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Indonesian Journal of Electrical Engineering and Computer Science
Vol. 31, No. 2, August 2023, pp. 933~944
ISSN: 2502-4752, DOI: 10.11591/ijeecs.v31.i2.pp933-944 933
Journal homepage: http://ijeecs.iaescore.com
An Otsu thresholding for images based on a nature-inspired
optimization algorithm
Khamael Raqim Raheem, Hafedh Ali Shabat
Technical Institute of Babylon, AL-Furat AL-Awsat Technical University (ATU), Kufa, Iraq
Article Info
ABSTRACT
Article history:
Received Oct 18, 2022
Revised Mar 12, 2023
Accepted Mar 24, 2023
Thresholding is a type of image segmentation, where the pixels change to
make the image easier to analyze. In bi-level thresholding, the image in
grayscale format is transformed into a binary format. The traditional methods
for image thresholding may be inefficient in finding the best threshold and
take longer computation time. Recently, metaheuristic swarm-based
algorithms were applied for optimization in different applications to find
optimal solutions with minimum computational time. The proposed work
aims to optimize the fitness function obtained by the Otsu algorithm using a
metaheuristic swarm-based algorithm called the bat algorithm. As a result, the
optimal threshold value for bi-level images in cloud detection was obtained.
Also, one of the trajectory-based algorithms called hill climbing was applied
to optimize the fitness function taken from the Otsu algorithm. The HYTA
dataset was used to evaluate the work, which was later confirmed through
testing. The findings of experiments indicated that the developed algorithm is
promising and the performance of the metaheuristic population-based
algorithm is better than the trajectory-based algorithm in terms of efficiency
and computational time for image thresholding.
Keywords:
Bat algorithm
Hill climbing algorithm
Image thresholding
Optimization
Otsu thresholding
This is an open access article under the CC BY-SA license.
Corresponding Author:
Khamael Raqim Raheem
Technical Institute of Babylon, AL-Furat AL-Awsat Technical University (ATU)
Kufa, Iraq
Email: khmrakrah@atu.edu.iq
1. INTRODUCTION
Thresholding is a simple but efficient technique in terms of segmenting images. Bi-level thresholding
and multi-level thresholding are the two types of thresholding that are used in practice. Over the past ten years,
bi-level thresholding has attracted a lot of attention from researchers [1], [2]. The study of multilevel
thresholding has also been ongoing [3]-[5]. The image in grayscale format is transformed into an image in binary
format using the technique of bi-level thresholding [6]. The best thresholding image can be obtained by choosing
an appropriate threshold value while separating the foreground from the background. The basic thresholding
algorithms are global thresholding, local thresholding, and hybrid thresholding. The methods used by global
thresholding algorithms are based on classification techniques, histograms, clustering, entropy, and Gaussian
distribution [7]. Thresholding is widely used in medical image segmentation [8], [9], engineering [10], stone
inscription [11], and document image [12]. The Otsu algorithm is a global thresholding algorithm, which falls
within the field of classification techniques.
Otsu's approach was improved by Sha et al. [13] by creating a two-dimensional histogram based on
an image that had been processed with median and average filters. This method also adds a region post-
processing phase to cope with noise and edge-filled pixel issues. Also, Indra et al. [14] used the Otsu
thresholding algorithm to separate objects and backgrounds to distinguish fertile and infertile domestic fowl
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eggs for the grayscale image. Additionally, a strategy in [15] was offered as a method for detecting green plants
in a maize crop. This technique is based on segmentation and dimensionality decrease using principal
component analysis, Otsu thresholding, threshold combination, and final thresholding. Meanwhile, brain image
segmentation using Otsu thresholding is proposed by Badriyah et al. [16] to determine the characteristics of a
specific stroke kind. They evaluated the results using the peak signal-to-noise ratio and mean-square error.
Additionally, [17] used Otsu thresholding to isolate the roads and residential areas from the vegetated areas in
remote sensing images. They used accuracy and precision for testing the results. A granule size selection
method based on the homogeneity histogram is also suggested by Lei and Fan [18] for bi-level thresholding
for images, which is useful in handling small objects and local changes in the images. In addition, by
investigating the link between pixel grayscale value and cumulative pixel number change, the study in Yang
et al. [19] improved the strategy for Otsu thresholding to adjust the threshold bias and as the adjusted threshold.
The ratio of pixel gray level value to a particular cumulative pixel number was chosen. For quantitative
evaluation, two regularly used measures were chosen: misclassification error and dice similarity coefficient.
Also, for gesture image segmentation, the work in [20] dealt with Otsu thresholding where a noise-adaptable
angle threshold was devised. To prevent interference from extreme noise by removing neighborhood extremes,
a two-dimensional histogram of gray value-neighborhood trimmed gray mean is initially constructed. After
then, adaptive filtering is used to increase the algorithm's overall applicability by calculating the likelihood that
each pixel is noise based on the current circumstances. To increase efficiency, the threshold search range is
compressed and the threshold space is finally transformed into an angled space from 0° to 90°.
Over the past forty years, the popularity of the nature-inspired and bio-inspired metaheuristic
optimization era has grown significantly [21]. The effectiveness of the metaheuristic population-based
algorithms is evaluated by looking at how well exploration and exploitation are balanced. The likelihood of
the algorithm becoming trapped in local optima, early convergence, and stagnation is higher when there is a
poor balance between exploration and exploitation [22]. It's interesting to note that the number of suggested
nature-inspired optimization algorithms has increased exponentially. These algorithms deal with many data
types, including text data [23] and image data [24]. Recently researchers have proposed a variety of techniques
to speed up image thresholding, including swarm intelligence optimization algorithms such as the particle
swarm algorithm [25], ant colony algorithm [26], and fruit fly optimization algorithm [27]. which have
achieved less computational cost. Mostly, these algorithms have been successful to minimize time complexity
and improve image quality to some extent, but there is further scope for improvement using other nature-
inspired optimization algorithms such as the bat algorithm. Bat algorithm is a global optimization intelligent
algorithm based on biological heuristics. To determine the ideal value, it mimics how the bat population
searches for food using echolocation. Practice demonstrates that Bat algorithm is a successful search algorithm
with quick convergence and great global optimization search capability. The algorithm has the characteristics
of high robustness and identification accuracy while being simple in concept and less constrained by
parameters.
The aim of the proposed work is to optimize the fitness function obtained from the Otsu algorithm
using the Bat algorithm for cloud detection and then compare its performance with a trajectory-based local
search algorithm called the hill climbing algorithm. In ground-based sky imager applications, cloud detection
is a prerequisite before other information (such as cloud cover) may be derived. In the literature, limited works
applied for bi-level image thresholding using metaheuristic algorithms. The contribution of this paper is to
demonstrate the feasibility of the Bat algorithm and Otsu algorithm for bi-level thresholding. Also, it offers a
new option to conventional methods due to its simplicity and efficiency with minimum computational time.
The remainder sections are constructed according as: section 2 explains the concepts of the hill
climbing algorithm, bat algorithm, and Otsu algorithm. Section 3 introduces the proposed thresholding
algorithm. The experimental results and discussion are illustrated in section 4. Finally, section 5 explains the
conclusion and future work.
2. THEORETICAL BASIS
2.1. Hill climbing algorithm
A relatively straightforward local search technique called "Hill climbing" aims to enhance a single
candidate solution from a randomly chosen starting point. Figure 1 illustrates the pseudo-code for the hill
climbing algorithm where the adjacent search space is assessed in relation to the current location. The search
shifts to a more suitable candidate solution if one is discovered. The algorithm ends if there isn't a better solution
in the vicinity. Since the procedure is comparable to climbing hills on the surface of the fitness function, the
technique has been referred to as "Hill climbing".
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Figure 1. Hill climbing algorithm [28]
2.2. Bat algorithm
The Bat algorithm is a nature-inspired metaheuristic based on a population that was put forth by Yang
[29]. The algorithm utilizes the echolocation of bats, It is well knowledge that sound pulses change into a
frequency that obstacles reflect. Bats navigate utilizing the delay of time between emission and reflection. After
hitting and reversal, bats use their pulse as beneficial data to assess how far away their target is. Yang
implemented the Bat algorithm by the three following broad guidelines: i) Echolocation is used by all bats to
locate distance, and in some mysterious way, they can also discern between background barriers and prey or
food. ii) Bats fly at random with a velocity of vi, a position of xi, a fixed frequency of fmin, a variable wavelength
λ, and loudness of A0 to find prey. They can automatically vary the wavelength of their produced pulses as
well as the rate of pulse emission rϵ[0,1] relying on how close their target is. iii) Though loudness can alter in
a variety of ways, it normally ranges from a big (positive) A0 to a little constant value Amin.
Figure 2 illustrates the flowchart of Bat algorithm steps, at the first the bat population is randomly
initialized. Namely, generating new solutions is performed by moving virtual bats by:
(1)
(2)
(3)
where βϵ[0,1] is a random vector taken from a uniform distribution. Here X* represents the existing best global
location (solution). This can be determined by comparing all of the bats' solutions. Each bat is initially assigned
a frequency chosen uniformly from [fmin, fmax] at random. In the local search that alters the existing optimal
solution, a random walk with direct exploitation is used as in (4).
(4)
Where ∂ϵ[-1,1] is a random number, whilst At is the average loudness of all the best at this time step.
By the rate ri of pulse emission, the local search is started. The loudness can be set to any convenient value
because, after a bat finds its prey, the loudness often drops while the rate of pulse emission rises. As a result,
both characteristics mimic those of natural bats. Mathematically, these characteristics are captured as:
(5)
where α and are constants. In reality, the parameter α has a role similar to the cooling factor of a cooling
schedule in the simulated annealing.
2.3. Otsu algorithm
Otsu algorithm was proposed by Otsu [30] in 1979 for image thresholding where a criterion function
generates some sort of measure of dissociation between regions of the image. Otsu thresholding selects the
threshold value that minimizes intra-class variation of the foreground and background pixels. According to
Bangree et al. [31] lists the steps of the Otsu thresholding algorithm as shown in:
- Step 1: Calculate a histogram for a two-dimensional image.
- Step 2: For a single threshold, determine the foreground and background variances (a measure of spread).
a. Do the background and foreground pixels' weight calculations.
b. Determine the mean value for both the background and foreground pixels.
- Step 3: Compute “within class variance”.
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Figure 2. The flowchart of Bat algorithm [32]
The range of grayscale values for the input image is i=0,1,…….., L-1, and the pixel numbers with the
grayscale are then the overall number of pixels in an image is computed as:
(6)
the probability of gray level k's occurrence is:
(7)
the gray level threshold t can separate the gray level of an image into class 1: (0,1,…….t), and class 2:
(t+1,t+2,….., L-1). The estimated class probabilities are as:
(8)
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(9)
and the means for the class are provided by:
(10)
(11)
the following are the individual class variances:
(12)
(13)
the goal is to pick the value that decreases the weighted within-class variance in (14).
(14)
3. METHOD
Figure 3 shows the block diagram of the proposed algorithm. Initially, the entered color image will
be converted to grayscale image. Then two optimization algorithms were applied, one of which is swarm-
based, which is the Bat algorithm, and the second is trajectory-based, which is the hill climbing algorithm.
Both algorithms will optimize the fitness function taken from the Otsu algorithm. The images resulted from
both algorithms will be evaluated in terms of F-score and computation time.
Figure 3. Block diagram of the proposed algorithm
Figure 4 shows the steps of the proposed algorithm using Bat algorithm to optimize fitness function
obtaining from Otsu algorithm.
- Step 1: The Bat algorithm produces in random an initial population of N solutions (bats) with one
dimension indicated by X where X=[x1, x2, ….., xN], xi is restricted into [0,…, L-1], and L represents the
maximum gray level of the input image, which are in the range [0,..., L-1]. All solutions' fitness values
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are examined, and cycle=1 is set. The Bat algorithm identifies the best effective solution as the best
solution before beginning the iterative search procedure.
- Step 2: Virtual bats are moved by (1), (2), and (3) to generate a new solution. Namely, by adjusting the
velocity matrix V and the frequency vector f using (1) and (2) respectively, new solutions are produced.
Following that, (3) was used in an update procedure for each solution in the search population X.
- Step 3: For the local search that updates the existing best solution vector by (4), a random walk with direct
exploitation is utilized. Namely, the local search is initiated with the proximity relying on pulse rate r.
- Step 4: The fitness function value (Otsu criterion) for the current best solution vector acquired in step 3
will be computed in this step using (14). Accept the new solution vector and change the old fitness value
if the fitness value of the solution vector is more than the old fitness value and the loudness A produced
by (5) is not loud. If not, preserve the best solution from before.
- Step 5: Keep the best solution vector with the best optimal solution. The cycle is increased by one.
- Step 6: Finish the algorithm if the cycle equals the maximum iterations allowed; otherwise, go to step 2.
Figure 4. Proposed algorithm using Bat algorithm and Otsu fitness function
Figure 5 shows the steps of the proposed algorithm using hill climbing to optimize the fitness function
obtaining from Otsu algorithm.
- Step1: The hill climbing algorithm produces an initial solution randomly indicated by x where, x is restricted
into [0,…, L-1], and L represents the maximum gray level of the input image, which are in the range [0,...,
L-1].
- Step2: Generating a new solution based on the neighbors of the current solution.
- Step3: The fitness function obtained from Otsu algorithm for the current best solution acquired in step
will be computed in this step using (14).
- Step4: Accept the new solution and change the old fitness value if the fitness value of the new solution is
better than the old fitness then go to 2, otherwise terminate the algorithm.
Figure 5. Proposed algorithm using hill climbing algorithm and Otsu fitness function
4. RESULTS AND DISCUSSION
The proposed algorithm was performed in python. Tests were applied on a PC with core (TM) i5 and
12 GB of RAM on the Windows 10 operating system. HYTA dataset is a repository that contains images and
ground-truth images that were used for the evaluation. The dataset prepared by the researchers in [33], stated
that the statistical properties of the cloud\sky images can be roughly split into two groups: unimodal and
bimodal. Typically, unimodal images consist of a single element (i.e., cloud or sky), while bimodal images are
made up of both sky and cloud components. In contrast to a bimodal image, which may have two or more
peaks and a big variance, the histogram of the unimodal image always has a single peak and a modest variance.
Step1: Producing the initial population of solutions randomly: X=[x1, x2, ….., xN] where
xi is restricted into [0,…, L-1], and L maximum gray level of input image.
Step2: Generation of new solutions using (1), (2), and (3).
Step3: Applying local searching using (4).
Step4: Generation of a new solution and computes fitness function based on Otsu criteria
in (14).
Step5: Keep track of the best solution.
Step6: Examine the termination criterion. If the cycle not equals the maximum iterations
go to Step 2, otherwise finish the algorithm.
Step1: Producing the initial solution randomly:
x where x is restricted into [0,…, L-1], and L maximum gray level of input image.
Step2: Generation new solution s from neighbors of x.
Step3: Compute Otsu fitness function using (14).
Step4: if fitness (s) is better than fitness(x) then s is the best solution and go to 2, otherwise
the algorithm finish.
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In the preprocessing, the input color image was converted into a grayscale image before applying the proposed
optimization algorithm. Figure 6 illustrates bimodal images from the HYTA dataset with their grayscale images
and histograms. 15 out of 32 images are selected from the HYTA dataset for evaluation. Several unimodal
images were excluded such as clear sky images as in Figure 7.
Figure 6. Grayscale images and histograms for bimodal images from HYTA dataset
Figure 7. Unimodal images in the HYTA dataset
Two experiments were conducted in the proposed work, the first experiment applied the Bat algorithm
to optimize the fitness function obtained from the Otsu algorithm. Based on practice work the best control
parameters obtained are: the size of population (N) is 10, number of iterations is 15, loudness (A) is 0.5, pulse
rate (r) is 0.5, minimum frequency (fmin) is 0, and maximum frequency (fmax) is 2. The second experiment uses
the hill climbing algorithm to optimize the fitness function obtained from the Otsu algorithm. Based on practice
work the best-selected parameters are: the number of iterations is 1000, and the step size is 0.7. Figure 8 shows
all the stages of the proposed algorithm in images, where the color image was converted to grayscale. The bat
algorithm was applied using the Otsu fitness function to get the first resulting image, and the hill climbing
algorithm was also applied using the Otsu fitness function to get the second resulting image. The resulting
images were evaluated by calculating the precision, recall, and f-score based on the ground truth image.
A comparison was made between the results of the two experiments, depending on the fitness function
value, as well as the computation time. Table 1 illustrates that the computational time of the hill climbing is
very slow compared to the Bat algorithm. The time needed by hill climbing for the first image is 3,407 seconds,
while the time consumed by the second algorithm is 0.693 seconds. Also, regarding the fitness function, the
Bat algorithm achieved better or close results. The fitness function for the second image is 556,084 using the
hill climbing and 549,719 using the Bat algorithm, where the lower value of the function indicates an optimal
threshold.
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Original Colored
Image
Grayscale image
Ground truth
image
Bat algorithm+Otsu
fitness function
Hill climbing+Otsu
fitness function
Figure 8. Resulted images for the proposed optimization algorithm
Table 1. A comparison between hill climbing and bat algorithm results
Input image
Hill climbing using Otsu algorithm
Bat algorithm using Otsu algorithm
Threshold
Fitness value
Time
Threshold
Fitness value
Time
91.77
575.296
3.407
90.749
575.554
0.693
136.504
556.084
2.65
137.284
549.719
0.735
136.504
476.8
7.168
139.833
475.7
1.182
Precision (P), recall (R), and F-score in (15), (16), and (17) were calculated to assess the proposed
work performance. As a first step, we use the output image and the ground truth image to calculate the
confusion matrix. A confusion matrix is utilized to assess how well a classification model works on a set of
test data whose true values are known. Table 2 illustrates the confusion matrix for binary classification. Each
pixel in the resulting image can belong to the foreground represented by 1 (white) or belong to the background
represented by 0 (black). True positives (TP) are pixels that were accurately predicted as positive values,
implying that the real class value is white and the predicted class value is also white. True negatives (TN) are
pixels that successfully predicted negative values, implying that the real class value is black and the predicted
class value is similarly black. False positives (FP) occur when a pixel's real class is black while its predicted
class is white. False negatives (FN) are pixels whose actual class is white but whose predicted class is black.
(15)
(16)
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(17)
Table 2. Confusion matrix for binary classification
Predicted class in output image
Actual class in ground truth image
White (Foreground)
Black (Background)
White
TP
FN
Black
FP
TN
Table 3 illustrates a comparison between the evaluation measures using the Bat algorithm and hill
climbing. We note that the P value for the both algorithms is close, but regarding the R, there is a clear
difference between them. Since the F-score represents the harmonic mean of a system's P and R values, the Bat
algorithm achieved the best performance.
Table 3. The performance measures for the proposed algorithm
Dataset
Algorithm
P
R
F-Score
HYTA
Hill climbing with Otsu algorithm
0.874533
0.676333
0.732733
Bat algorithm with Otsu algorithm
0.882944
0.757644
0.800833
The hill climbing algorithm is a trajectory-based and local search algorithm, it is more probable to
trap in local optima, premature convergence, and stagnation. This algorithm begins with one solution and tried
to find the best based on the neighbors therefore more computational time is consumed. Figure 9 shows the
change in the value of the fitness function during the cycles of the hill climbing algorithm until the best solution
is reached, which represents the best threshold value to represent the resulting image. The best solution is
indicated using the red dotted line.
Figure 9. Fitness function and candidate solution using hill climbing algorithm
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By utilizing fewer control parameters than other population-based algorithms, Bat algorithm is
straightforward, adaptable, and superior. In contrast to previous computational intelligence algorithms, our
technique does not require adjusting extraneous parameters like mutation, cross-over rate, etc. The simulation
experiment clearly demonstrates that the Bat algorithm's addition increases the effectiveness of image
thresholding while essentially maintaining its original accuracy. Also, the computational time is very low
compared with the non-population algorithms such as the hill climbing algorithm. Figure 10 shows the best
solution obtained using the Bat algorithm, the best solution represents the best threshold value to represent the
resulting image, also this Figure shows the set of solutions found by the Bat algorithm, the optimal solution
was indicated by the red dotted line.
Original Image
Resulted image
Threshold
Best solution
90.749
137.284
139.833
Figure 10. Best threshold value using Bat algorithm with Otsu fitness function
5. CONCLUSION
The proposed work has proven that the Bat algorithm can optimize the fitness function obtained from
the Otsu algorithm to quickly select the optimal threshold for image in cloud detection. The best threshold
value was obtained based on the Otsu criterion that represents the intra-class variance. trajectory-based
algorithms such as hill climbing is nonefficient because more time is needed for computation. On the other
hand, metaheuristic, swarm-based algorithms are more effective in relation to accuracy, and computational
time. Promising results have been obtained, as it provides an opportunity in the future for improving the image
thresholding algorithms by making a combination between the Bat algorithm and other nature-inspired
algorithms such as particle swarm optimization and ant colony.
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BIOGRAPHIES OF AUTHORS
Khamael Raqim Raheem received the B.Sc. degree in Computer Science from
the University of Babylon, Iraq, the M.Sc. degree in Information Technology-AI Department
from the University of UKM, Malaysia., and the Ph.D. degree in Information Technology
with specialization in image processing from the University of Babylon, Iraq. Her research
areas are text mining, image processing, named entity recognition, and recommendation
system. She can be contacted at email: khmrakrah@atu.edu.iq.
Hafedh Ali Shabat received the B.Sc. degree in Computer Science from the
University of Babylon, Iraq, the M.Sc. degree in Information Technology-AI Department
from the University of UKM, Malaysia., and the Ph.D. degree in Information Technology
with specialization in text mining from the University of Babylon, Iraq. His research areas
are text mining, classification, machine learning, named entity recognition, and optimization.
he used to hold an administrative post with the technical Institute of Babylon, AL-Furat AL-
Awsat Technical University (ATU) director of the Centre of the computer. He can be
contacted at email: h.ali@atu.edu.iq.
