Retinal Vessel Segmentation based on Hunger Games Search and
Reptile Search Algorithms
MEHMET BAHADIR ÇETİNKAYA1, HAKAN DURAN2
1Department of Mechatronics Engineering,
University of Erciyes,
38039, Melikgazi, Kayseri,
TURKEY
2Graduate School of Natural and Applied Sciences,
University of Erciyes,
38039, Melikgazi, Kayseri,
TURKEY
Abstract: - Metaheuristic algorithms may provide effective performance in image processing due to their
strengthened random search abilities. In most of these algorithms, the intelligent collective behavior of animal
swarms or individual intelligent behaviors of each animal is simulated. In this work, two recently proposed
metaheuristic algorithms of hunger games search (HGS) and reptile search (RSA) algorithms are improved as
clustering-based and then applied to the clustering of retinal image pixels. A detailed performance comparison
is realized between HGS and RSA algorithms in terms of convergence speed, sensitivity, specificity, accuracy,
mean squared error, standard deviation, and CPU time. Although HGS and RSA algorithms produce similar
results in terms of clustering performance, it is observed that the HGS algorithm presents relatively better
performance than the RSA algorithm in terms of all performance metrics. The simulation results obtained prove
that HGS and RSA algorithms can successfully be used in retinal vessel segmentation.
Key-Words: - Retinal vessel segmentation, Clustering, DRIVE database, Metaheuristic algorithms, Hunger
Games search algorithm, Reptile search algorithm.
Received: August 2, 2023. Revised: November 8, 2023. Accepted: December 19, 2023. Published: December 31, 2023.
1 Introduction
Segmentation of retinal vessels with high accuracy
is vital in the diagnosis and treatment of retinal
diseases. However, the analysis of retinal images is
a complex process because of the close pixel values
between the different regions of the image. To
distinguish pixel values effectively, the clustering
process has to be performed.
Before the segmentation process, firstly, the
retinal images are subjected to pre-processings of
band selection, bottom-hat transformation, and
contrast enhancement. As a result of the band
selection process, it is observed that the Green (G)
layer of the Red-Green-Blue (RGB) image produces
the best performance in terms of contrast and
brightness. Afterward, the regions with worse
contrast are enhanced by using a structural filter
element in bottom-hat transformation. The
expression of the bottom-hat transformation can be
shown in Equation 1:
( ) ( )bottom hat g g g nB
(1)
where g is the retinal image, B is the structural
element that preferred as a disk with a radius of 8,
and n is the bottom-hat transformation. Finally, the
pixel values locally concentrated in narrow pixel
intervals are distributed homogeneously to the
whole pixel interval of [0 255] by applying a
contrast enhancement process.
To present a more comprehensive analysis, the
simulations were carried out on both healthy and
diseased retinal images taken from the digital retinal
images for vessel extraction (DRIVE) database and
shown in Figure 1.
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(a) Healthy (b) Diseased
Fig. 1: Retinal images taken from the DRIVE
database
The retinal images obtained as a result of the
three pre-processing operations are represented in
Figure 2.
(a) (c)
(b) (d)
Fig. 2: (a) and (c) are the green layer images
obtained as a result of band selection, (b) and (d) are
the enhanced retinal images obtained after the
bottom-hat transformation and contrast
enhancement.
Metaheuristic algorithms perform the clustering
operations directly on the retinal images given in
Figure 2(b) and Figure 2(d).
2 Literature Review
To overcome the difficulties encountered in retinal
vessel segmentation, metaheuristic algorithms can
successfully be used. In literature, there are several
works including the application of metaheuristic
algorithms to retinal vessel segmentation. In [1], the
authors proposed a glowworm swarm optimization
(GSO) algorithm that automated detection of optic
cups from retinal fundus images. An ant colony
optimization (ACO) based approach is improved in
[2], for optic cup segmentation in retinal fundus
images. In work [3], the authors introduced an
adaptive ant colony optimization (adaptive ACO)
approach for edge detection-based retinal vessel
segmentation. An improved binary processing-based
artificial bee colony (ABC) algorithm is proposed in
[4], for the aim of retinal vessel segmentation. The
authors presented an accurate methodology in [5],
that combines the lateral inhibition (LI) and the
differential evolution (DE) approaches for retinal
vessel and optic disc segmentation. In [6], a three-
step methodology including a novel chaotic
weighted elephant herding optimization (CWEHO)
approach is introduced for retinal vessel
segmentation. A novel approach that uses neural
architecture search to optimize a U-net architecture
using a binary teaching learning-based (BTLBO)
algorithm is proposed in [7], for retinal vessel
segmentation. In another work, an intelligent coyote
optimization algorithm combined with deep learning
is presented with the aim of detection and grading
on retinal fundus images, [8]. In work [9], a hybrid
approach consisting of an ant colony optimization
algorithm and a machine learning technique is
improved to classify the retinal pixels into regions
containing blood vessels and not containing blood
vessels. A novel neural architecture search approach
for U-shaped networks is proposed in [10], with the
aim of improving deep neural networks having high
segmentation performance and lower inference time.
In [11], the authors improved a novel differential
evolution algorithm-based cross-entropy
minimization procedure to perform an accurate pixel
classification in retinal images. A new bio-inspired
blood vessel segmentation hybrid technique using a
bird swarm algorithm (BSA) and river formation
dynamics (RFD) algorithm is presented in [12]. In
work [13], an unsupervised retinal blood vessel
segmentation approach based on the elite-guided
multi-objective artificial bee colony (EMOABC)
algorithm is proposed. The authors in [14], proposed
a novel methodology for retinal vessel segmentation
that is based on a bat algorithm and random forest
classifier. In work [15], the authors presented a
detailed and comparative research work including
the application of the most effective heuristic
algorithms to retinal vessel segmentation. Finally, in
[16], a novel vessel segmentation approach using
the multi-threshold-based remora optimization
(MTRO) algorithm is presented.
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3 Material and Methods
Hunger games search and reptile search algorithms
are population-based metaheuristic approaches that
simulate the intelligent behavior of animal herds or
groups. In this work, HGS and RSA algorithms are
improved as clustering-based and then applied to the
retinal vessel segmentation.
HGS and RSA algorithms have the common
control parameters of
N
and
MaxCycle
. In both
algorithms,
N
represents the population size and
MaxCycle
represents the maximum number of
cycles.
3.1 Hunger Games Search Algorithm
HGS algorithm is a population-based metaheuristic
algorithm inspired by the hunger driven activities
and behavioral choices of animals. It was proposed
in 2021, [17]. HGS algorithm can provide enhanced
exploration and exploitation behaviors during the
optimization process.
HGS algorithm includes five initialized
parameters as
N
,
MaxCycle
,
l
and
SHungary
.
Here,
SHungary
can be defined as the total number
of individuals feeling hungry while
l
and
E
are the
control parameters that optimize the initial positions
and search mode, respectively.
1
W
and
2
W
are the
hunger weights that prevent the algorithm from
getting stuck inside into a local minimum. Finally,
R
is a parameter used to optimize the variation rate
of the search step,
b
X
represents the best solution
of the current cycle, and
BF
is the best fitness of
the current cycle.
The detailed pseudo-code of a basic HGS
algorithm can be given as the following,
Initialize the parameters of
, , ,N MaxCycle l SHungry
Initialize individual positions,
( 1,2,..., )
i
X i N
Cycle=1
While
Cycle MaxCycle
Calculate the fitness value of all individuals and
determine the best solution producing the minimum
Euclidean distance.
Update
,,
b
BF WF X
Calculate the
SHungry
by,
0, ( )
() ( ) , ( )
AllFitness i BF
hungry i hungry i H AllFitness i BF
where;
SHungry
is the sum of hungry feelings of
all individuals, namely,
()hungry i
and
()AllFitness i
represents the fitness of each
individual in the current cycle.
Calculate the
1
W
by,
43
1
3
()
1
,1
()
,1
N
hungry i x SHungry xr r
Wi
r
where;
3
r
and
4
r
are randomly produced numbers
in the interval of [0,1].
Calculate the
2
W
by,
25
()
( ) 1 2
hungry i SHungry
W i e x r x
where;
5
r
is a randomly produced number in the
interval of [0,1].
For Each Individual
Calculate
E
by,
sec ( ( ) )E h F i BF
where;
(1,2,..., )iN
,
()Fi
represents the
fitness value of each individual and
2
sec ( ) xx
hx ee
is a a hyperbolic function.
Update
R
by,
2 [0,1]R xshrink xrand shrink
where;
shrink
can be determined as
2 (1 )
Current Cycle
MaxCycle
x
is a hyperbolic function.
Update all positions by,
11
2 1 2
12
3 1 2
12
: ( ) (1 (1)), 1
: ( ) ,
( 1) ;
: ( ) ,
;
bb
bb
Game
Game
Game
X t x rand r
W x X R xW x X X t
X t r l r E
W x X R xW x X X t
r l r E
where;
(1)rand
is a random number satisfying
normal distribution and also
1
r
and
2
r
are randomly
produced numbers in the interval of [0,1].
End For
Cycle= Cycle+1
End While
Return
,b
BF X
UNTİL (termination criteria are met)
3.2 Reptile Search Algorithm
The RSA which was proposed in 2022 is a
population based optimizer which simulates the
hunting behavior of reptiles, especially crocodiles
[18]. The encircling and the hunting phases of the
RSA correspond to the exploration and exploitation
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phases, respectively. The RSA can provide effective
global search and local search abilities due to its
robust exploration and exploitation behaviors.
is a control parameter which optimizes the
exploration accuracy for the encircling phase and
is a control parameter which optimizes the
exploration accuracy for the hunting phase.
Evolutionary Sense (
()ES t
) represents a probability
ratio taking randomly decreasing values between 2
and −2 throughout the cycles. In addition,
( , )ij
parameter denotes the hunting operator for the
th
j
position in the
th
i
solution,
( , )ij
R
is a value used to
reduce the search space, and finally
( , )ij
P
is the
percentage difference between the
th
j
position of
the optimal solution obtained so far and the
th
j
position of the current solution.
In RSA, to strengthen the encircling phase, the
positions of the reptiles are updated via the
following equation,
( , ) ( , )
( , ) ( , )
( ) ( ( )) ( )
[0,1], 4
( 1) ( ) ( )
[0,1], 2 44
ji j i j
ij jrj
Best R
xBest
t x t x t
MaxCycle
x rand t
tt x x x ES t
TT
x rand t and t
where;
()
j
Best t
represents the
th
j
position of the
optimal solution obtained so far and
( , )rj
x
corresponds to a random position of the relevant
solution (
[( 1, 2,..., ), ]r r rN j
x
).
The detailed pseudo-code of a basic RSA
algorithm can be given as the following,
Initialize the parameters of
, , , , ,,N MaxCycle RP
Randomly initialize the individual positions,
: 1,2,...,X i N
Cycle=1
While
Cycle MaxCycle
Calculate the fitness value for the candidate solutions and
determine the best solution producing the minimum
Euclidean distance.
Update
ES
by,
1
( ) 2 1()ES t x r MaxCycle
x
where;
r
denotes to a random integer number
between in [-1,1].
For
1,2,...,iN
Update
,,RP
parameters by,
( , ) ( , )
()
i j j i j
Best Ptx
2
( , )
( , )
()
()
j r j
ij
j
Best x
RBest
tx
t
( , )
( , )
()
( ) ( )
i j i
ij
j j j
x
PBest
Mx
t x ub lb
where;
a is a small value defined to prevent the
denominator from being zero
If : High Walking Phase
4
Current Cycle MaxCycle
( , ) ( , )
( , )
( 1) ( ) ( ( ))
( ) [0,1]
j
i j i j
ij
x Best
R
t t x t x
t x rand
Else : Belly Walking Phase
2
44
Current Cycle
MaxCycle MaxCycle
( , ) ( , )
( 1) ( ) ( )
[0,1]
j
i j r j
x Bestt t x x x ES t
x rand
Else : Hunting Cooperation Phase
3
44
2Current Cycle
MaxCycle MaxCycle
( , ) ( , )
( , )
( 1) ( ) ( ( ))
( ) [0,1]
j
i j i j
ij
x Best
R
t t x t x
t x rand
End If
End For
Cycle= Cycle+1
End While
Return
( ) :Best X best solution
UNTİL (termination criteria are met)
For both HGS and RSA algorithms, the
population size is chosen as 10 and the maximum
cycle number is chosen as 100.
In the HGS algorithm, the value of the
l
parameter determines the rule to be chosen (
1
Game
,
2
Game
, …,
X
Game
) so the value of this parameter
will be equal to the number of rules. The control
parameter
E
controls the variation of all positions
and its value can be calculated by using the formula
given in pseudo code. Finally, the value of the
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SHungry
parameter is adaptively updated at each
cycle depending on the hunger feelings of all
individuals. In this work, the initial value of the
SHungry
parameter is set to zero.
In the RSA algorithm, the values of the
and
parameters are set to 0.1. The value of the
,R
and
P
parameters are adaptively updated at each
cycle depending on the equations given in the
pseudo code. In this work, the initial value of the
SHungry
parameter is set to zero.
While measuring the success of the pixel
clustering process, the Mean-Squared Error (MSE)
criteria given in Equation 2 is used.
2
1
1()
N
ii
i
MSE f y
N
(2)
where; N represents the total number of pixels, fi is
the value of the cluster center closest to the
pixel i and yi represents the pixel value of the ith
pixel.
4 Simulation Results
When the clustering based metaheuristic HGS and
RSA algorithms improved for retinal vessel
segmentation are applied to the retinal images given
in Figure 1, the segmentation results obtained are
shown in Figure 3. As seen from the results, HGS
and RSA algorithms can distinguish the vessel and
background pixels with high accuracy.
(a) HGS
(b) HGS
(c) RSA
(d) RSA
Fig. 3: Retinal images obtained after applying
segmentation to the images given in Figure 1(a) and
Figure 1(b) by using the clustering based HGS and
RSA algorithms
In order to compare the convergence speeds of
the algorithms, the mean convergence
characteristics obtained for 20 random runs are
shown in Figure 4. From the figure, it can be
concluded that HGS can converge to the lower MSE
values at fewer cycles.
Fig. 4: Convergence speeds of the HGS and RSA
algorithms
For a more detailed and fair comparison, the
performances of the algorithms have also been
evaluated in terms of sensitivity (Se), specificity
(Sp), and accuracy (Acc) for all 20 retinal images in
the DRIVE database. The mathematical expressions
of Se, Sp, and Acc are represented in Equation 3-5
and the results obtained for each of the 20 retinal
images are given separately in Table 1.
()
TP
Se TP FN
(3)
()
TN
Sp TN FP
(4)
()
TP TN
Acc TP FN TN FP
(5)
In the equations given above, true positives (TP)
represent the number of pixels that are vessels and
have been detected as vessels. True negatives (TN)
represent the correctly classified background pixels
which can be considered non-vessel pixels. False
positives (FP) represent the number of background
pixels that are incorrectly classified as vessel pixels.
False negatives (FN) represent the vessel pixels that
have been incorrectly detected as background
pixels. As a result, Se is the ratio of correctly
classified vessel pixels while Sp is the ratio of
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correctly classified background pixels and Acc is the
ratio of correctly classified both the vessels and
background pixels.
From the results obtained, it is observed that the
performance of the HGS algorithm in terms of Se,
Sp, and Acc is relatively better when compared to
the RSA algorithm.
Table 1. The performance measures for the 20 different images taken from the DRIVE database
Image
Sensitivity
Specificity
Accuracy
HGS
RSA
HGS
RSA
HGS
HSA
1
0.8775
0.8869
0.9749
0.9793
0.9644
0.9625
2
0.8587
0.8502
0.9655
0.9698
0.9635
0.965
3
0.8616
0.873
0.9855
0.9807
0.9437
0.9294
4
0.8464
0.8378
0.9685
0.9648
0.9606
0.9626
5
0.8567
0.8487
0.9777
0.9665
0.9629
0.931
6
0.8458
0.8301
0.9718
0.9702
0.945
0.9271
7
0.8696
0.8282
0.9808
0.9622
0.9557
0.9406
8
0.8551
0.8623
0.9869
0.99
0.9225
0.8845
9
0.8847
0.8565
0.9973
0.9819
0.9367
0.9068
10
0.8589
0.8472
0.978
0.9855
0.9673
0.9457
11
0.8795
0.8474
0.9982
0.9716
0.9629
0.9633
12
0.8879
0.8398
0.9842
0.9879
0.9313
0.9405
13
0.8461
0.8461
0.9758
0.9599
0.9513
0.9513
14
0.8856
0.8379
0.9857
0.9714
0.9485
0.9408
15
0.8657
0.8257
0.9746
0.9746
0.9571
0.9571
16
0.8776
0.8599
0.9734
0.9813
0.9668
0.9552
17
0.8601
0.8695
0.9845
0.9818
0.9409
0.9178
18
0.8325
0.8625
0.971
0.971
0.9573
0.9573
19
0.861
0.8366
0.9759
0.9713
0.9593
0.9553
20
0.8952
0.8493
0.987
0.9821
0.9285
0.9372
Mean
0.86531
0.84978
0.97986
0.97519
0.95131
0.94155
The MSE values reached by the algorithms are
also an important performance criterion. Simulation
results represent that the HGS algorithm can
converge to lower mean MSE values when
compared to the RSA. Another performance metric
to be analyzed is the standard deviation (
) which
represents the spread around the mean value. If the
algorithm reaches close MSE values at each run, it
can be defined as a statistically stable algorithm.
From the results obtained, it is seen that HGS is
more stable than RSA due to its lower standard
deviation value. Finally, the CPU time which
identifies the time interval required for a run, is
another important performance metric. In this work,
the simulations are realized on an Intel i7-10700
CPU with 2.0 GHz frequency and 16 GB RAM. In
addition, the operating system is chosen as 64-bit
Windows 10 Pro. When the minimum CPU time
values obtained among 20 random runs for each
algorithm are examined, it is seen that HGS
produces better results than of RSA.
The results obtained for minimum MSE value,
standard deviation, and CPU time are given in Table
2.
Table 2. Performance comparison of HGS and RSA
algorithms in terms of minimum MSE values
reached standard deviation, and CPU time
Minimum
MSE
Standard
Deviation
CPU time
(seconds)
HGS
0.7234
2.16438e-09
2.526588
RSA
0.8307
7.58405e-06
2.582861
To detect the statistically significant differences
between the HGS and RSA algorithms, the
Wilcoxon rank sum-test is also applied for the
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confidence interval of 95% (p<0.05) and the results
are given in Table 3.
Table 3. Wilcoxon sum-rank test results (p<0.05)
Better than
HGS
RSA (6.7860e-08)
RSA
-
As seen from the Wilcoxon rank sum-test results,
HGS produces more statistically significant results
when compared to RSA.
5 Conclusion
In this work, HGS and RSA which are among the
most novel metaheuristic algorithms are improved
as clustering-based and then applied to retinal vessel
segmentation. It has been observed that HGS and
RSA algorithms can successfully distinguish the
vessel pixels and background pixels which have
close pixel values. The convergence analysis results
show that the HGS algorithm requires 15 cycles to
reach its optimal MSE value while the RSA requires
25 cycles. Furthermore, the HGS algorithm
produces similar but a bit better results in terms of
Se, Sp, and Acc metrics when compared to RSA.
Similarly, the performance of the HGS algorithm in
terms of the minimum MSE value reached and CPU
time seems a bit better according to the RSA
algorithm. Finally, the higher standard deviation
value of HGS proves that it is statistically more
stable than the RSA algorithm. In future works, the
HGS and RSA algorithms will be improved as
clustering-based for the analysis of different
biomedical images and then their performances will
be compared with other novel metaheuristic
algorithms.
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WSEAS TRANSACTIONS on SIGNAL PROCESSING
DOI: 10.37394/232014.2023.19.24
Mehmet Bahadir Çeti
nkaya, Hakan Duran
E-ISSN: 2224-3488
228
Volume 19, 2023
