Emes 2017 Paper 55 [626717]

Multilevel Image Thresholding
Using Elephant Herding Optimization Algorithm
Eva Tuba
Faculty of Mathematics
University of Belgrade
Belgrade, Serbia
[anonimizat] Alihodzic
Faculty of Mathematics
University of Sarajevo
Sarajevo, BiH
[anonimizat] Tuba
Graduate School of Computer Science
John Naisbitt University
Belgrade, Serbia
[anonimizat]
Abstract —Digital images are widely used and numerous ap-
plication in different scientific fields use digital image processing
algorithms where image segmentation is a common task. Thresh-
olding represents one group of algorithms for solving that task
and Kapur’s and Otsu’s methods are well known criteria often
used for selecting thresholds. Finding optimal threshold values
by these two methods represents a hard optimization problem
and swarm intelligence algorithms have been successfully used for
solving such problems. In this paper we adjusted recent elephant
herding optimization algorithm for multilevel thresholding by
Kapur’s and Otsu’s method. Performance was tested on stan-
dard benchmark images and compared with four other swarm
intelligence algorithms. Elephant herding optimization algorithm
outperformed other approaches from literature and it was more
robust.
Keywords — Multilevel image thresholding, Kapur’s method,
Otsu’s method, Swarm intelligence, Elephant herding optimiza-
tion.
I. I NTRODUCTION
Digital images are widely used in various areas. One of the
main reasons is simplicity of digital image processing. Digital
images are matrices of integers and their processing reduces
to applying mathematical formulas and algorithms to matrix
elements. Algorithms for digital image processing have been
proven to be powerful tools for many different applications in
various fields such as medicine [1], astronomy [2], etc.
Image segmentation represents an important task in nu-
merous applications and it can be described as a problem
of dividing an image into disjunctive parts [3], [4], [5]. The
result of segmentation is partitioned image where each part
represents some feature such as background, objects, persons,
etc. Segmentation is widely used method hence many different
approaches were proposed [6], [7]. Some of the well known
methods for image segmentation are thresholding techniques
using criteria such as Kapur’s and Otsu’s method. Finding
optimal threshold values by these two methods represents hard
optimization problem. For these type of problems, beside other
methods, swarm intelligence algorithms such as particle swarm
optimization [8], artificial bee colony [9], firefly algorithm
[10], etc. have been used.
In this paper we propose adjustment of the recent swarm
intelligence algorithm, elephant herding optimization (EHO),
for multilevel image thresholding using Kapur’s and Otsu’s
criteria.
M. Tuba was supported by the Ministry of Education, Science and
Technological Development of Republic of Serbia, Grant No. III-44006.The rest of the paper is organized as follows. Section
II describes Kapur’s and Otsu’s criteria for multilevel im-
age thresholding. Elephant herding optimization algorithm
is described in Section III. Experimental results along with
comparison with other algorithms from literature are given in
Section IV. At the end, the conclusion and future development
are given in Section V.
II. O PTIMAL THRESHOLDING MODEL
In literature, different algorithms for image segmentation
were proposed. One group of such algorithms is based on
thresholding. Based on one or more threshold values, image
is partitioned. Pixels whose values are between two successive
threshold values are marked with the same gray shade or color.
For finding optimal threshold values different approaches
have been proposed and in these paper two of them will be
presented and tested.
A. Kapur’s Thresholding Method
Kapur’s thresholding method is based on image entropy
which measures the spread of the pixels’ gray levels [11].
Entropy is minimal for one shade images while entropy
reaches its maximal value for the image where all possible
pixel values are equally occupied. Formal definition of image
entropy is given as follows. Let IbeLlevel gray image
with an intensity histogram xand probabilities piof appearing
intensity values iwherei= 1;2;:::;L1. Entropy of the
imageIis defined by the following equation:
H(x) =nX
i=1piln(pi) (1)
Kapur’s method is defined for an image Iwithnpixels
of gray levels from the set f0;1;:::;L1g. Number of
pixels at gray level iis denoted as h(i)while probabilities
of occurrences of that gray level are pi=h(i)=n. Kapur’s
method defines the optimal threshold values as maximal value
for the following objective function:
f(t0;t1;:::;t k1) =kX
i=0Hi (2)
where the entropies Hiare calculated as:

H0=t01X
i=0pi
w0lnpi
w0; w 0=t01X
i=0pi
H1=t11X
i=t0pi
w1lnpi
w1; w 1=t11X
i=t0pi
…
Hk=L1X
i=tk1pi
wklnpi
wk; w k=L1X
i=tk1pi(3)
B. Otsu’s Thresholding Method
Otsu’s method [12] obtains optimal thresholds by classi-
fying gray values so that the intra-class variance is minimal
while between-class variance is maximized. For image I
represented by Lgray levels with the probabilities piof pixels
at leveliOtsu’s method is defined as follows. The first step
is to find cumulative probabilities for each class Aiwhere
i= 0;1; :::;k :
w0=t01X
i=0pi; w 1=t11X
i=t0pi; :::; w k=L1X
i=tk1pi(4)
wheretlare threshold values. Optimal kthreshold values in
Otsu’s method are calculated by maximizing the following
objective function:
f(t0;t1;:::;t k1) =kX
i=0i (5)
where thefunctions are:
0=w0 t01X
i=0ipi
w0L1X
i=0ipi!2
1=w1 t11X
i=t0ipi
w1L1X
i=0ipi!2
…
k=wk0
@L1X
i=tk1ipi
wkL1X
i=0ipi1
A2(6)
In both cases, for Kapur’s and Otsu’s method, global
optimum for objective functions can be found by exhaustive
search. Exponential growth with number of needed thresh-
olds makes exhaustive search intractable and finding optimal
thresholds represents hard optimization problem. For hard
optimization problems swarm intelligence algorithms were
successfully used. In this paper we propose adjustment of the
recent elephant herding optimization algorithm to maximize
objective functions defined by Eqs. 2 and 5.
III. E LEPHANT HERDING OPTIMIZATION ALGORITHM
Elephant herding optimization algorithm was proposed by
Wang et. al. in 2016 [13]. For purposes of creating swarm in-
telligence algorithm, elephant herding behavior was simplified
to the three rules: elephant population is composed of clans
where elephants live under the leadership of a matriarch andfixed number of elephants in each generation leave families
and live far away from their clans.
Formal description of the EHO is as follows. Elephant
population is divided into kclans. Each clan is leaded by
matriarch. Each member jof clanimoves according to
matriarchci[13]:
xnew;ci;j =xci;j+(xbest;cixci;j)r (7)
wherexnew;ci;j represents new position of elephant jin clan
iwhilexci;jis its old position, xbest;ci is matriarch or the
best solution of clan ci,2[0;1]is a scale factor which
determines the influence of the matriarch and r2[0;1]is
random number that can improve diversity of the population
in later stages of the algorithm. Position of matriarch, the best
elephant in clan is updated by the following equation [13]:
xnew;ci =xcenter;ci (8)
where2[0;1]is parameter that controls influence of the
xcenter;ci which is defined as:
xcenter;ci;d =1
ncinciX
l=1xci;l;d (9)
where 1dDisdthdimension,Dis total dimension of
the space and nciis the number of elephants in clan i.
Male elephants that separate from the group are used to
model exploration. In each generation and in each clan mci
elephants with the worst fitness values are moved according
to the following equation:
xworst;ci =xmin+ (xmaxxmin+ 1)rand (10)
wherexminandxmax represent lower and upper bound of the
search space, respectively. Parameter rand2[0;1]is random
number from uniform distribution.
A. EHO Applied for Multilevel Thresholding Problem
The number of threshold values represents the dimension
of the problem. Each threshold could be any integer from the
range [0;255] since in this paper all test images have 256
levels of gray. EHO algorithms is proposed for search in real
space and threshold values need to be integers. This problem
is overcome by simply rounding the obtained solution since
light intensity in reality is real function but the standard is to
store it as integer numbers.
The second specific condition for multilevel thresholding
task is that threshold values need to be sorted, i.e. threshold
values have to satisfy inequality ti< ti+1. This problem is
also easy to solve. Elements of the generated solution vector
by EHO are sorted and then used further in the algorithm.
IV. E XPERIMENTAL RESULTS
The proposed algorithm was implemented using Matlab
R2016a. Experiments were performed on the platform with the
following features: Intel R
CoreTMi7-3770K CPU at 4GHz,
8GB RAM, Windows 10 Professional OS.
The proposed method was tested on six standard benchmark
images: Barbara, Living room, Boats, GoldHill, Lake and
Aerial. Images are chosen so that results can be compared with

TABLE I
COMPARISON OF THE MEAN VALUES AND STANDARD DEVIATIONS OF KAPUR ’S ENTROPY CRITERIA OPTIMIZED BY PSO, DE, CS, FA AND EHO
Alg. KBarbara Living room Boats
Mean values St. Dev. Mean values St. Dev. Mean values St. Dev.
PSO2 12.668336540 5.33E-15 12.405792709 1.64E-04 12.574798244 1.42E-14
3 15.747087798 1.42E-14 15.552015642 2.82E-03 15.820679619 8.84E-04
4 18.549612938 1.94E-02 18.467328310 6.64E-03 18.640100415 3.00E-02
5 21.241857967 6.71E-03 21.131564234 2.18E-02 21.392020144 4.12E-02
DE2 12.668336540 5.33E-15 12.405985592 5.33E-15 12.574798244 1.42E-14
3 15.747087798 1.42E-14 15.552578874 3.03E-04 15.820902860 8.88E-15
4 18.556749938 1.51E-04 18.470970822 3.16E-04 18.655660844 1.64E-04
5 21.245566656 2.34E-04 21.149062508 1.78E-03 21.401458219 3.21E-04
CS2 12.668336540 5.33E-15 12.405985592 5.33E-15 12.574798244 1.42E-14
3 15.747087798 1.42E-14 15.552622213 1.07E-14 15.820902860 8.88E-15
4 18.556786861 2.49E-14 18.471055578 2.49E-14 18.655733570 1.07E-14
5 21.245645311 1.42E-14 21.149400604 1.64E-03 21.401608305 7.11E-15
FA2 12.668336540 5.33E-15 12.405985592 5.33E-15 12.574798244 1.42E-14
3 15.747087798 1.42E-14 15.552622213 1.07E-14 15.820902860 8.88E-15
4 18.556786861 2.49E-14 18.471014902 2.85E-04 18.655723798 4.79E-05
5 21.245645311 1.42E-14 21.149483979 1.46E-03 21.401583877 7.33E-05
EHO2 12.668336540 0.00E-15 12.405985592 1.98E-14 12.574798244 1.43E-15
3 15.747087798 2.01E-14 15.552622213 1.13E-13 15.820902860 1.91E-15
4 18.556786861 1.14E-10 18.471014902 3.52E-03 18.655730289 6.84E-06
5 21.245645311 1.93E-12 21.149483979 1.33E-03 21.400103248 1.21E-04
Alg. KGoldhill Lake Aerial
Mean values St. Dev. Mean values St. Dev. Mean values St. Dev.
PSO2 12.546393623 7.11E-15 12.520359742 5.33E-15 12.538208248 1.78E-15
3 15.607747002 1.42E-14 15.566286745 1.24E-14 15.751881495 5.33E-15
4 18.414173744 2.07E-04 18.357505953 2.02E-02 18.615899102 1.78E-14
5 21.099092699 1.28E-04 21.015922726 4.40E-02 21.192396874 5.44E-02
DE2 12.546393623 7.11E-15 12.520359742 5.33E-15 12.538208248 1.78E-15
3 15.607743578 2.40E-05 15.566286745 1.24E-14 15.751881495 5.33E-15
4 18.603017275 1.78E-03 18.365579671 2.79E-04 18.615769177 6.36E-04
5 21.409946039 3.55E-15 21.024780111 4.59E-04 21.210411012 1.12E-04
CS2 12.546393623 7.11E-15 12.520359742 5.33E-15 12.538208248 1.78E-15
3 15.607747002 1.42E-14 15.566286745 1.24E-14 15.751881495 5.33E-15
4 18.414197322 6.53E-05 18.365636309 1.78E-14 18.615899102 1.78E-14
5 21.099125539 6.59E-05 21.024962923 5.95E-05 21.210455499 1.78E-15
FA2 12.546393623 7.11E-15 12.520359742 5.33E-15 12.538208248 1.78E-15
3 15.607747002 1.42E-14 15.566286745 1.24E-14 15.751881495 5.33E-15
4 18.414213765 2.13E-14 18.365636309 1.78E-14 18.615899102 1.78E-14
5 21.099138996 0.00E-00 21.024982760 0.00E-00 21.210455499 1.78E-15
EHO2 12.546393623 1.91E-14 12.520359742 1.08E-14 12.538208248 1.71E-15
3 15.607747002 1.13E-14 15.566286745 4.54E-14 15.751881495 5.25E-15
4 18.414213765 2.13E-14 18.365636309 2.13E-10 18.615899102 1.28E-15
5 21.099138996 0.00E-00 21.024982760 0.00E-00 21.210455499 1.12E-15
results presented in [6] where particle swarm optimization,
differential evolution, cuckoo search and firefly algorithm
were tested for the same problem. Images are available
freely for download: Barbara, Boats and Goldhill are
from https://homepages.cae.wisc.edu/ ece533/images/,
Living room and Lake are from
http://www.imageprocessingplace.com/root files V3/
image databases.htm, while Aerial image was taken from
http://sipi.usc.edu/database/database.php?volume=misc.
EHO algorithm parameters were set as follows. Population
size was set to 200 and the number of clans was 5. Stopping
criteria for the algorithm was maximal evaluation number
which was set to 50,000. Each test was run 30 times. Mean and
standard deviation were presented as results. Optimal threshold
values were searched for 2, 3, 4 and 5 level thresholding
problem. In [6] optimal thresholds obtained by exhaustive
search were presented.
In Table I results for Kapur’s method are presented. For the
first test image, Barbara, DE and PSO failed to find optimal
threshold values for 5-level and 4-level thresholding while
EHO, FA and CS found optimal thresholds for all tests. For
test image Living room, all algorithms except FA and EHO
failed to find the best solution for 5-level image thresholding,
however EHO had smaller standard deviation than FA, which
means that it is more robust. For 4-level thresholding, EHOalong with CS obtained optimal value of fitness function, while
the others did not. EHO, CS and FA found the best solution for
2 and 3 level thresholding which was not the case with PSO
and DE. For Boats, CS found the best solution for 5-level
thresholding, while EHO was better than PSO, but worse than
FA and DE. For 4-level thresholding again only CS found the
best solution. For 2 and 3 level thresholding again FA, CS
and EHO provided better results, but EHO had the smallest
standard deviation. The fourth test image, Gold hill was not a
problem for FA and EHO, while CS, PSO and DE failed to find
best solutions for 4 and 5 level thresholding. Again, optimal
threshold values for 2 and 3 level thresholding were found
by EHO, CS and FA, while PSO has shown worse results for
both levels. In case of the last two test images, EHO, CS and
FA found optimal solutions, while PSO and DE did not for 4
and 5 level thresholding.
In Table II the results for Otsu’s method are presented. The
only case where EHO did not obtain optimal value is for 5-
level thresholding for image Boats. In this case none of the
algorithms found the optimal value for fitness function. In most
of the cases FA and CS both found optimal fitness values but
EHO had smaller values for standard deviation which means
that it is more robust than FA and CS.

TABLE II
COMPARISON OF THE MEAN VALUES AND STANDARD DEVIATIONS OBTAINED FOR THE PSO, DE, CS, FA AND EHO BASED ON OTSU’S CRITERION
Alg. KBarbara Living room Boats
Mean values St. Dev. Mean values St. Dev. Mean values St. Dev.
PSO2 2608.610778507 1.82E-12 1627.909172752 0.00E-00 1863.346730649 0.00E-00
3 2785.163280467 2.27E-12 1760.103018395 2.27E-13 1994.536306242 1.59E-12
4 2856.260804034 6.66E-03 1828.864376614 1.59E-12 2059.866220175 4.22E-04
5 2890.975549258 5.05E-02 1871.984827146 2.29E-02 2092.771150715 8.36E-03
DE2 2608.610778507 1.82E-12 1627.909172752 0.00E-00 1863.346730649 0.00E-00
3 2785.162093432 8.31E-03 1760.103018395 2.27E-13 1994.535269293 7.26E-03
4 2856.261305066 2.80E-03 1828.860328016 1.30E-02 2059.865271461 6.85E-03
5 2890.971346990 2.05E-02 1871.976701063 2.34E-02 2092.766907541 2.71E-02
CS2 2608.610778507 1.82E-12 1627.909172752 0.00E-00 1863.346730649 0.00E-00
3 2785.163280467 2.27E-12 1760.103018395 2.27E-13 1994.536306242 1.59E-12
4 2856.261511717 2.45E-03 1828.864376614 1.59E-12 2059.866280428 1.36E-12
5 2890.976540127 4.85E-04 1871.990230213 2.70E-03 2092.775817560 1.03E-03
FA2 2608.610778507 1.82E-12 1627.909172752 0.00E-00 1863.346730649 0.00E-00
3 2785.163280467 2.27E-12 1760.103018395 2.27E-13 1994.536306242 1.59E-12
4 2856.262131671 4.55E-13 1828.864376614 1.59E-12 2059.866280428 1.36E-12
5 2890.976609405 3.64E-12 1871.990616316 0.00E-00 2092.773515829 3.57E-03
EHO2 2608.610778507 0.00E-00 1627.909172752 0.00E-00 1863.346730649 0.00E-00
3 2785.163280467 0.00E-00 1760.103018395 1.07E-13 1994.536306242 1.52E-12
4 2856.262131671 5.65E-10 1828.864376614 1.01E-14 2059.866280428 6.23E-13
5 2890.976609405 1.78E-12 1871.990616316 2.78E-09 2092.773321720 1.41E-05
Alg.K Goldhill Lake Aerial
Mean values St. Dev. Mean values St. Dev. Mean values St. Dev.
PSO2 2069.510202452 4.55E-13 3974.738214185 3.64E-12 1808.171050536 2.27E-13
3 2220.372641501 1.36E-12 4112.631097687 4.55E-12 1905.410606582 1.14E-12
4 2295.380095430 1.48E-03 4180.883976390 7.41E-03 1955.085619462 7.65E+00
5 2331.156479206 3.56E-04 4216.942888298 3.99E-03 1979.170306260 2.51E+00
DE2 2069.510202452 4.55E-13 3974.738214185 3.64E-12 1808.171050536 2.27E-13
3 2220.372641501 1.36E-12 4112.631097687 4.55E-12 1905.410606582 1.14E-12
4 2295.380095430 1.48E-03 4180.883976390 7.41E-03 1955.085619462 7.65E+00
5 2331.156479206 3.56E-04 4216.942888298 3.99E-03 1979.170306260 2.51E+00
CS2 2069.510202452 4.55E-13 3974.738214185 3.64E-12 1808.171050536 2.27E-13
3 2220.372641501 1.36E-12 4112.631097687 4.55E-12 1905.410606582 1.14E-12
4 2295.380469158 2.27E-12 4180.886161109 0.00E-00 1957.017965982 0.00E-00
5 2331.155240485 4.76E-03 4216.943583790 9.09E-13 1980.651043072 1.16E-02
FA2 2069.510202452 4.55E-13 3974.738214185 3.64E-12 1808.171050536 2.27E-13
3 2220.372641501 1.36E-12 4112.631097687 4.55E-12 1905.410606582 1.14E-12
4 2295.380469158 2.27E-12 4180.886161109 0.00E-00 1957.017965982 0.00E-00
5 2331.156597921 2.27E-12 4216.943583790 9.09E-13 1980.656737348 9.09E-13
EHO2 2069.510202452 2.31E-13 3974.738214185 2.47E-12 1808.171050536 2.03E-13
3 2220.372641501 9.28E-13 4112.631097687 3.92E-12 1905.410606582 6.91E-13
4 2295.380469158 1.16E-12 4180.886161109 0.00E-00 1957.017965982 3.56E-13
5 2331.156597921 1.79E-12 4216.943583790 1.42E-12 1980.656737348 3.49E-13
V. C ONCLUSION
In this paper, we adjusted and tested recently proposed
elephant herding optimization algorithm for multilevel image
thresholding problem solved by Kapur’s and Otsu’s method.
Precision and robustness of the proposed algorithm was tested
on standard benchmark images and results were compared
with other approaches from literature. It has been shown that
elephant herding optimization algorithm successfully solved
multilevel thresholding problem in more cases than other
algorithms and additionally had smaller variance in practically
all cases which proves the robustness of the algorithm. As
further research EHO can be used using different multilevel
threshold methods such as Tsallis method and it can be tested
for larger number of thresholds.
ACKNOWLEDGMENT
M. Tuba was supported by the Ministry of Education, Sci-
ence and Technological Development of Republic of Serbia,
Grant No. III-44006.
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