OTSU BASED DIFFERENTIAL EVOLUTION METHOD FOR IMAGE SEGMENTATION Afreen Shaikh

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OTSU BASED DIFFERENTIAL EVOLUTION METHOD
FOR IMAGE SEGMENTATION
Afreen Shaikh
National Institute of Technology, Warangal
safreen@student.nitw.ac.in
Botcha Sharmila
National Institute of Technology, Warangal
bsharmila@student.nitw.ac.in
Murali Krishna
National Institute of Technology, Warangal
mmuralikrishna@student.nitw.ac.in
Dr. Sushil Kumar
National Institute of Technology, Warangal
kumar.sushil@nitw.ac.in
ABSTRACT
This paper proposes an OTSU-based differential evolution method for satellite image segmenta-
tion and compares it with four other methods such as Modified Artificial Bee Colony Optimizer
(MABC)[
1
], Artificial Bee Colony (ABC), Genetic Algorithm (GA) and Particle Swarm Optimization
(PSO) using the objective function proposed by Otsu for optimal multilevel thresholding. The experi-
ments conducted and their results illustrate that our proposed DE+OTSU algorithm segmentation can
effectively and precisely segment the input image, close to results obtained by the other methods. In
the proposed DE+OTSU algorithm, instead of passing the fitness function variables, the entire image
is passed as an input to the DE algorithm after obtaining the threshold values for the input number of
levels in the OTSU’s algorithm. The image segmentation results are obtained after learning about the
image instead of learning about the fitness variables. In comparison to other segmentation methods
examined, the proposed DE+OTSU algorithm yields promising results with minimized computational
time comparison to some algorithms.
1 INTRODUCTION
Image segmentation has a vital part as a pre-processing step in image processing. In particular, it aims at grouping and
partitioning pixels within meaningful regions to analyze the image in a detailed manner. Image segmentation applies to
varied Computer Vision tasks like Content-based image retrieval, Medical Imaging, Object detection and identification,
and Object recognition tasks (like face and fingerprint), among others.
Segmentation methods can be subdivided broadly as (a) edge and line-oriented segmentation methods, (b) region
growing methods, (c) clustering, and (d) region splitting methods. Ant Colony Optimisation (ACO), Particle Swarm
Optimization (PSO), Bacterial Foraging (BF), and Differential Evolution (DE) are regarded as popular choices for the
segmentation of complex images due to their exhaustive searching capability. Because of its clearness and stability,
thresholding is coined as one of the most popular image segmentation methods. Typically, satellite images have
insignificant illumination features because of multiple kinds of environmental distributions. They contain diverse
objects (regions), like vegetation, water bodies, and territory. However, these areas lack clear demarcation because of
low spatial resolution. Hence, segmenting various land cover parts in these images is a complicated task.
One of the key aspects of image segmentation is thresholding (Agrawal et al., 2013)[
12
]. Many algorithms to perform
global level thresholding can be found in the existing literature which aim at segmenting images and extract compelling
and meaningful patterns (Rosin, 2001; Portesde et al., 2004; Zahara et al., 2005).
arXiv:2210.10005v1 [cs.CV] 18 Oct 2022
Afreen et al.
Otsu in the year 1979 [
13
] presented a method for selecting threshold from grey-level histograms. But, inadequate
articulation of between-class variance raises the cost of computation of the algorithm, specifically in the selection of
multi-level threshold. Otsu’s thresholding aims at automatic threshold selection and region-based segmentation and is
one of the most accurate techniques for image thresholding because of its simple calculation. Differential Evolution is a
reasonably recent population-based evolutionary model which depends on the mutation operation as its prominent step.
It efficiently explores large search spaces and exhibits superior results in the following criteria: (1) shorter convergence
speed than other evolutionary algorithms, (2) fewer number of parameter adjustments, making it particularly easy to
implement.
Tsai (1985)[
14
] uses the moment-preserving principle to determine thresholds of grey-level input images - the Tsallis
entropy technique, a prominent function used for image thresholding. Kittler et al.(1986) work with the assumption that
the grey levels of every entity within an image are usually distributed. Kapur et al. (1985) further introduced a robust
method for grey-level image thresholding by utilizing the histogram entropy (Kapur et al., 1985)[15].
Entropy-based approaches have earned popularity among all the distinctive image thresholding methods. PCO,
influenced by the social behaviours like flocking of birds or schooling of fishes (Akay et al., 2013[
16
]; Maitra et al.
2008[
17
]; Yin, et al. 2007[
18
]), ant colony optimization (ACO) influenced by the pasturing conduct of ant colonies
(Ye et al., 2005[
20
]; Tao et al., 2007[
19
]) Artificial Bee Colony (ABC) inspired by the pasturing conduct of honey bee
swarm (Cuevaset al., 2012 [21], Akay et al., 2013;).
Another recent area of research inspired by the coordinated intelligence in a swarm of insects or animals has also
emerged called Swarm intelligence. One of the widespread and recently developed Swarm Intelligence-based techniques
is the ABC algorithm, presented by Karaboga D. (2005)[
22
], that simulates the foraging behavior of honey bee colonies.
Numerous studies have demonstrated that the performance of Artificial Bee Colony (ABC) method is competitive and
comparable with other population-based techniques.
The MABC method given by Bhandari et al.(2014) introduces an advanced solution search formula (Gao et al., 2012)
in charge for its more promising search solution. Within this search equation, the bee explores only closer to the best
solution of the iteration before to improve exploitation. The results demonstrate that MABC is best suited for multilevel
thresholding of images to attain optimal thresholds for satellite images in comparison to Artificial Bee Colony based
algorithms and Particle Swarm Optimization based techniques. Evaluating the advantages, such algorithms are the
preferred choice for finding the optimum thresholds in simple images. For example, the Genetic Algorithm (GA) and
the improved Genetic Algorithm (Zhang et al., 2014 [23]) are frequently in use to multilevel thresholding scenarios.
The Swarm Intelligence based computing methods can find efficient and optimal solutions for any objective function
and have been widely used with an ability to generate highly accurate results in case of complex problems as well. It
has also been found by statistical analysis that the Swarm Intelligence based algorithms perform well in multi-level
thresholding scenarios (Kurban et al., 2014 [24]).
2 BRIEF EXPLANATION OF THE ALGORITHMS USED IN THIS STUDY
2.1 Otsu’s thresholding
2.1.1 Bi-level thresholding
In Bi-level thresholding, the aim is to find a threshold to minimize the variance between classes in the segmented image.
Otsu’s algorithm tends to achieve better results when two different peaks are present in the histogram of the original
image, one corresponding to the background and the other to the foreground. The entire range of pixels are iterated and
the Otsu’s threshold is determined when the between-class variances are minimum. Hence, the Otsu’s threshold tends to
be decided by the class with greater variance.Hence, Otsu’s method tends to produce sub-optimal results when there is
an occurrence of two or more peaks within the histogram of the image or if one of the classes has a significant variance.
The total mean and variance are calculated based on the following formulas: The entire set of pixels are distributed into
2 classes,
C1pixels having grey levels [1, t]
C2pixels having grey levels [t+ 1, ..., L].
where tcorresponds to Otsu’s threshold
The probability distribution of the two classes is denoted by:
C1:p1
w1(t), ..., pr
w1(t)(1)
Otsu based Differential Evolution method for Image Segmentation
and
C2:pr+1
w2(t), ..., pL
w2(t)(2)
Where, w1(t) = Pr
i=1 piand w2(t) = PL
i=r+1 pi
The class mean for the two classes µ1and µ2are defined by:
µ1=
r
X
i=1
ipi
w1(t)(3)
µ2=
L
X
i=r+1
ipi
w2(t)(4)
Otsu’s between-class variance based on discriminate analysis of the threshold image is defined as:
σ2
B=w1(µ1µT)2+w2(µ2µT)2(5)
For bi-level thresholding, the optimal threshold t* is chosen to maximize between-class variance n, i.e.
t=argt<lmaxσ2
B(t)(6)
2.1.2 Multilevel Thresholding
The first step in the algorithm is to obtain the Otsu’s threshold and the class means of the two classes divided by the
Otsu’s threshold. Further, in multi-level thresholding, the pixels of the image are divided into three categories instead of
two categories determined by Otsu’s threshold. The three categories correspond to the following: (a) the ’foreground’
region - group of pixel with values >= the larger mean, (b) the ’background’ region - group of pixels with values <=
to the smaller mean and (c) the ’to-be-determined (TBD)’ region - group of pixels with values between the two class
means.
In iteration
i+ 1
, the algorithm retains the ’foreground’ and ’background’ regions from iteration
i
and re-applies the
Otsu’s method only on the ’to-be-determined’ region to further divide it into three classes again. When this iteration
stops after satisfying a pre-defined criterion, the final ’to-be-determined (TBD)’ region is then divided into two classes -
foreground and background instead of three. Lastly, the foreground regions from all the iterations are combined to get
the final foreground class and the final background region is also determined likewise.
For an image represented by
L
no.of grey levels
0,1, ..., L 1
, we could develop the image histogram
H=
{f0, f1, ..., fL1}, where fiis the frequency of grey level iin the image. Let
N=
L1
X
i=0
fi
determine the total no. of pixels in the image. The occurrence probability of ith grey level is defined by:
pi=fi
N(7)
It can be easily be illustrated that pi0and PL1
i=0 pi= 1.
Otsu’s algorithm divides the image into
K+ 1
clusters
{C0, C1, ..., CK}
using
K
no. of thresholds chosen from the set
T={(t1, t2, ..., tK)|0< t1< ... < tK< L}
where
CK
is the set of pixels with grey levels
{tK, tK+1, ..., tK+1 1}
.
Where
t0= 0
and
tK+1 =L
. For every cluster
CK
, the cumulative probability
wK
and mean grey level
µK
are defined
by:
wk=X
iCk
, k{0,1,2, ..., K}(8)
µk=X
iCk
ipi
wk
, k{0,1,2, ..., K}(9)
Afreen et al.
The mean intensity of the whole image µTand the between-class variance σ2
Bare defined by:
µT=
K
X
k=0
wkµk=
L1
X
i=0
ipi(10)
and
σ2
B=
K
X
k=0
wk(µkµT)2=
K
X
k=0
wkµ2
kµ2
T(11)
In Otsu’s method, the threshold levels for each cluster are selected on the basis of maximizing the variance among
means of the cluster (Huang et al., 2011). The optimal thresholds at maximum between-class variance are determined
by:
(t
1, t
2, ..., t
K) = {σ2
B(t1, t2, ..., tK)}(12)
3 DIFFERENTIAL EVOLUTION (DE)
In comparison to other evolutionary algorithms, the Differential Evolution (DE) algorithm aims to reserve the global
search strategy based on population and employs a simple mutation function of the differential and one-on-one
competition, reducing the operation’s genetic complexity. At the same time, the specific memory ability of DE allows
it to dynamically track the current search to adjust its search strategy with robust global convergence. Hence, it is
suited for the complex environments of the optimization problem. Fundamental operations like selection, crossover,
and mutation are the foundation of the Differential Evolution algorithm.
3.1 How DE is used in the proposed algorithm?
Initially, the image to be segmented is made to run through OTSU’s multilevel thresholding, on the basis of the number
of levels(
L
) the image has to be segmented. The output of this step yields us with ‘
L
’ threshold values which act as
partitions for the pixel intensities. These partitions divide the pixel intensity range (0-255) into ‘
L+ 1
’ clusters. Based
on the pixels belonging to the image that fall into a particular cluster, the cluster centre is defined using the mean of the
pixels (falling in that cluster).
Now, the image to be segmented is given as input to the DE algorithm. Each of the ‘
G
’ generations has Np number of
populations, where population size is equal to the count of the image pixels. After each generation, the best population
is evaluated based on the least value of fitness function, which is a measure to the MSE (mean square error) distance
of each pixel in the population to its corresponding cluster centre. The next generations are populated using this best
population as described later in the algorithm. The best population of the last generation is again reshaped into image
format, which form the segmented image.
4 PROPOSED ALGORITHM
4.1 Algorithm pre-processing
In our implementation an input image and the number of levels (
L
) are given as input to the algorithm which would
return the cluster partition values (cp1, cp2, ..., cpL).
Cluster ranges,
(0, cp1),(cp1+ 1, cp2), ..., (cpL+ 1,255)
are computed from the cluster partition values obtained after
the thresholding of the image.
Cluster centres, (cc1, cc2, ..., ccL+1)are calculated as follows :
cci=Ppixi
|pixi|(13)
Where,
pixi= pixels in the cluster range (0, cpi)
|pixi|= pixels in the cluster range (0, cpi)
摘要:

OTSUBASEDDIFFERENTIALEVOLUTIONMETHODFORIMAGESEGMENTATIONAfreenShaikhNationalInstituteofTechnology,Warangalsafreen@student.nitw.ac.inBotchaSharmilaNationalInstituteofTechnology,Warangalbsharmila@student.nitw.ac.inMuraliKrishnaNationalInstituteofTechnology,Warangalmmuralikrishna@student.nitw.ac.inDr.S...

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