher accuracy of 98.71%.
1. Introduction
Photoacoustic tomography (PAT) is a kind of hybrid imaging approach which integrates the advantages of both
ultrasonic and optical imaging. In PAT, ultrasonic waves are
stimulated by the pulsed laser that has embodied both ultrasonic deep penetration and optical absorption contrast
[1]. Various real-time applications are being studied to
demonstrate their great opportunities in both clinical and
preclinical imaging, such as breast cancer diagnostics and
small animal entire body imaging [2]. In addition, multispectral PAT has exclusive benefits from monitoring the
functional data of biological tissues, for example, metabolism and blood oxygen saturation (sO2). Especially,
2
photoacoustic computed tomography (PACT) allows realtime imaging performances that disclose great possibilities
for medical application. In order to attain the image in the
PA signal, the image reconstruction approach plays a major
part. Traditional noniterative reconstruction approaches,
such as filtered back-projection (FBP), are widespread because of their fast speed. But, the imperfection delay-andsum (DAS) of traditional approaches exist several artifacts
that lead to distorted images, particularly in restricted view
configuration [3–5]. In such cases, the iterative methods are
well-adopted when using an appropriate regularization.
PAT is a noninvasive combined physics biomedical imaging
approach that conveniently integrates the higher contrast of
pure optical imaging through the higher spatial resolution of
ultrasound imaging [6]. It can be dependent upon the
generation of acoustic waves through illuminating a semitransparent biological or clinical object with a shorter optical
pulse. The induced time-based acoustic wave is measured
outside of the samples using an acoustic detector, and the
measured information is utilized for recovering an image of
the interior [7].
Vessel segmentation is a fundamental process for analyzing biomedical imaging. Hence, it is complicated for
providing accurate and reliable vessel segmentation on PA
imaging. [8] shows better segmentation performance on
the blood vessels taken from photoacoustic computed
tomography (PACT). Optical resolution photoacoustic
microscopy (OR-PAM) features simple imaging reconstruction and higher spatial resolution [9] and therefore has
initiated broad application in vascular imaging. Up till
now, several attempts have focused on the segmentation of
the blood vessel taken by the OR-PAM method. Image
segmentation has been considered an essential task in
image processing and plays a significant part in image
research in various areas of application such as pattern
recognition, computer vision, medical imaging, robotic
vision, cryptography, and agriculture [10]. When the results of segmentation are not correct, the classification
approach might fail. Multiple challenges have been widely
resolved by the segmentation method. The major purpose
of segmentation is to split an image into many homogeneous segments/regions with common features such as
color, texture, contrast, brightness, size, and form
depending upon certain thresholding value(s) [11]. Often,
it is extensively employed for distinguishing background
and foreground as the primary phase for interpreting and
identifying images.
Various methodologies, like threshold-based, regionbased, feature-based, and edge-based clustering, were proposed for solving present challenges and enhance quality of
the research. The most popular image segmentation
methods are multilevel thresholding that tries to group the
pixel which allocates features to a finite amount of pixels.
Image thresholding methods are easier to produce and
implement efficient than segmentation performances [12].
Thresholding comprises 2 classes: bi and multilevel. A single
threshold value is utilized in the preliminary class for separating the images into 2 homogeneous background and
foreground regions. The latter methods are employed for
Contrast Media & Molecular Imaging
segmenting an image into more than 2 areas according to the
pixel intensity called a histogram. Therefore, it can be
expressed as an optimization issue with parametric/nonparametric methods.
Since the vessel segmentation on PAI is a difficult
process, this paper employs metaheuristic optimizationbased vascular segmentation techniques for PAI. This study
employs two different types of vessel segmentation techniques such as Shannon’s entropy function and Otsu
thresholding. In addition, the threshold value and entropy
function in the segmentation process are optimized using
three metaheuristics such as the cuckoo search (CS),
equilibrium optimizer (EO), and harmony search (HS) algorithms. For examining the improved performance of the
proposed model, a wide range of simulations take place and
the results are inspected under various aspects.
The rest of the paper is organized as follows: Section 2
offers the related works, Section 3 provides the proposed
model, Section 4 gives the experimental validation, and
Section 5 concludes the study.
2. Literature Review
Luke et al. [13] proposed a novel deep neural network (DNN)
method for concurrently estimating the oxygen saturation in
blood vessels and segmenting the vessels in the nearby
background tissues. The network was trained on evaluating
early pressure distribution from a 3D Monte Carlo simulation
of light transport in breast tissues. Bench et al. [14] illustrate
the capacity of DNN for processing entire three-dimensional
images and outputting three-dimensional maps of vascular
sO2 from realistic tissue images or models. The 2 separate
fully convolutional neural network (FCNN) methods have
been trained for producing three-dimensional maps of vascular blood oxygen saturation and vessel position from
multiwavelength simulated images of tissue models.
In [15], a novel segmentation system is developed for
PAI which directly produces an assessment of its consistency. Segmentation based on parameters has a natural
tendency to improve consistency as the parameter value
monotonically changes. The consistency is measured by
calculating the classification of an image voxel with distinct
parameters. In [16], U-net and FCN have been individually
employed in PA imaging for vascular segmentation, and a
hybrid network consists of both that is integrated by a voting
system on the PA vascular image. The result is qualitatively
related and estimated on intersection of union (IoU), dice
coefficients, accuracy, and sensitivity.
In [17], tumor vessel is quantified and segmented in a
whole three-dimensional framework. It has been tested from
the phantom experiment that the three-dimensional
quantification outcomes have higher performance when
compared to two dimensions. Furthermore, in vivo vessel
images have been quantified with two- and three-dimensional quantification systems correspondingly. Additionally,
the variation between these 2 outcomes is important. Zhao
et al. [18] presented an approach adoptive to the microvascular segmentation in photoacoustic image that includes
morphological connection and a Hessian matrix
Contrast Media & Molecular Imaging
3
enhancement operator. The precision of these vascular
segmentation approaches is quantitatively estimated by
several criteria. In order to attain continuous and accurate
microvascular skeletons, an enhanced skeleton extractionbased multistencil fast marching (MSFM) approach has been
presented.
Boink et al. [19] suggest conjointly obtaining the photoacoustic segmentation and reconstruction by altering a
newly presented partially learned model based on the CNN
method. They examine the stability of the method against
modifications in early pressure and photoacoustic system
settings. This insight is utilized for developing a method, i.e.,
strong input and system setting. This method could simply
be employed in other imaging models and adapted to implement other higher-level processes dissimilar to segmentation. Feng et al. [20] proposed a vivo experiment and
numerical simulation on human subjects for investigating
the opportunity of segmentation of photoacoustic signals
and ultrasound guided detection from bone tissues in vivo in
a noninvasive method.
3. Materials and Methods
In this study, a set of metaheuristic optimization-based
vascular segmentation techniques have been developed for
PAI. The goal of the study is to inspect the outcome of the
dissimilar metaheuristics on two segmentation approaches.
In order to successfully segment the vessels, the SEF and
MLOT techniques are applied. Furthermore, three optimization algorithms such as CS, EO, and HS are applied for
optimal choice of entropy function and threshold values.
Figure 1 demonstrates the overall block diagram of the
proposed method.
3.1. Image Segmentation Approach. In this study, SEF and
MLOT techniques were applied to segment the vessels on
PAI. The detailed workings of these two segmentation approaches are provided in the following:
3.1.1. Design of Shannon’s Entropy Function. Shannon’s
entropy model is an important concept from the field of
“information theory and coding.” This theory has been
utilized for probabilistically determining the count of data
broadcast with some data. Consider that an image is a (k +
1) homogeneous area with a k threshold gray level at
t1 , t2 , t3 , . . . , tk , then the following equation is obtained:
h(i) �
fi
,
N
i � 0, 1, 2, , 255,
t2
255
i�0
i�t1 +1
i�tk
P1i �
P2i �
Pki �
H � − P1i ln P1i − P2i ln P2i − · · · − Pki ln Pki , (2)
h(i)
,
t1
h(i)
i�0
for 0 ≤ i ≤ t1 ,
h(i)
,
t2
h(i)
i�t
1 +1
h(i)
,
h(i)
255
i�tk +1
for t1 + 1 ≤ i ≤ t2 ,
(3)
for tk + 1 ≤ i ≤ 255.
The Shannon entropy function H from equation (1) has
been executed as an objective function that can be maximized using the metaheuristic optimization algorithms such
as CS, HS, and EO algorithms.
3.1.2. Design of Multilevel Ostu Thresholding (MLOT)
Technique. Otsu [22] is a widely employed segmentation
approach utilized for finding a better threshold value of an
image dependent upon maximizing the between-class variance. These techniques were utilized for finding the
threshold optimal value which split the image into several
classes. This technique recognizes the Lv intensity level of
gray images and the probability distribution has been estimated in equation (2). It could be utilized to color images,
in that Otsu has been implemented to all channels.
hi �
hi
,
NP
(4)
NP
Phi � 1,
i�1
where il refers the intensity level identified from the range of
(0 ≤ il ≤ Lv − 1). NP signifies the entire amount of image
pixels. hi indicates the amount of the presence of intensity il
under the image signified as the histograms. The histogram
has been normalized from the probability distributions of
Phi . According to the probability distribution/thresholding
value (th), the classes have been defined to bilevel segmentation as follows:
C1 �
Ph1
Phth
Phcth+1
PhL
,...,
and C2 �
, (5)
,...,
ω0 (th)
ω0 (th)
ω1 (th)
ω1 (th)
where ω0 (th) and ω1 (th) are cumulative probability distribution to C1 and C2 , respectively, as it can be demonstrated in equation (4).
th
L
i�1
th+1
ω0 (th) � Phi and ω1 (th) � Phi .
(1)
where fi represents the frequency of ith gray levels, N
implies the entire amount of gray levels existing from the
images, and h(i) refers the normalization frequency. The
Shannon entropy function has been defined as follows [21]:
t1
where
(6)
It can be required for finding the average intensity levels
μ0 and μ1 which are utilized in equation (5). If these values are
c, the Otsu based on class σ 2B is determined in equation (6).
th
L
iPhi
iPhi
and μ1 �
, σ 2B � σ 1 + σ 2 .
ω
(th)
ω
(th)
i�1 0
i�th+1 1
μ0 �
(7)
4
Contrast Media & Molecular Imaging
Training Images
Data Collection
Training Set
Testing Set
Tuning Process
Segmentation Process
Cuckoo Search
Shannon’s Entropy Function
Equilibrium Optimizer
Otsu Thresholding
Harmony Search
Performance Evaluation
Dice Coefficient
IoU
Sensitivity
Accuracy
Figure 1: Overall process of the proposed method.
Noticeable σ 1 and σ 2 in equation (6) are the differences
of C1 and C2 which are identified as follows:
σ 1 � ω0 μ0 + μT and σ 2 � ω1 μ1 + μT ,
2
2
(8)
where μT � ω0 μ0 + ω1 μ1 and ω0 + ω1 � 1 are dependent
upon the values σ 1 and σ 2 , and equation (8) offers the objective functions. So, the optimized issue has been decreased
for finding the intensity level that maximizes in equation (8).
Fotsu (th) � maxσ 2B (th) where 0 ≤ th ≤ L − 1,
(9)
where σ 2B (th) stands for Otsu’s alteration to provided th
value. An objective function Fotsu (th) in equation (8) is also
altered to several thresholds as follows:
Fotsu (TH) � Maxσ 2B (th) where 0 ≤ thi ≤ L − 1 an d i
� [1, 2, 3, . . . , k] (9),
(10)
where TH � [th1 , th2 , . . . , thk − 1] has been a vector
comprising several thresholds, L refers to the maximal gray
level, but the alterations are computed in equation (10).
k
σ 2B � σ i
i�1
(11)
k
� ω1 μ1 − μT ,
2
i�1
where i demonstrates the particular class, and ωi and μj implies
the probability of existence and the mean of level, respectively.
Multilevel thresholding values are attained as follows:
L
ωk− 1 (th) � Phi .
(12)
i�thk +1
With respect to the mean values as defined in equation
(12), the followingequationis obtained:
L
μk− 1 �
i�thk
iPhi
.
ω
thk
+1 1
(13)
In this study, the threshold values can be optimally
chosen by the use of three optimization algorithms, namely,
CS, HS, and EO algorithms.
3.2. Metaheuristic Optimization Models. In this section, the
algorithmic procedures of the CS, EO, and HS algorithms are
elaborated in detail. These algorithms are employed for the
proficient selection of the entropy function in SEF and the
threshold value in the MLOT technique.
3.2.1. Process Involved in the CS Algorithm. The CS technique is simulated by the social performances of cuckoos.
The CS is a population-based search technique for identifying an optimum result of optimized issues. A novel set of
experimental results utilizing this technique tries to determine, on previous initiation, the optimum experimental
results. The general framework and competence to explain
these issues with distinct execution can be carried out with
the CS technique. The CS has been established in concern of
the social pensive ability of the cuckoo bird. Generally, the
cuckoo bird places its eggs from the nest of another alien
bird. The alien bird is declaring that the egg has the associated probability of pa ∈ [0, 1]. Therefore, it is also the egg
that has been thrown in the nest or forsaken which nest to
construct a novel one with the alien bird. Thus, all the eggs of
the alien nest carried out a solution.
Mathematically, the CS algorithm is expressed in three
major levels. Initially, the accessibility of the host nest was
set. The next posit is that all cuckoos locate only a single egg
at a timestamp for a randomly chosen host nest, and finally,
the maximum quality eggs from the optimum nest are
surplus to the next generations [23]. Assume that Xi (t)
implies the current search space of cuckoo
iwherei � 1, 2, · · · , N at a time t, represented as
Xi � (x1i , x2i , . . . . . . , xni ) from the n dimension quandary.
Afterward, the initial search space Xi (t + 1) to the later
generations at time t + 1 has been mathematically computed
as follows:
Contrast Media & Molecular Imaging
5
Xi (t + 1) � Xi (t) + αLevy(λ),
(14)
Initial a random population of n host nest
where α > 0 represents the step-size that is similar to the
scales of the quandary of the curiosity. In maximal cases α is
generally taken as 1.
It offers a random walk, and their random steps have
been drawn in Levy distribution to immensely colossal steps
that are demonstrated as follows:
− λ
Levy (λ)u � t ,
where 1 < λ < 3.
A Cuckoo randomly generated by levy flight, i
Evaluation of cuckoo fitness, F
Select a nest among n randomly as j
(15)
The 2 very famous techniques are Mantegna’s technique
and McCulloch’s technique. The Levy step size has been
attained in the Mantegna technique as initialized, which is as
follows:
v
Levy � 1/(λ− 1) .
(16)
|]|
The conditions for forsake probabilities, the entire size of
populations, and the maximal number of cuckoos reproduced in a lifetime are fixed to the utilizer; however, primary
terms at the starting has been reached. Figure 2 depicts the
flowchart of the CS technique.
Assume that t symbolizes the current generation, tmax
signifies the determined greatest span of animating being life
redundancy, and that the cuckoo influence roams from the
lifetime. Therefore, an n-dimension issue to cuckoo at the
starting generation t � 1 is that set up and it can be represented in equation (16).
xn1 (t � 1) � randn × Uppern − Lowern ,
(17)
where Lowern and Uppern refer the lowermost as well as
uppermost outer restricts of the search space of n th attributes, respectively. These maintain the mastery capable
time-optimized technique to stay within the individual
perimeter.
In equation (15), υ and ] demonstrate the taken in
normal distributions. That means υ ∼ N(0, δ2 ) and
] ∼ N(0, 1) with the following:
δ �
Γ(1 + β)sin(ππ/2)
,
Γ(1 + β/2)β × 2((β− 1)/2)
1/β
(18)
where Γ stands for the gamma function, and it can be
demonstrated as follows:
Γ(p) � e− t tp− 1 dt&β ∈ [0, 2] is a scale factor.
(19)
0
3.2.2. Process Involved in the EO Algorithm. EO follows a
dynamic mass balance process that works to control volume.
The mathematical formula has been utilized for representing
the mass balance for defining the focus of nonreactive
components in the dynamic environments of control volume and this formula as a function with their different
processes in the changes of source and sink. The entire
theoretical explanation of EO according to these terms is
defined as follows:
Fitness (i) <Fitness (j)
No
Yes
Let j as the solution
Replace j by the new solution
Keep and Rank the best current nests
No
Stopping criterion met?
Yes
Optimal Results
Figure 2: Flowchart of the CS algorithm.
The arbitrary population (primary concentration) was
initialized by utilizing a uniform distribution dependent
upon the amount of particles and dimension in the provided
search region as follows:
Cinitial
� Cmin + randi Cmax − Cmin i � 1, 2, . . . , n,
i
(20)
where Cinitial
represents the vector of primary concentration
i
of ith particle, Cmin and Cmax refer the lower as well as upper
bounds, randi signifies the uniform arbitrary numbers
created in intervals from 0 to 1, and n defines the size of
populations.
In order to determine the equilibrium state (global
optimum), a pool of 4 optimum candidates is identified, that
comprises of particles with a concentration identical to
arithmetic mean of 4 particles. These particles produced a
pool vector, as ffgiven in (20).
→
→
→
→
→
→
C eq.pool � C eq(1) , C eq(2) , C eq(3) , C eq(4) , C eq(ave) . (21)
In the evolution procedure, initial particles upgrade their
concentration
from the initial generation dependent upon
→
C eq(1) , and then
→ in the second generation, the upgrading can
take place on C eq(ave) . Afterward, all the particles with every
candidate solution have been upgraded by the completion of
the evolution procedure.
The exponential term F demonstrates that it assists EO
with attaining the appropriate balance amongst diversification as well as intensification [24]. The term λ has been an
6
Contrast Media & Molecular Imaging
arbitrary value from the intervals 0 and 1 for controlling the
turnover rate from real control volume.
⇀
⇀
F � e− λ(t− t0 ) ,
(22)
where t has been provided as function of the amount of
iteration (Iter) and is determined as follows:
Iter
Iter
t � 1 −
a2
,
Max− iter
Max− iter
(23)
where Iter � current iteration, Max iter � maximal iteration, and parameter a2 was employed for controlling
exploitation capability of EO. For ensuring convergence
while improving global as well as local search capability of
the technique, in written form is also employed as
follows:
⇀
1
t0 � ⇀
λ
ln− a1 sign( r − 0.5)1 − e−
⇀
⇀
λt
+ t,
(24)
where a1 and a2 have been utilized for controlling global as
well as local search capability of the EO technique. The terms
⇀
sign ( r − 0.5) have been responsible of the nearby path of
explorations as well as exploitations. In EO, the values of a1
and a2 are elected to be 2 and 1, respectively.
With replacing equation (23) in (21), the terms are altered as follows:
F � a1 sign ( r − 0.5)e−
⇀
⇀
⇀
λt
− 1.
(25)
The generation rate in the EO technique was implemented for improving exploitation that is employed as a
function of time. The 1st order exponential decay procedure
from the method of generation rate of a multipurpose
technique is determined as follows:
⇀
⇀
⇀
G � G0 e− k(t− t0 ) ,
(26)
where G0 � primary value and k � decay parameters.
Eventually, the generation rate appearance considering
k � λ has been determined as follows:
⇀
G�
�
⇀
⇀
G0 e− λ(t− t0 ) ,
⇀ ⇀
G0 F0 .
(27)
In equation (26), G0 has been estimated as follows:
⇀
⇀
⇀
⇀⇀
G0 � GCPCeq − λ C,
⇀
GCP �
0.5r1 ,
r2 ≥ 0,
0,
r2 < 0,
(28)
where r1 , r2 demonstrate 2 arbitrary numbers from intervals
0 and 1 and GCP denotes generation rate control parameter
control generation rate. By means of all the abovementioned
expressions, the last upgrade formula of concentration
(particle) is determined as follows:
⇀
⇀
⇀
⇀
C � Ceq + C − Ceq F
⇀
G
⇀
⇀
(29)
+ ⇀ (1 − F).
λV
The upgraded formula has 3 terms: 1st term is equilibrium concentration; the 2nd term is employed to global
search; and 3rd term is in charge of local search for achieving
exact solution.
3.2.3. Process Involved in the HS Algorithm. In HSA, the
feasible solution (or element from the solution spaces) is called
“harmony” that is an n-dimension real vector whose arbitrary
values have been allocated to the primary population and loaded
from harmony memory (HM). During the next step, an estimated novel candidate (nest generation/iteration) harmony was
formed regarded as the element from HM, either by changing
the pitch or by arbitrarily choosing to upgrade the element from
HM. As the last step, the element from the harmony memory is
correlated with the least HM vector and recently calculated
candidate harmony, and the entire procedure is repeated an
amount of times for satisfying the end condition.
The HS optimization technique parameters are as follows:
(i) size of HM, (ii) HM consideration rate (HMCR), (iii) pitch
adjusting rate (PAR), and (iv) distance bandwidth (BW), and
the number of iterations or improvisations (NI). During this
step, it can be vital for configuring the primary HM modules
(HMS vectors). Assume that xi � {xi(1), xi(2), . . . xi(n)}
represents an arbitrarily calculated HM vector:
xi(k) � Xl (k) + (Xu (k) − Xl (k)) ∗ rand (0, 1) for k �
1, 2, . . . , nandi � 1, 2, . . . , HMS which is the length of HM.
So, the lower as well as upper restricts of feasible search space
are represented as Xl (k) and Xu (k), respectively [25]. Next,
in the HM matrix, all components are a harmony vector, so it
can be that HMS has a vector present.
x1
⎤⎥
⎡⎢⎢⎢
⎢⎢⎢ x ⎥⎥⎥⎥⎥
2 ⎥
⎢
⎥⎥.
⎢
HM � ⎢⎢⎢
⎢⎢⎢ ⋮ ⎥⎥⎥⎥⎥
⎦
⎣
xHMS
(30)
In the HM matrix, xnew , a novel harmony vector, has
been created utilizing 3 functions: (i) memory consideration,
(ii) arbitrary reinitialization, and (iii) pitch adjustment.
During the initial stage, the primary decision value xnew (1)
was chosen arbitrarily in harmony provided as
x1 (1), x2 (1) . . . .xHMS (1). In order to choose xnew (1) an
arbitrary number r1 with a range of 0 and 1, when this
arbitrary number has been under HMCR, xnew (1) has been
created as a memory consideration, otherwise xnew (1) has
been captured in the search range [Xl (k), Xu (k)]. In the
same manner, xnew (2), xnew (3), . . . . . . , xnew (n) are chosen
so that the 2 functions such as memory consideration and
arbitrary reinitialization are determined as follows:
Contrast Media & Molecular Imaging
xi ∈ x1 (k) . . . . . . . . . . . . .xHMS (k),
⎧
⎪
⎪
⎨
xnew (k) � ⎪ Xl (k) + Xu (k) − Xl (k) ∗ ran d(0, 1),
⎪
⎩
with probability of 1-HMCR.
7
(31)
All recently created xnew values were examined to determine whether they can be pitch adjusted or not. To resolve
this, the pitch adjustment rate (PAR) has been developed
which is a composition of frequency and bandwidth factor
(BF). These 2 factors are modified to obtain a novel xnew
value in local search for the chosen solutions of HM. The
pitch modified novel solution xnew has been computed as
xnew (k) + / − rand(0, 1) · BW with probabilities PAR. This
pitch adjustment is most same as the mutation procedure
used in some evolutionary bioinspired techniques. The range
of pitch adjustment has been restricted as [Xl (k), Xu (k)].
From the last phase, xnew , a novel harmony vector
created, the HM has been estimated/upgraded as a novel
completion to fitness amongst xnew and a worse harmony
vector xw in the HM. Accordingly xw has been changed by
xnew and developed as part of HM. To maximize the objective function (interclass variance), HSA has been utilized.
The harmony or solution utilizes k distinct elements for
deciding the optimized technique. These variables have been
threshold values thk which is more utilized to multilevel
segmentation. The population of the technique has been
expressed as follows:
HM � x1 , x2 . . . , x1HMS T ,
xi � th1 , th2 . . . . . . thk .
(32)
In the abovementioned formula T represents the
transpose of the matrix, the maximal size of HM has been
represented as HMS, and all the elements from HM have
been demonstrated as xi, where the range of i is [0, k].
Figure 3 demonstrates the flowchart of the HS technique.
4. Experimental Validation
Table 1 provides the results analysis of the SEF with three
optimization algorithms under five distinct runs. Figure 4
showcases the results analysis of the SEF-CS technique on
five test runs. The results demonstrated that the SEF-CS
technique has accomplished maximum performance under
all runs. For instance, with run-1, the SEF-CS technique has
attained a dice coefficient of 84.89%, an IoU of 73.92%, a
sensitivity of 96.76%, and an accuracy of 98.38%, respectively. In addition, under run-3, the SEF-CS technique has
offered a dice coefficient of 83.52%, an IoU of 72.32%, a
sensitivity of 95.26%, and an accuracy of 98.07%, respectively. Moreover, the SEF-CS technique has provided an
average dice coefficient of 84.92%, an IoU of 73.82%, a
sensitivity of 96.66%, and an accuracy of 98.46%,
respectively.
Figure 5 illustrates the results analysis of the SEF-EO
technique on five test runs. The results demonstrated that the
SEF-EO technique has accomplished maximum performance under all runs. For instance, with run-1, the SEF-EO
technique has attained a dice coefficient of 83.77%, an IoU of
71.75%, a sensitivity of 95.26%, and an accuracy of 98.09%,
respectively. Besides, under run-3, the SEF-EO approach has
offered a dice coefficient of 84.93%, an IoU of 73.55%, a
sensitivity of 96.87%, and an accuracy of 98.49%, respectively. Furthermore, the SEF-EO technique has provided an
average dice coefficient of 85.44%, an IoU of 73.39%, a
sensitivity of 96.76%, and an accuracy of 98.55%,
correspondingly.
Figure 6 depicts the results analysis of the SEF-HS
technique on five test runs. The results demonstrated that the
SEF-HS technique has accomplished maximum performance under all runs. For instance, with run-1, the SEF-HS
technique has attained a dice coefficient of 83.59%, an IoU of
72.25%, a sensitivity of 95.65%, and an accuracy of 98.18%,
respectively. At the same time, under run-3, the SEF-HS
technique has offered a dice coefficient of 85.45%, an IoU of
73.55%, a sensitivity of 97.55%, and an accuracy of 98.69%,
respectively. Finally, the SEF-HS technique has provided an
average dice coefficient of 85.27%, an IoU of 73.69%, a
sensitivity of 97.23%, and an accuracy of 98.62%,
correspondingly.
Table 2 provides the results analysis of the MLOT with
three optimization techniques under five distinct runs.
Figure 7 demonstrates the results analysis of the MLOT-CS
technique on five test runs. The results demonstrated that the
MLOT-CS technique has accomplished maximum performance under all runs. For instance, with run-1, the MLOTCS technique has attained a dice coefficient of 85.31%, an
IoU of 72.25%, a sensitivity of 95.80%, and an accuracy of
98.25%, respectively. Likewise, under run-3, the MLOT-CS
technique has offered a dice coefficient of 86.51%, an IoU of
73.82%, a sensitivity of 97.60%, and an accuracy of 98.55%,
respectively. Eventually, the MLOT-CS technique has provided an average dice coefficient of 86.55%, an IoU of
73.83%, a sensitivity of 97.44%, and an accuracy of 98.67%,
respectively.
Figure 8 showcases the results analysis of the MLOT-EO
technique on five test runs. The results demonstrated that the
MLOT-EO technique has accomplished maximum performance under all runs. For instance, with run-1, the MLOTEO technique has attained a dice coefficient of 85.31%, an
IoU of 72.25%, a sensitivity of 96.15%, and an accuracy of
98%, respectively. Moreover, under run-3, the MLOT-EO
technique has offered a dice coefficient of 87.21%, an IoU of
78.85%, a sensitivity of 97.65%, and an accuracy of 98.18%,
respectively. Then, the MLOT-EO technique provided an
average dice coefficient of 87.07%, an IoU of 73.97%, a
sensitivity of 97.63%, and an accuracy of 98.64%,
correspondingly.
Figure 9 exhibits the results analysis of the MLOT-HS
technique on five test runs. The results demonstrated that the
MLOT-HS technique has accomplished maximum performance under all runs. For instance, with run-1, the MLOTHS technique has attained a dice coefficient of 85.41%, an
IoU of 72.60%, a sensitivity of 96.97%, and an accuracy of
98.01%, respectively. Followed by, under run-3, the MLOTHS technique has offered a dice coefficient of 86.91%, an IoU
of 74.30%, a sensitivity of 98.12%, and an accuracy of 98.90%,
respectively. Finally, the MLOT-HS technique has provided
8
Contrast Media & Molecular Imaging
Initialization of an algorithm parameters
Initialization of harmony memory
Improvisation of a new harmony
A new harmony is
better than a stored
harmony in HM
Yes
Updating HM
No
No
Termination
Criterion satisfied?
Yes
Stop
Figure 3: Flowchart of the HS algorithm.
Table 1: Result analysis of SEF with three optimization algorithms
IoU
Sensitivity
Accuracy
83.52
84.37
84.89
85.54
86.29
84.92
72.32
72.92
73.92
74.52
75.42
73.82
95.26
96.26
96.76
97.26
97.76
96.66
98.07
98.28
98.38
98.68
98.89
98.46
83.77
84.34
84.93
85.72
86.44
85.04
71.75
72.65
73.55
74.15
74.85
73.39
95.26
96.04
96.87
97.41
98.20
96.76
98.09
98.15
98.49
98.88
99.15
98.55
83.59
84.52
85.45
86.17
86.64
85.27
72.25
72.85
73.55
74.45
75.35
73.69
95.65
96.85
97.55
97.95
98.15
97.23
98.18
98.35
98.69
98.88
99.02
98.62
100
SEF-CS Values (%)
Dice coefficient
95
90
85
80
75
70
Dice Coefficient
IoU
Run-1
Run-2
Run-3
Sensitivity
Accuracy
Run-4
Run-5
Figure 4: Result analysis of the SEF-CS model with different runs.
an average dice coefficient of 87.09%, an IoU of 74.30%, a
sensitivity of 98.22%, and an accuracy of 98.71%,
correspondingly.
Finally, a comprehensive comparison study of the
proposed and existing techniques takes place in Table 3.
Figure 10 investigates the dice coefficient analysis of the
proposed with existing techniques. The results show that the
maximum entropy, region growing, DCNN-FCN, thresholding segmentation, and K-means clustering techniques
have accomplished ineffective outcomes compared to the
other techniques. At the same time, the DCNN-UNet,
100
SEF-EO Values (%)
No. of runs
SEF-CS
Run-1
Run-2
Run-3
Run-4
Run-5
Average
SEF-EO
Run-1
Run-2
Run-3
Run-4
Run-5
Average
SEF-HS
Run-1
Run-2
Run-3
Run-4
Run-5
Average
95
90
85
80
75
70
65
Dice Coefficient
Run-1
Run-2
Run-3
IoU
Sensitivity
Accuracy
Run-4
Run-5
Figure 5: Result analysis of the SEF-EO model with different runs.
Contrast Media & Molecular Imaging
9
MLOT-CS Values (%)
SEF-HS Values (%)
100
95
90
85
80
75
100
95
90
85
80
75
70
70
Dice Coefficient
IoU
Sensitivity
Run-1
Run-2
Run-3
Dice Coefficient
Accuracy
IoU
Run-1
Run-2
Run-3
Run-4
Run-5
Figure 6: Result analysis of the SEF-HS model with different runs.
Sensitivity
Accuracy
Run-4
Run-5
Figure 7: Result analysis of the MLOT-CS model with different
runs.
Dice coefficient
IoU
Sensitivity
Accuracy
85.31
86.01
86.51
87.11
87.81
86.55
72.25
72.93
73.82
74.81
75.35
73.83
95.80
96.70
97.60
98.20
98.90
97.44
98.25
98.45
98.55
98.95
99.16
98.67
85.31
86.21
87.21
87.91
88.71
87.07
72.25
73.25
73.85
74.85
75.65
73.97
96.15
96.95
97.65
98.45
98.96
97.63
98.00
98.18
98.78
99.10
99.14
98.64
85.41
86.41
86.91
87.91
88.81
87.09
72.60
73.50
74.30
75.30
75.80
74.30
96.97
97.73
98.12
99.05
99.25
98.22
98.01
98.54
98.90
98.97
99.13
98.71
DCNN-Hy-Net, SEF-CS, SEF-EO, and SEF-HS techniques
have accomplished moderately closer dice coefficient values.
Followed by the MLOT-CS and MLOT-EO techniques, they
have resulted in certainly improved dice coefficient values of
86.55% and 87.07%, respectively. However, the MLOT-HS
technique has gained effective performance with a higher
dice coefficient of 87.09%.
Figure 11 examines the IoU analysis of the proposed with
existing techniques. The results show that the maximum
entropy, region growing, DCNN-FCN, thresholding segmentation, and K-means clustering techniques have accomplished ineffective outcomes compared to the other
techniques. In line with the DCNN-UNet, DCNN-Hy-Net,
SEF-CS, SEF-EO, and SEF-HS techniques, they have accomplished moderately closer IoU values. Following that the
MLOT-CS and MLOT-EO techniques have resulted to
100
95
90
85
80
75
70
Dice Coefficient
IoU
Run-1
Run-2
Run-3
Sensitivity
Accuracy
Run-4
Run-5
Figure 8: Result analysis of the MLOT-EO model with different
runs.
MLOT-HS Values (%)
No. of runs
MLOT-CS
Run-1
Run-2
Run-3
Run-4
Run-5
Average
MLOT-EO
Run-1
Run-2
Run-3
Run-4
Run-5
Average
MLOT-HS
Run-1
Run-2
Run-3
Run-4
Run-5
Average
MLOT-EO Values (%)
Table 2: Result analysis of MLOT with three optimization
algorithms.
100
95
90
85
80
75
70
Dice Coefficient
Run-1
Run-2
Run-3
IoU
Sensitivity
Accuracy
Run-4
Run-5
Figure 9: Result analysis of the MLOT-HS model with different
runs.
50
1
2
3
4
6
10
11
12
13
3
4
5
MLOT-HS, 74.30
2
MLOT-EO, 73.97
1
MLOT-CS, 73.83
35
SEF-HS, 73.69
40
SEF-EO, 73.39
45
6
7
8
Methods
9
10
11
12
13
Figure 11: Comparative analysis of the proposed method in terms
of IoU.
6
7 8
Methods
MLOT-HS, 98.22
MLOT-EO, 97.63
MLOT-CS, 97.44
5
SEF-CS, 96.66
4
9
10 11 12 13
1
2
3
4
5
6 7 8
Methods
9
MLOT-HS, 98.71
MLOT-CS, 98.67
SEF-EO, 98.55
SEF-HS, 98.62
96
SEF-CS, 98.46
Accuracy (%)
MLOT-HS, 87.09
MLOT-EO, 87.07
MLOT-CS, 86.55
SEF-HS, 85.27
SEF-CS, 84.92
DCNN-Hy-Net, 83.91
DCNN-FCN, 68.67
SEF-EO, 85.04
9
SEF-CS, 73.82
50
DCNN-Hy-Net, 72.65
55
98
92
7 8
Methods
DCNN-UNet, 70.37
60
100
88
DCNN-FCN, 52.40
65
K-Means clustering, 61.13
70
Maximum entropy, 35.53
Threshold segmentation, 56.49
Region Growing, 49.57
75
102
94
Figure 10: Comparative analysis of proposed method interms of
dice coefficient.
80
104
90
5
3
MLOT-EO, 98.64
55
DCNN-UNet, 82.38
65
K-Means clustering, 75.51
70
Maximum entropy, 50.87
Threshold segmentation, 71.18
Region Growing, 64.80
106
75
2
Figure 12: Comparative analysis of the proposed method in terms
of sensitivity.
90
80
1
SEF-HS, 97.23
50
SEF-EO, 96.76
60
DCNN-Hy-Net, 89.14
70
108
60
IoU (%)
80
DCNN-UNet, 83.89
97.46
91.22
97.99
96.83
98.09
98.28
98.46
98.55
98.62
98.67
98.64
98.71
DCNN-Hy-Net, 98.28
52.36
95.85
71.22
70.62
83.89
89.14
96.66
96.76
97.23
97.44
97.63
98.22
DCNN-UNet, 98.09
49.57
35.53
61.13
52.40
70.37
72.65
73.82
73.39
73.69
73.83
73.97
74.30
K-Means clustering, 71.22
64.80
50.87
75.51
68.67
82.38
83.91
84.92
85.04
85.27
86.55
87.07
87.09
90
DCNN-FCN, 70.62
97.80
DCNN-FCN, 96.83
61.74
Region Growing, 97.46
Maximum entropy, 91.22
K-Means clustering, 97.99
56.49
95
85
Dice Coefficient (%)
71.18
Sensitivity (%)
Threshold
segmentation
Region growing
Maximum entropy
K-means clustering
DCNN-FCN
DCNN-UNet
DCNN-Hy-net
SEF-CS
SEF-EO
SEF-HS
MLOT-CS
MLOT-EO
MLOT-HS
100
IoU Sensitivity Accuracy
Threshold segmentation, 97.80
Dice
coefficient
Methods
Maximum entropy, 95.85
Table 3: Comparative results analysis of proposed versus existing
techniques.
Region Growing, 52.36
Contrast Media & Molecular Imaging
Threshold segmentation, 61.74
10
10 11 12 13
Figure 13: Comparative analysis of the proposed method in terms
of accuracy.
certainly improved IoU values of 73.83% and 73.97%,
correspondingly. However, the MLOT-HS technique has
gained effective performance with a higher IoU of 74.30%.
Figure 12 considers the sensitivity analysis of the proposed with existing techniques. The results show that the
maximum entropy, region growing, DCNN-FCN, thresholding segmentation, and K-means clustering techniques
have accomplished ineffective outcomes compared to the
other techniques. Simultaneously, the DCNN-UNet,
DCNN-Hy-Net, SEF-CS, SEF-EO, and SEF-HS techniques
have accomplished moderately closer sensitivity values.
Also, the MLOT-CS and MLOT-EO techniques have
resulted to certainly improved sensitivity values of 97.44%
and 97.63%, respectively. However, the MLOT-HS technique has gained effective performance with a higher sensitivity of 98.22%.
Figure 13 explores the accuracy analysis of the proposed
with existing techniques. The results show that the maximum entropy, region growing, DCNN-FCN, thresholding
Contrast Media & Molecular Imaging
segmentation, and K-means clustering techniques have
accomplished ineffective outcomes compared to the other
techniques. Concurrently, the DCNN-UNet, DCNN-HyNet, SEF-CS, SEF-EO, and SEF-HS techniques have accomplished moderately closer accuracy values. Similarly, the
MLOT-CS and MLOT-EO techniques have resulted to
certainly improved accuracy values of 98.67% and 98.64%,
respectively. Lastly, the MLOT-HS technique has gained
effective performance with a higher accuracy of 98.71%. By
looking into the abovementioned tables and figures, it is
ensured that the MLOT-HS technique is found to be effective compared to other techniques.
5. Conclusion
In this study, a set of metaheuristic optimization-based
vascular segmentation techniques have been developed for
PAI. The goal of the study is to examine the outcomes of the
different metaheuristics on two segmentation approaches. In
order to effectively segment the vessels, the SEF and MLOT
techniques are applied. Moreover, three optimization algorithms such as CS, EO, and HS are utilized for optimal
selection of entropy function and threshold values. For
examining the improved performance of the proposed
model, a wide range of simulations take place and the results
are inspected under various aspects. The experimental results pointed out that the proposed MLOT-HS technique has
gained maximum performance over the other existing approaches. Thus, it can be employed in real-time brain imaging related applications such as brain and cancer imaging
such as prostate cancer, breast cancer, and ovarian cancer. In
the future, the vessel segmentation performance of the
proposed model can be improved by the use of deep learning
models.
Data Availability
No datasets were generated during this study.
Ethical Approval
This article does not contain any studies with human participants performed by any of the authors.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Authors’ Contributions
The manuscript was written by contributions from all authors. All authors have given approval to the final version of
the manuscript.
Acknowledgments
This research was supported by Taif University Researchers
Supporting Project (number TURSP-2020/314), Taif University, Taif, Saudi Arabia.
11
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