Research Journal of Applied Sciences, Engineering and Technology 4(2): 104-107, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: September 23, 2011
Accepted: October 24 , 2011
Published: January 15, 2012
Multi-level Threshold Image Segmentation Based on PSNR
using Artificial Bee Colony Algorithm
1,2
Cao Yun-Fei, 1Xiao Yong-Hao, 1,2Yu Wei-Yu and 1Chen Yong-Chang
1
School of Electronic and Information Engineering, South China University
of Technology Guangzhou, P. R. China 510641
2
Provincial Key Laboratory for Computer Information Processing Technology,
Soochow University, Suzhou, Jiangsu 215006, China
Abstract: Image segmentation is still a crucial problem in image processing. It hasn yet been solved very well.
In this study, we propose a novel multi-level thresholding image segmentation method based on PSNR using
artificial bee colony algorithm (ABCA). PSNR is considered as an objective function of ABCA. The multi-level
thresholds (t*1, t*2 ,...., t*n-1, t*n) are those maximizing the PSNR. We compare entropy and PSNR in
segmenting gray-level images. The experiments results demonstrate proposed method is effective and efficient.
Key words: Artificial bee colony algorithm, image segmentation, multi-level threshold, PSNR
PSNR is always used for evaluating the quality of the
image coding and denoising. However, there is a question,
that is, “an the PSNR be applied to image segmentation?”
Thus, in this study, we use PSNR to evaluate
segmentation results. For developing the efficiency of
experiment, we introduced the ABCA to evaluate the
PSNR of an image.
INTRODUCTION
Image segmentation is a very important task in many
applications of image processing and computer vision.
The fast and accurate image segmentation algorithm is the
basis of follow-up target feature extraction, stereo
matching, three-dimensional reconstruction and
identification.
Ostu algorithm (Qidan Zhu et al., 2010) had been
widely applied in image processing. 1-D Ostu method
considered only grayscale information of a pixel, while 2D Ostu method considered both the gray value of a pixel
and the average gray value of its neighborhood. Jiao (Jiao
et al., 2006) gave an improved approach of threshold
selecting, through the gray level and gradient mapping
function. Minimum Cross Entropy (MCE) is developed by
(Li and Lee, 1993) as a criterion for determining the
thresholds of image segmentation. Sahoo (Prasanna and
Arorab., 2004) presented an automatic global thresholding
technique based on 2-D Renyi entropy which is
determined by using the gray values of the pixels and the
local average gray values of the pixels.
Swarm intelligence is promising in the field of
optimization and researchers have developed a lot of
algorithms by simulating the behaviors of swarm of
animals and insects such as ants, termites, bees, birds and
so on. Karaboga (Karaboga, 2005) proposed a new swarm
algorithm called Artificial Bee Colony Algorithm
(ABCA) to optimize multi-dimensional and multi-modal
problems. (Basturk and Karaboga., 2006) further studied
ABCA which was tested on five multi-dimensional
benchmark functions.
Artificial bee colony algorithm: In ABCA, the foraging
bees are classified into three categories mployed,
onlookers and scouts. First half of the bee colony is
composed of employed bees, whereas the latter half
contains the onlookers. The ABCA assumes that there is
only one employed bee for every food source. Bees that
are currently exploiting a food source are mployed The
employed bees bring tons of nectar from the food source
to the hive and may share the information on food source
with onlooker bees. Scouts are those bees which are
currently searching for new food sources in the vicinity of
the hive. Onlookers are those bees that are waiting in the
hive for the information to be shared by the employed
bees about their food sources.
The probability Pi of selecting a food source i is
determined using Eq. (1):
Pi 
0.9  f i
max f i
f i  
. , i  0,1,..., FN
 01
1
, Obji  0
Obji  1
(1)
f i  1  Obji , Obji  0
Corresponding Author: Cao Yun-Fei, School of Electronic and Information Engineering, South China University of Technology
Guangzhou, 510641-P. R. Chinat
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Res. J. Appl. Sci. Eng. Technol., 4(2): 104-107, 2012
where, f(i) is the fitness of the solution represented by the
food source i, FN is the total number of food sources, and
Obj(i) means the objective function value of a new
solution. After all onlookers have selected their food
sources, each of them determines a food source in the
neighborhood of its chosen food source and computes its
fitness.
If a solution represented by a particular food source
does not improve after a predetermined number of
iterations (limit) then the food source will be abandoned
by its associated employed bee. It becomes a scout, and it
will search for a new food source randomly. After the new
location of each food source is determined, another
iteration of ABCA begins. The process is repeated till the
termination condition is satisfied. Formally, suppose each
solution consists of D parameters and let Ti = (ti1, ti2, ...,
tiD) be a solution with a set of parameter values
t1,t2,...,tD. In order to determine a solution Ti the
neighborhood of Ti, a solution parameter j and another
solution TK = (tk1 , tk2, ..., tkD) are selected randomly.
Except for the value of the selected parameter j, all other
parameter values of Ti! are same as Ti i.e., Ti! = (Ti1, Ti2,
..., Ti(j-1), Tij, Ti(j+1), ..., TiD). The value Ti! of the selected
determined using Eq. (2):
Ti!j = Tij + u(Tij - Tkj)
t0 , 0  I (i , j )  t1

t1 , t1  I (i , j )  t2
I (i , j )  ...,
t
 D  1 , t D  1  I (i , j )  t D
tD , t D  I (i , j )  255

t 
 p
i  t1
t2 1
 p
i
i  t1

,..., tD  1 
255
i. pi
i  t D 1
t D 1
 p
i
i  t D 1
 i. p
i
i tD
, tD  255
 p
i
itD
where p’i is the probability of gray-level value of an
image i .
The optimum D-dimensional vector t*1, t*2, ..., t*D–1,
t*D which can maximize Eq. (3) is defined in Eq. 5:
t*1, t*2, ..., t*D–1, t*D =
max (Fp(t1, t2, ..., tD–1, tD ))
(5)
PSNR-based Artificial Bee Colony Thresholding
(PABCT) algorithm: The parameters of PABCT are
listed as follows: NP denotes the number of bee colony
including employed bees and onlooker bees, FN
represents the number of food sources which equals the
half of the colony size, FN is the number of cycles, and
limit max cycle indicates the number of trials.
2
Set NP = 40, FN = 20, maxCycle = 100, limit =100
(3)
Step 1: Initialize population of solutions.Generate food
sources. Ti (i = 1, 2, ..., FN) is denoted by matrix
in Eq. (6):
T = [T1, T2, ..., TFN], Ti ,= (Tí1, Tì2, ..., TiD) (6)
where, Tij is the j-th component value of the i-th
food source that is restricted into [0, ..., 255] and
Tij<Tij+1 for j. The fitness value of all solutions
Ti is evaluated and then set cycle = 1 and the
trial number of each solution Ti traili = 0.
Step 2: Assign the employed bees on their food sources.
Each employed bee produces a new solution Ti
by using Eq.2. If the fitness of the new solution
is better than that of the previous one, the
employed bee memorizes the new position and
replaces the original one; otherwise, the
employed bee retains the original solution.
RMSE (t1 , t2 ,... t D 1 , t D )

i
, t 
t D 1
where, RMSE is abbreviation of root mean-squared error,
which is defined in Eq. (4). (t1, t2, ..., tD–1, tD) is a vector
containing a set of thresholds for segmentation. Î(i,j)
denotes the pixel value in the original image (Fig. 1) I,
Î(i, and j) and denotes the pixel value in the segmented
image. D represents the number of thresholds.
2
i0
t1  1
i
Proposed approach:
PSNR criterion based measure: When applied to multilevel thresholding image segmentation, the objective
function can be defined in Eq. (3):
 I i, j   Ii, j
 i. p
i0
where, u is an uniform varying in [-1, 1]. If the resulting
value falls outside the acceptable range for parameter j, it
is set to the corresponding extreme value in that range.
M N
 
i 1 j 1
 i. p
i
(2)
 255 
Fp  t1 , t2 ,..., t D1 , t D   10 log10 

 RMSE 
t2 1
t1  1
(4)
MN
where,
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Res. J. Appl. Sci. Eng. Technol., 4(2): 104-107, 2012
Table 1: The experimental results
D=2
---------------------------------------------MEABCT
PABCT
Threshold/
Threshold/
Original image
Entropy
PSNR
Lena
96,163
91,149
/12.4017
/22.9252
Cameraman
127,192
69,142
/12.1688
/24.3911
Peppers
88,160/
82,151/
12.5267
23.7850
D=3
-----------------------------------------EABCT
PABCT
Threshold/
Threshold/
Entropy
PSNR
80,126,175
80,125,169
/15.3913
/25.9406
43,103,192
56,115,154
/15.2274
/26.0619
83,143,197
70,113,169
/15.7724
/25.9947
D=4
------------------------------------------------MEABCT
PABCT
Threshold/
Threshold/
Entropy
PSNR
63,96,138,179
73,113,145,180
/18.1096
/28.0417
43,96,145,196
41,94,139,169
/18.3955
/27.8797
67,115,158,201
64,97,136,188
/18.6964
/27.5406
D=2
D=3
D=4
D=2
D=3
D=4
D=2
D=3
D=4
Fig1: The original image
D=2
D=2
D=2
D=3
D=3
D=3
D=4
D=4
Fig. 3: 2-4 threshold images using MEABCT
[0, 1]. If this number is less than Pi , the solution
is updated and i is increased by 1. This process
is repeated until all onlookers have been
distributed to solutions.
Step 4: The scout bees randomly research the neighbor
area to discover new food sources. Through
Steps 2-3, the traili of solution Ti will be
increased by 1. If the solution Ti is not better
than through Steps 2-3, the solution Ti will be
abandoned in case that the traili of solution will
be increased by 1. If the traili of solution exceeds
the predetermined “limit” the solution Ti is
considered to be an abandoned solution. At the
same time, the employed bee will be changed
into a scout. The scout randomly produces the
new solution by Eq. 7, and compares the fitness
of new solution with that of its old one. If the
new solution is better than the old solution, it
will replace the old one and set its own traili into
D=4
Fig 2: 2-4 threshold images using PABCT
Step 3: Assign onlooker bees to the food sources
depending on their amount of nectar. Calculate
the probability value Pi of the solution Ti
according to their fitness values using Eq. 1. A
onlooker bee updates its solution depending on
the probabilities and determines a neighbor
solution around the chosen one. In the selection
procedure for the i-th onlooker (the initial value
of i is 1), a random number is produced between
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Res. J. Appl. Sci. Eng. Technol., 4(2): 104-107, 2012
0. This scout will be changed into an employed bee.
Otherwise, the old one is retained in the memory:
better segmentation performance from subjectivity. Thus,
proposed method is effective and efficient. Our ongoing
and further works include adaptive determination for the
number of the threshold and faster bee colony algorithm.
Tij = Tmin,j + rand(0,1).(Tmax,j–Tmin,j)
j = 1, 2, ..., D
(7)
ACKNOWLEDGMENT
where, the Tmin,j and Tmax,j are the minimum and
maximum of the j-th component of all solutions,
the rand (0, 1) is a function that generates the
random number between [0, 1].
Step 5: The best solution is recorded and increases the
cycle by 1.
Step 6: The algorithm is end if the cycle is equal to the
maximum cycle number (max cycle), otherwise
go to Step 2.
This study is supported by the National Natural
Science Foundation of China (Grant No. 60872123,
60972133), the Joint Fund of the National Natural Science
Foundation and the Guangdong Provincial Natural
Science Foundation (Grant No. U0835001), the
Fundamental Research Funds for the Central Universities,
SCUT, Provincial Key Laboratory for Computer
Information Processing Technology, Soochow University,
(Grant No. KJS0922).
Experimental results and comparative performance:
In this section, we compared proposed approach
(PABCT) with the Maximum Entropy Artificial Bee
Colony Thresholding algorithm (MEABCT) presented in
(Ming-Huwi, 2011). We tested some standard gray-level
images using Matlab 2009 software running at a 2.8GHz
CPU, 4GHz Memory computer (Table 1).
We can evaluate the segmentation results
subjectively. It obvious that the contrast between the
object and the background is much higher in Fig. 2 than
that of Fig. 3. Especially in the results of cameraman, the
gray-level of the man and the camera is deeper than that
of the background. It is obvious that Lena and Peppers in
Fig. 2 is more highlighted. And the segmentation results
of PABCT is superior to those of MEABCT.
REFERENCES
Basturk, B. and D. Karaboga, 2006. An Artificial Bee
Colony (ABC) Algorithm for Numeric Function
Optimization. IEEE Swarm Intelligence Symposium,
USA.
Jiao, S., G. Xue and X. Li, 2006. An improved Ostu
method for image segmentation. ICSP Proceedings.
Karaboga, D., 2005. An Idea Based on Honey Bee Swarm
for Numerical Optimization. Technical Report-TR06
(Erciyes University, Computer Engineering
Department, Turkey.
Li, C.H. and C.K. Lee, 1993. Minimum cross entropy
thresholding. Pattern Recognition, 26: 617-625.
Ming-Huwi, H., 2011. Multilevel thresholding selection
based on the artificial bee colony algorithm for image
segmentation. Expert Sys. Appl., 37(6): 4146-4155.
Prasanna, K.S. and G. Arorab, 2004. A thresholding
method based on 2-D Renyi entropy. Pattern
Recognition, 37: 1149-1161.
Zhu, Q., L. Jing and R. Bi, 2010. Exploration and
improvement of Ostu threshold segmentation
algorithm Proceedings of the 8th World Congress on
Intelligent Control and Automation.
CONCLUSION
PSNR is a very important criterion for evaluating the
quality of image restruction and de-noising. In this study,
we applied PSNR to multi-thresholding image
segmentation using ABCA. Furthermore, we compare the
proposed PABCT with MEABCT. The experiments
results demonstrate that the proposed method provides
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