A novel method for multi-level image thresholding using Particle Swarm Optimization algorithms

Abstract

The selection of threshold is one the general methods in image segmentation, but often the selection of the optimal value for threshold is a challenge for researchers. In this paper we proposed a fast and optimal method for selection of good enough threshold value based on Particle Swarm Optimization algorithms (PSOa). To achieve the fast speed in the proposed method, five types of PSO algorithms have been evaluated. The brief Introduction of the principle OTSU, as the fitness function of PSO algorithm is given. Moreover, the proposed method has been applied in various experiments in comparison with famous methods based on several standard test Images. Experimental results demonstrated that the proposed method outperformed better in comparison of other methods.

Full text

A Novel Method for Multi-Level Image Thresholding Using Particle Swarm
Optimization Algorithms
Somayeh Nabizadeh
a
,
Karim Faez
a,b
,
Sude Tavassoli
c
,
Alireza Rezvanian
a
a
Department of Computer Engineering, Islamic Azad University, Qazvin branch, Iran
b
Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran
c
Department of Computer Engineering, Islamic Azad University, Rudsar branch, Iran
E-mail
a
:
s_nabizadeh@qiau.ac.ir
Abstract- The selection of threshold is one the general methods
in image segmentation, but often the selection of the optimal
value for threshold is a challenge for researchers. In this paper
we proposed a fast and optimal method for selection of good
enough threshold value based on Particle Swarm Optimization
algorithms (PSOa). To achieve the fast speed in the proposed
method, five types of PSO algorithms have been evaluated.
The brief Introduction of the principle OTSU, as the fitness
function of PSO algorithm is given. Moreover, the proposed
method has been applied in various experiments in
comparison with famous methods based on several standard
test Images. Experimental results demonstrated that the
proposed method outperformed better in comparison of other
methods.
Keywords— Image Processing, Image Segmentation, Multi-
Level Thresholding, Particle Swarm Optimization
I. INTRODUCTION
Image segmentation consists of one or more processes to
partitioning image into several areas in where features of
intra-area have the most similarity and inter-areas have the
lowest similarity between each others areas. Usually After
some enhancement on images [1], the image segmentation is
used often as a basic method in image pre-processing to
image analysis [2]. In general, all segmentation methods are
divided into two categories: threshold based methods and
spatial based methods. Thresholding-based method as
simple and basic methods have been became popular among
researchers in most cases [2]. According to the Information
Scientific Institute (ISI) knowledge, high volume of
published papers about this topic indicates the importance of
the image segmentation [2], so the column chart of indexed
published papers in ISI from 2004 to 2009 is shown in
Figure 1.
Figure 1. Comparison of published papers about image segmentation in ISI
knowledge
The threshold based methods change the image into two
main areas: foreground and background, so that they create a
binary image from the initial gray level image. In this case
for thresholding if we assume a threshold value equals to T,
then thresholding process can be considered by equation (1):
(1)
⎩
⎨
⎧
≤
>
=Tyxf
Tyxf
yxg ),( if 0
),( if 1
),(
In this case a histogram chart is considered for a sample
image as figure 2 that the T value corresponding to valley of
the chart for threshold [2].
Figure 2. A typical histogram with one treshold (T)
If the threshold value generalized as multiple (multi-
level image), makes multi-threshold mode, in which case the
form of histogram becomes as figure 3.
Figure 3. A typical histogram with two treshold (T1 and T2)
Although the ideal histogram of image in grayscale is
like two peaks with one valley as figure 2, Most of the real
images are same figure 3, so it is not easy to be able to
obtain the proper threshold value simplicity. To solve this
problem at the first, Otsu principle [4] proposed in 1979,
Otsu considered statistical properties of image for the
selection of proper threshold value. Moreover, the numerous
expansions methods based on Otsu principle have been
proposed [3], [6], [7]. In [8] error based neuro-fuzzy method
V4-271
978-1-4244-6349-7/10/$26.00 c
2010 IEEE
Authorized licensed use limited to: Amirkabir Univ of Tech Trial user. Downloaded on July 02,2010 at 07:16:11 UTC from IEEE Xplore. Restrictions apply.

is used to obtain the optimum threshold value, but this
method needs a training process, which is time consuming
and proper sampling for training. Also selection of the
optimal threshold value have been presented by evolutionary
methods such as Ant Colony Optimization [8], Genetic
Algorithm in standard modes [9], Improved [10] and
Quantum [11] and Differential Evolutionary algorithm [12].
In this paper, using Particle Swarm Optimization
algorithms is proposed. In section 2, The Otsu principle is
introduced as a fitness function, since used in Particle
Swarm Optimization algorithm. The section 3 is assigned to
introduce Particle Swarm Optimization algorithms and their
features. Details of the proposed method presented in section
4. Finally the proposed method is evaluated and some
experimental results are presented in section 5.
II. THE OTSU PRINCIPLE FOR IMAGE SEGMENTATION
As mentioned, one way of obtaining the proper
threshold value is using the Otsu principle. The Otsu
principle is a simple method and significant to selection of
the threshold value. In following, the standard Otsu principle
is described [3].
At First, total pixels are calculated by the equation (2):
(2)
∑
=
=
255
0ii
nN
In this equation, the gray value of a gray-scale map is 0-
255. The total number of pixels is defined N,
i
n
is the
number of pixels which is gray value is i. The probability of
the pixels with gray value of i is calculated by equation (3):
(3)
N
n
p
i
i
=
As
i
p
is the probability value of presence of different
amounts. While assuming the threshold value for the
segmentation is m, then the
i
ω
is probability of background,
and
i
μ
is the mean value of background can be calculated
by the equation (4) and (5):
(4)
∑
=
m
i
p
0
0
ω
(5)
0
0
0
ω
μ
∑
×
=
m
i
pi
The probability and the value of background are
obtained by equation (6) and (7):
(6)
∑
+
=
255
1
1mi
p
ω
(7)
1
255
1
1
ω
μ
∑
+
×
=
mi
pi
The amount of variance between background and
foreground can be defined as equation (8):
(8)
()()
2
11
2
00
2
TTB
μμωμμωσ
−+−=
In this equation
2
B
σ
is the amount of variance between
background and foreground and the value of threshold
average are defined as equation (9):
(9)
∑
×=
255
0iT
pi
μ
By computing the equations (6), (7), (8) and (9) can be
obtained the equation (10):
(10)
()
2
1010
2
μμωωσ
−×=
B
Actually the variance as a criterion is for uniformity
distribution, the greater the difference between the
foreground and the background. Therefore, the threshold
which makes the variance yields maximal is the optimal
threshold.
III. PARTICLE SWARM OPTIMIZATION ALGORITHMS
Particle swarm optimization (PSO) is a stochastic
population-based algorithm which was originally introduced
by Kennedy and Eberhart [14]. This algorithm is motivated
by intelligent collective behaviour of some animals such as
flocks of birds or schools of fish. As in other evolutionary
algorithms, in PSO, a population of potential solutions is
evolved through successive iterations. The most important
advantages of the PSO, compared to other optimization
strategies, are that PSO is easy to implement and there are
few parameters to adjust. Successful application of this
algorithm in many optimization problems verifies its good
performance. The main idea from the swarm behaviour of
fishes or birds when searching the food is inspired. Each
particle has a fitness value is calculated by a fitness function.
Whatever the particle in search space is closer than goal
(food for birds), has the fittest, also each particle has a
velocity leads to particle movement. Each particle with
following optimal particles in current mode continues to
move in problem space.
Start of working of Particle Swarm Optimization is that a
group of particles (solutions) create randomly and with
update in generations try to find optimal solution. In each
step, every particle updates based on the two best values.
The first case is the best position that since the particle has
been reached to it successfully. The mentioned position is
known as lbest. Another best value that is used by the
algorithm is the best position ever obtained by a population
of particles. This status is displayed by gbest.
After finding the best values, velocity and position of each
particle update based on equations (11) and (12):
V4-272 2010 2nd International Conference on Computer Engineering and Technology [Volume 4]
Authorized licensed use limited to: Amirkabir Univ of Tech Trial user. Downloaded on July 02,2010 at 07:16:11 UTC from IEEE Xplore. Restrictions apply.

(11)
()
()
[][]()2
[][]()1[][]
xgbestrandc
xlbestrandcvwv
−××
+−××+×=
(12)
[][][] vxx +=
In equations (11) and (12), v[] is the velocity of particle
and x[] is the current position of particle, which both are
arrays with length of dimensions of solutions. Rand()
generate random values in [0,1]. c
1
and c
2
are acceleration
constants, If c
1
is set to 0 (and c2≠0), the PSO algorithm
turns into the social-only model and if c
2
is set to 0 (and
c
1
≠0), then it becomes a cognition-only model. And usually
are considered fixed and equal. w is the inertia coefficient
that can be a fixed coefficient, random coefficient, a linear
function with time or even a nonlinear function with time
and adaptive. Thus at first, more part of current velocity of
particle affect its future velocity and with time, this rate will
decrease. In other words, at first particles have rather to
explosive movements and new experience and over time
follow the bests more. This method can decreases converge
to the local optimum in many cases. Particle velocities in
each dimension are limited to a value v
max
. If Total
acceleration cause velocity in a dimension be more than the
v
max
, velocity value is in this dimension equal to v
max
.
Original PSO algorithm has great simplicity and efficiency,
but if the issue was mentioned local optimum problem
cause to presented different versions for the PSO algorithm
by researchers.
As mentioned, the diversity of these algorithms for
proposed methods moreover the standard method [14], for
different methods are used to obtain best method, Based on
the best method in this condition for thresholding we can
obtain best results. Inertia coefficient in most of methods
updates by equations which is mentioned in table 1. We
categorized update inertia types in 4 categories: random
update, linear update, nonlinear update and adaptive update
for the inertia coefficient. This classification of methods is
also provided in table 1.
TABLE I.
UPDATE EQUATIONS OF PROPOSED METHODS FOR
THRESHOLDING
Update inertia Equation of update inertia
Random [15]
2
()
5.0 rand
w+=
Linear [16]
()
minmi nmax
max
max
www
iter
iteriter
w
cur
+−
−
=
Nonlinear [17]
cur
iter
uww ×=
Adaptive [18]
avg
lbest
gbest
w−=
1.1
In mentioned equations in table 1, w is as the inertia
coefficient, w
max
is maximum value of inertia coefficient,
w
min
is minimum value of inertia coefficient, Rand() is
generator function of variable between 0 to 1, iter
max
is
maximum number of algorithm iterations, iter
cur
is number
of current iterations, u is constant in the range of 1.0001 to
1.005, gbest is the best global solution and lbest
avg
is
average of the best local solutions.
The fifth section is assigned to compare of these methods
using experiments.
IV. THE PROPOSED METHOD
Now with considering the mentioned cases can present
the proposed method as the following steps:
A) Representation of particles
According the amounts of pixels in gray level is 0 to 255,
the threshold values in some particles can be 0 to 255.
B) Initializing
Five groups of particles as a primary solution are created
randomly.
C) Fitness function
The equation (10) can be used as a fitness function, global
and local optimal values are calculated.
D) Change of position
Considering one of the cases in inertia coefficient update
types, the equation (12) update velocity and position of the
particles.
E) Termination condition
Considering the termination condition that 50 steps is
considered, the algorithm ends.
To Better demonstration, the flow chart diagram of
proposed method is presented for segmentation by PSO in
figure 4.
Figure 4. The flow chart diagram of the proposed method
The proposed method is compared and evaluated in the
next section.
[Volume 4] 2010 2nd International Conference on Computer Engineering and Technology V4-273
Authorized licensed use limited to: Amirkabir Univ of Tech Trial user. Downloaded on July 02,2010 at 07:16:11 UTC from IEEE Xplore. Restrictions apply.

V. TITLE AND AUTHOR DETAILS
To evaluate the proposed method in this section were
given various experiments that in various aspects comparing
and evaluating were done. At first in the proposed method to
select the appropriate algorithm among all PSO algorithms,
the time of each method is compared, which table 2
indicates the execution time of 5 different methods of PSO
algorithms for Lena, Peppers and Hafez images.
TABLE II. C
OMPARISON OF RUN
-
TIME PERFORMANCE FOR PROPOSED
PSO
METHODS
Methods Lena Peppers Hafez
Standard 0.0689 0.0663 0.0717
Random 0.0659 0.0695 0.0697
Linear 0.0654 0.0718 0.0719
Nonlinear 0.0648 0.0664 0.0699
Adaptive 0.0723 0.0657 0.01791
Mentioned methods also have been evaluated in term of
velocity of convergence that is shown in figure 5.
Figure 5. Evaluations of proposed methods for image thresholding
According to results of table 2 and figure 5 can obtain
this result for images segmentation by the proposed method
using the PSO algorithm in the inertia coefficient changes
mode, as nonlinear is faster than other methods. Although
the difference between other methods is not so much, but the
proper nonlinear method is diagnosed proper.
By respect the PSO algorithm in nonlinear mode to
evaluate experiments of the proposed method and all results
are presented in following. Table 3 indicates implementing
results of the proposed method in compared with Otsu and
Entropy methods.
TABLE III. R
ESULTS OF THRESHOLD VALUE FOR
O
TSU
,E
NTROPY
,
G
ENETIC AND
P
ROPOSED METHODS
Methods Lena Peppers Cameraman
Otsu [5] 117 115 89
Entropy [8] 124 108 92
Genetic
[11]
93 113 85
Proposed 92 114 81
The proposed method of run-time is compared with the
Otsu method and the genetic algorithm based method in
table 4.
TABLE IV. R
UN
-
TIME PERFORMANCE OF
O
TSU
,G
ENETIC AND
P
ROPOSED METHOD FOR
L
ENA
,P
EPPERS AND
C
AMERAM AN
Method Lena Peppers Cameraman
Otsu
0.9367 0.9378 0.3741
Genetic
1.1810 1.3093 0.4267
Proposed
0.8511 0.7995 0.2524
results from implementation of the proposed method on
Hafez, Cameraman and Peppers images are shown in figure
6, figure 7, and figure8 respectively so the segmentation
process by threshold values in case of two, three and four
levels have been seen in figures.
(a) Original image (b) T=81
(c) T=63, 138 (d) T=52, 112, 149
Figure 6. Segmentation results on Cameraman image by proposed method.
(a) The original image, (b) single threshold, (c) Two threshold, (d) Three
threshold
(a) Original image (b) T=114
(c) T=65, 130 (d) T=59, 112, 161
Figure 7. Segmentation results on Peppers image by proposed method. (a)
The original image, (b) single threshold, (c) Two threshold, (d) Three
threshold
V4-274 2010 2nd International Conference on Computer Engineering and Technology [Volume 4]
Authorized licensed use limited to: Amirkabir Univ of Tech Trial user. Downloaded on July 02,2010 at 07:16:11 UTC from IEEE Xplore. Restrictions apply.

(a) Original image (b) T=17
(c) T=12,23 (d) T=9, 16, 24
Figure 8. Segmentation results on Hafez image by proposed method. (a)
The original image, (b) single threshold, (c) Two threshold, (d) Three
threshold
Finally, in table 5 the run-time and the Otsu value for
different levels of threshold are listed
TABLE V. R
UN
-
TIME
C
OMPARISONS OF
O
TSU ALGORITHM FOR
L
ENA
,P
EPPERS
,C
AMERAM AN
,H
AFEZ
Image name Threshold Run-Time (s) Otsu Value
20.8511 0.6992
30.8685 0.8566
Lena
41.0056 0.9294
20.7995 0.7514
30.8482 0.8749
Peppers
40.8403 0.9343
20.2524 0.8463
30.2606 0.9392
Cameraman
40.2618 0.9586
20.1590 0.7946
30.1124 0.9119
Hafez
40.1558 0.9523
The Increase of run time and the Otsu value with
increasing of total thresholding levels in images have direct
relevancy that in table 5 is shown clearly.
VI. CONCLUSION
In This paper for image thres holding using the PSO
algorithm was presented with target of the threshold value
optimization by respect of result run-time, 5 different
methods of PSO algorithms was selected and tested to best
and fastest method be used. The proposed method has not
any difficulty in learning process and learning sampling and
by considering statistical information of image using the
particle Swarm optimization algorithm, extracts the optimal
threshold value for the mentioned image. In this paper,
various experiments were implemented to evaluate and
compare in different case. Utilizing the proposed method on
damaged images by noise and color images are considered
to future works of authors.
REFERENCES
[1] Alireza Rezvanian, Karim Faez, Fariborz Mahmoudi, "A Two-pass
Method to Impulse Noise Reduction from Digital Images Based on
Neural Networks", in IEEE 5th International Conference on
Electrical and Computer Engineering (ICECE 2008), Dhaka,
Bangladesh, pp. 400-405, 20-22 Dec. 2008.
[2] Alireza Rezvanian, Saba Rezvanian, "A Review of Medical Image
Segmentation", in 1st National Conference on Software Engineering
Applications (CSEA 2009), Lahijan, Iran, 3-5 March 2009.
[3] M Raghuvanshi, R. Dharaskar, Adarsh Raut Shital Raut, "Image
Segmentation - A State-Of-Art Survey for Prediction," in
International Conference on Advanced Computer Control, pp. 420 –
424, 2008.
[4] ISI Web of Knowledge. [Online]. http://www.isiknowledge.com,
December 2009.
[5] Nobuyuki Otsu, "A Threshold Selection Method from Gray-Level
Histograms," IEEE Transactions on Systems, Man and Cybernetics,
vol. 9, no. 1, pp. 62 - 66, Jan. 1979.
[6] Jian Yu Dongju Liu, "Otsu Method and K-means," in Fifth
International Conference on Hybrid Intelligent Systems, 2009 (HIS
'09), vol. 1, pp. 344 – 349, 12-14 Aug. 2009.
[7] Jinglu Hu Jun Zhang, "Image Segmentation Based on 2D Otsu
Method with Histogram Analysis," in International Conference on
Computer Science and Software Engineering, vol. 6, pp. 105 – 108,
12-14 Dec. 2008.
[8] Mohammad Mehdi Ebadzadeh Shermin Bazazian, "A Novel
Method for Image Thresholding Using Error-based Fuzzy Neural
Network," in In Proceedings of the 13th International CSI Computer
Conference (CSICC 2008), Kish Island, Iran, March 2008.
[9] Y. Zhang, X. Shen, F. Shen, "An Improved Two-Dimensional
Entropic Thresholding Method Based on Ant Colony Genetic
Algorithm," in Global Congress on Intelligent Systems, pp. 163 -
167, 2009.
[10] Shaomin Nie Shukui Li, "Image Segmentation Method of Heavy
Forgings Based on Genetic Algorithm," in 2nd International
Congress on Image and Signal Processing (CISP '09), pp. 1 – 4, 17-
19 Oct. 2009.
[11] C. Shi, A. Min-si, W. Y. Hui, "Application of an Improved Genetic
Algorithm in Image Segmentation," in International Conference on
Computer Science and Software Engineering, pp. 898 – 901, 2008.
[12] M. Koudil, Y. Boukir, N. Benkhelat K. Benatchba, "Image
Segmentation Using Quantum Genetic Algorithms," in 32nd Annual
Conference on IEEE Industrial Electronics (IECON 2006), pp. 3556
– 3563, 6-10 Nov. 2006.
[13] Y. Zhao, Z. L. Zhenkui Pei, "Image segmentation based on
Differential Evolution algorithm," in International Conference on
Image Analysis and Signal Processing (IASP 2009), pp. 48 – 51,
11-12 April 2009.
[14] R. Eberhart, J. Kennedy, "Particle swarm optimization," in IEEE
International Conference on Neural Networks, vol. 4, pp. 1942 –
1948, 27 Nov.-1 Dec. 1995.
[15] Y. H. Shi R. C. Eberhart, "Tracking and Optimizing Dynamic
Systems with Particle Swarms," in Proceedings of the 2001
Congress on Evolutionary Computation, vol. 1, pp. 94 – 100, 27-30
May 2001.
[16] Eberhart R. C, and Y. Shi, Comparing inertia weights and
constriction factors in particle swarm optimization, IEEE Congress
on Evolutionary Computation (CEC 2000), pp. 84–88, 2000.
[17] B. Jiao, Z. Lian, X. Gu, "A Dynamic Inertia Weight Particle Swarm
Optimization Algorithm," Chaos, Solitons & Fractals, vol. 37, no. 3,
pp. 698 - 705, 2008.
[18] M.V.C. Rao, M. S. Arumugam, "On the Improved Performances of
the Particle Swarm Optimization Algorithms with Adaptive
Parameters, Cross-over," Applied Soft Computing, vol. 8, pp. 324 -
336, 2008.
[Volume 4] 2010 2nd International Conference on Computer Engineering and Technology V4-275
Authorized licensed use limited to: Amirkabir Univ of Tech Trial user. Downloaded on July 02,2010 at 07:16:11 UTC from IEEE Xplore. Restrictions apply.