A Fully Adaptive and Hybrid Method for Image Segmentation Using Multilevel Thresholding

Abstract

High level tasks in image analysis and understanding are based on accurate image segmentation which can be accomplished through multilevel thresholding. In this paper, we propose a new method that aims to determine the number of thresholds as well as their values to achieve multilevel thresholding. The method is adaptive as the number of thresholds is not required as a prior knowledge but determined depending on the used image. The main feature of the method is that it combines the fast convergence of Particle Swarm Optimization (PSO) with the jumping property of simulated annealing to escape from local optima to perform a search in a space the dimensions of which represent the number of thresholds and their values. Only the maximum number of thresholds should be provided and the adopted encoding encompasses a continuous part and a discrete part that are updated through continuous and binary PSO equations. Experiments and comparative results with other multilevel thresholding methods using a number of synthetic and real test images show the efficiency of the proposed method.

Full text

I.J. Image, Graphics and Signal Processing, 2013, 1, 46-57
Published Online January 2013 in MECS (http://www.mecs-press.org/)
DOI: 10.5815/ijigsp.2013.01.07
Copyright © 2013 MECS I.J. Image, Graphics and Signal Processing, 2013, 1, 46-57
A Fully Adaptive and Hybrid Method for Image
Segmentation gnisU Multilevel Thresholding
Salima Ouadfel
College of Engineering, MISC laboratory, CICS Group,
Department of Computer Science, University Mentouri – Constantine, Algeria
souadfel@yahoo.fr
Souham Meshoul
College of Engineering, MISC laboratory, CICS Group,
Department of Computer Science, University Mentouri – Constantine, Algeria
smeshoul@umc.edu.dz
Abstract— High level tasks in image analysis and
understanding are based on accurate image
segmentation which can be accomplished through
multilevel thresholding. In this paper, we propose a new
method that aims to determine the number of thresholds
as well as their values to achieve multilevel threnholding.
The method is adaptive as the number of thresholds is
not required as a prior knowledge but determined
depending on the used image. The main feature of the
method is that it combines the fast convergence of
Particle Swarm Optimization (PSO) with the jumping
property of simulated annealing to escape from local
optima to perform a search in a space the dimensions of
which represent the number of thresholds and their
values. Only the maximum number of thresholds should
be provided and the adopted encoding encompasses a
continuous part and a discrete part that are updated
through continuous and binary PSO equations.
Experiments and comparative results with other
multilevel thresholding methods using a number of
synthetic and real test images show the efficiency of the
proposed method.
Index Terms— Image segmentation, Multilevel
thresholding, Particle swarm optimization, Simulated
annealing
I. INTRODUCTION
Multilevel thresholding is an important technique that
has many applications in image processing, including
segmentation, clustering and object discrimination. It
aims to separate the objects and the background of the
image into non overlapping regions. Thresholding may
require the use of one or more thresholds depending on
the number of classes that should be depicted in an
image. Therefore, based on this assumption,
thresholding methods can be divided into two main
categories namely bi-level thresholding and multi-level
thresholding. In bi-level thresholding, pixels within an
image are classified into two classes that consist of the
object class and the background class depending on
whether their values are above or below a given
threshold. By extension, multilevel thresholding
involves several thresholds to classify pixels into more
classes. A good review of bi-level and multilevel
thresholding algorithms can be found in [1].
Depending on the way to find the thresholds, both bi-
level and multilevel thresholding methods can be
divided into parametric and nonparametric approaches.
The parametric approach is based on a statistical model
of the pixel grey level distribution. Generally, a set of
parameters that best fits the model is derived using least
square estimation. This typically leads to nonlinear
optimization problems that are computationally
expensive and time-consuming [2, 3]. In the
nonparametric approach, the search of the optimal
thresholds is done by optimizing an objective function
based on some discriminating criteria such as between
class variance [4] and entropy [5].
A large number of thresholding methods have been
proposed in the literature in order to perform bi-level
thresholding and most of them are easily extendable to
multilevel thresholding. Despite the straightforwardness
of this extension process, the computational time will
increase sharply when the number of thresholds is too
high because of the exhaustive searching they perform
[6]. This weakness makes the multilevel thresholding
methods unsuitable in many applications and explains
the need to use faster and robust optimization methods
for multilevel thresholding problem [7]. As a
consequence, several fast techniques have been
proposed in the literature such as recursive algorithms
[8]. Huang and Wang [9] propose a two-stage multi-
threshold based on Otsu‘s method. Wang and Chen [10]
applied an improved shuffled frog-leaping algorithm to
the three dimensional Otsu thresholding. Li and Tam
presented a fast iterative implementation for the
minimum cross entropy thresholding method [11].
Chung and Tsai [12] proposed a fast implementation of
binarization algorithm using an efficient heap and
quantization based data structure. A recursive
programming technique using the maximum cross
entropy was proposed by Yin [13]. Shelokar et al. [14]
selected the optimal threshold by minimizing the sum of

A Fully Adaptive and Hybrid Method for Image Segmentation Using Multilevel Thresholding 47
Copyright © 2013 MECS I.J. Image, Graphics and Signal Processing, 2013, 1, 46-57
the fuzzy entropies. Despite the good results of these
methods, they still suffer from the problem of long
processing time when the number of threshold increases,
due to their iterative process.
This limitation has motivated the researchers to find
new optimization methods that require moderate
memory and computational resources, and yet produce
good results. Therefore, metaheuristics have been used
as computationally efficient alternatives to traditional
multilevel thresholding methods to solve the multilevel
thresholding problem. A metaheuristic is a high-level
general purpose search strategy which helps exploring
large search spaces in order to find good quality feasible
solutions. Metaheuristics have been most generally
applied to NP-Complete problems and to other
combinatorial optimization problems for which
a polynomial-time solution exists but is not practical.
Since their apparition, metaheuristics have proven their
efficiency in solving complex and intricate optimization
problems arising in various fields. The most popular and
used ones are the Genetic algorithm (GA) [15], Particle
Swarm Optimization (PSO) [16], Differential Evolution
(DE) algorithm [17], Simulated Annealing (SA) [18],
Artificial Bee Colonies (ABC) Algorithm [19], Bacterial
Foraging (BF) algorithm [20] … etc. Due to their
capacity to escape from local optima and their ability to
find good quality solutions within a reasonable time,
several researchers have applied metaheuristics in
multilevel thresholding context. Examples of such
attempts include the use of GA algorithm [7, 21, 22, 23],
DE algorithm [24, 25, 26], PSO algorithm [27, 28, 29,
30], ABC algorithm [31, 32], BFA algorithm [33]. A
good review of metaheuristic algorithms for multilevel
thresholding can be found in [34].
Despite the relative efficiency of most of methods in
the literature to find the optimal thresholds, they all
require the number of thresholds to be specified in
advance. However, in many practical cases, it is difficult,
even impossible to determine the exact number of
thresholds without a prior knowledge. Few algorithms
have been designed to automatically determine the
suitable number of thresholds. Fuzzy entropy is used in
[35] to select automatically the optimal number of
thresholds and their location in the image histogram.
Yen et al. [36] proposed a new criterion for multilevel
thresholding, called Automatic Thresholding Criterion
(ATC). This criterion includes a bi-level method that
correlates the discrepancy between the original and
thresholded image and the number of bits used to
represent the segmented image [1, 36]. In this strategy,
the histogram image is divided into two more
sequentially up to the minimum of the cost function
ATC is reached [36]. In each step the distribution with
the largest variance is further dichotomized in two more
distributions by applying the same bi-level thresholding.
A new dichotomization process of the ATC method was
proposed in [37].
Although the dichotomization techniques are fast
algorithms, they are sub-optimal techniques and so they
do not allow providing the optimal threshold values [7].
The GA presented in [7] determines the threshold
number as well as the optimal threshold values. In their
method, the wavelet transformation is used to reduce the
length of the histogram and the GA algorithm optimizes
the ATC criterion. Recently, Djerou et al. proposed in
[38] an automatic multilevel thresholding approach,
based on Binary PSO algorithm, which uses the Otsu‘s
criterion and the Kapur‘s entropy as objective function.
In [39] author adapts the intelligent water drops (IWDs)
algorithm to optimize a modified Otsu‘s criterion for
automatic multilevel thresholding.
PSO is a population-based metaheuristic introduced
by Kennedy and Eberhart in 1995 [16] as an alternative
to the standard Genetic Algorithm (GA). PSO was
inspired by social behavior of bird flocking or fish
schooling. Each particle within a swarm searches the
solution space for the best solution by changing its
position with time according to its own experience, and
to the experience of neighboring particles. The main
advantages of PSO are its flexibility, its robustness and
its inherent parallelism. It has been applied in many
kinds of engineering problem widely and has proved its
large capability to competing with other classical
optimization algorithms [40, 41, 42, 43, 44]. However,
observations reveal that the PSO suffers from a
premature convergence: it converges rapidly in the early
stages of the searching process, but can be trapped in a
local optimum in the later stages. To overcome this
drawback of diversity loss, different hybrid PSOs with
others metaheuristics like SA, GA, DE have been
proposed. A good and recent review of hybrid PSO can
be found in [45, 46].
In this paper, we propose a new automatic multilevel
thresholding technique based on PSO. The new method
is able to determine both the appropriate number of
thresholds and the appropriate threshold values by
optimizing ATC [36]. We adopt AMT-PSOSA
(Automatic Multilevel Thresholding with PSO and SA)
as an acronym to the algorithm we propose in this paper.
AMT-PSOSA uses a new hybrid representation to allow
particles to contain different thresholds numbers within a
given range defined by minimum and maximum
threshold number. Particles are initialized randomly to
process different cluster numbers in a specified range
and the goal of each particle is to search the optimum
number of thresholds and the optimum threshold values.
In order to allow PSO jump out of a local optimum, SA
is applied to some particles of the swarm if no
improvement occurs in their best local fitness during a
number of iterations. Thus, at the start of SA most
worsening solutions may be accepted, but at the end only
improving ones are likely to be accepted. This procedure
will help PSO to jump out of a local minimum.
The rest of this paper is organized as follows: Section
2 introduces, briefly, PSO and SA algorithms. Section 3
is devoted to detailed descriptions of AMT-PSOSA. The
experimental results are evaluated and discussed in
section 4. Finally, conclusions are given in section 5.

48 A Fully Adaptive and Hybrid Method for Image Segmentation Using Multilevel Thresholding
Copyright © 2013 MECS I.J. Image, Graphics and Signal Processing, 2013, 1, 46-57
II. BACKROUND
A. Particle swarm optimization
Particle swarm optimization (PSO) is a population-
based evolutionary computation method first proposed
by Kennedy and Eberhart [16]. It is inspired from the
natural behavior of the individuals in a bird flock or fish
school, when they search for some target (e.g., food).
The PSO algorithm is initialized with a swarm of
particles (called potential solutions) randomly
distributed over the search area. Particles fly through the
problem space by following the current optimum
particle and aim to converge to the global optimum of a
function attached to the problem.
Each particle i in the swarm is represented by two
elements: its current position (pi), and its velocity (vi).
Its movement through the search space is influenced by
its personal best position pbesti it has achieved so far
and the local best value lbest, obtained so far by any
particle in the neighbors of the particle. When a particle
takes all the population as its topological neighbors, the
lbest value is a global best and is called gbest. If the
problem space is D-dimensional and the swarm size is
Np, at each iteration t, the particle‘s new position and its
velocity are updated as follows:
)(
)(
1
22
1
11
1




t
ijgbest
t
ijbest
t
ij
t
ij
pprc
pprcwvv
(1)
t
ij
t
ij
t
ij vpp  1
(2)
where i= 1,2, . . . , Np; j= 1,2, . . . ,D
The parameter w is an inertia weight [47] used in
order to control the values of the velocity. The inertia
weight w is equivalent to a temperature schedule in the
simulated annealing algorithm and controls the
influence of the previous velocity: a large value of w
favors exploration, while a small value of w favors
exploitation. As originally introduced in [47], w
decreases linearly during the run from wmax to wmin.
c1 and c2 are two constants which control the influence
of the social and cognitive components such that
4
21  cc
.
1
r
and
2
r
are two random values in the
range [0,1].
The main steps of PSO algorithm are presented in
algorithm 1.
The particle swarm optimization approach presented
above works on continuous space. However, for some
optimization problems, a discrete binary representation
is better for the particles than a real representation. To
deal with this kind of optimization problems, Kennedy
and Eberhart proposed in [48] the Binary PSO (BPSO).
Algorithm 1
Initialize all parameters
Initialize particle‘s positions and velocities
Set pbest for each particle
Compute gbest
repeat
for each particle do
Calculate fitness value
Update pbest if improvement
end
Update gbest
for each particle do
Calculate particle velocity according to (1)
Update particle position according to (2)
end
until maximum iterations is not attained
BPSO preserves the fundamental concept of the Real
PSO algorithm and differ from it essentially in two
characteristics: first, candidate solutions consists of
binary strings each representing a particle‘s position
vector. Second, the velocity represents the probability of
bit pi taking the value 1.
The position update equation is defined by:









)( if 1
)( if 0
1
1
t
t
t
ij
ij
ij vfr
vfr
p
(3)
with
)exp(1
1
)( 1
1



t
t
ij
ij v
vf
(4)
where r is a random value with range [0, 1]. To avoid
saturation of the sigmoid function in (4), the velocity
can be limited in the range [-Vmax,Vmax].
Despite the fast convergence of PSO, it has been
observed that the PSO algorithm can be trapped in a
local minimum. This premature convergence occurs
because particles fly to local, or near local, optimums,
therefore, the balance between the exploration process
(searching of the search space) and exploitation process
(convergence towards the optimum) is disturbed. In
order to overcome this problem, the PSO technique can
be combined with some other evolutionary optimization
technique to yield an even better performance [43]. In
this paper, PSO algorithm is hybridized with the SA
algorithm. The hybrid algorithm takes both of fast
searching ability in PSO and the advantages of
probability jumping property of SA. Other applications
of hybrid PSO and SA algorithm can be found [49, 50,
51, 52, 53].
B. Simulated Annealing (SA) algorithm
The original concept of SA was proposed by
American physicist Metropolis et al. [54]. It is inspired
from the annealing process in metallurgy, which is a
method using heat and controlled cooling of a material
to increase the size of its crystals. The heat destabilizes
the atoms from their first positions and wanders
randomly through states of higher energy. It has
observed that when the cooling is slow, it gives the

A Fully Adaptive and Hybrid Method for Image Segmentation Using Multilevel Thresholding 49
Copyright © 2013 MECS I.J. Image, Graphics and Signal Processing, 2013, 1, 46-57
atoms more chances of finding configurations with
lower internal energy than the initial one.
Kirkpatrick et al. gives in [18] a mathematical model
of the annealing process and uses this model for finding
solutions for combinatorial optimized problems, and
was the first literature to successfully utilize SA. The
principle of SA is to accept solutions of worse quality
than the current solution in order to escape from local
optima. The probability of accepting such worst
solutions is decreased during the search.
A standard SA procedure begins by generating
random initial solution called current solution cs. At the
initial stages, SA attempts to replace the current solution
cs by random solution cs’ that is generated by making a
small random change in the current solution cs. The
objective function f(cs’) of the new solution is
calculated and the metropolis acceptance rule is then
used to determine if the generated solution should be
accepted or not as the new current solution. A move to
the new solution cs‘ is made if it improves the current
solution cs that is f(cs’) is better than f(cs) otherwise it
may be accepted with a probability that depends both on
the difference between the corresponding function
values f(cs) and f(cs’) and also on a global
parameter T (called temperature) that is gradually
decreased during the cooling process. In rejection case,
a new solution is generated and evaluated. Typically this
step is repeated until the system reaches a solution that
is good enough for the problem, or until a given number
of iterations is reached. The probabilistic metropolis
acceptance mechanism is defined by the following
 
TE
eP /

(5)
where
P
: Probability for acceptance.
E
: The fitness difference between both the fitness
of the new generated solution cs‘ and the fitness of the
current solution cs.
T: Temperature value.
The temperature T is decreases during the search
process; at the beginning of the search process, the
solutions with the worst fitness value are accepted with
a high probability and this probability is gradually
decreased at the end of the search process.
The pseudo-code of SA algorithm is given in
algorithm 2.
Algorithm 2
Let cs the current solution
Evaluate cs and store its fitness value f (cs)
Initialize best_solution with the current solution cs
Initialize T0 (initial temperature) and Tf (final
temperature)
Initialize T to T0
while T>Tf do
for a fixed number of iterations do
Generate new solution cs’ in the neighborhood of
the current solution cs
Evaluate the fitness value of the new solution cs’
)()'( csfcsfE 
if
E
<0 then cs=cs’
else if rand (0,1) <
 
TE
e/
then cs=cs’
end
Update best_ solution with the new generated
solution cs’
end
TT *


End
The SA algorithm has a strong ability to find the local
optimistic result. With its jump probability, it can avoid
the problem of local optimum, but its ability of finding
the global optimistic result is weak. In order to improve
the results of SA algorithm, it can be used with other
techniques like PSO to improve the results.
III. AMT-PSOSA: THE PROPOSED AUTOMATIC
MULTILEVEL THRESHOLDING METHOD
In this section, we describe a new automatic image
segmentation algorithm using multilevel thresholding
based on a hybridization of PSO with SA.
Given a gray level image I to be segmented into
meaningful regions. Let there be L gray level values
lying in the range {0,1, 2,…..,(L-1)}. For each gray level
i, we associate h(i) which represents the number of
pixels having the ith gray level as a value. Therefore, the
probability pi of the ith gray level is defined as pi=h(i)/N
where



1
0
)(
L
i
ihN
denotes total number of pixels in
the image I .
Suppose image I is composed of M+1 regions. Hence,
M thresholds, {t1,t2,…….,tM} are required to achieve the
subdivision of the image into regions: C0 for
 
1,...., 10 tt
, C1 for
 
1,...., 21 tt
,….., CM for
 
1,...., LtM
,such that
MM tttt  121 ...
. The
thresholding problem consists in choosing the set of
optimal thresholds
),......,,( **
2
*
1M
ttt
that maximizes an
objective function f that is:
))((argmax )t,.....,t,(t *
M
*
2
*
1tf
(6)
where t is a potential solution in the feasible region.
The aim of AMT-PSOSA algorithm is to search both
the numbers of thresholds as well as the optimal
threshold values using the global search capability of
PSO and its fast convergence combined with the
efficiency of SA to escape from local minimum.
The framework of the AMT-PSOSA algorithm is
given in algorithm 3 below.

50 A Fully Adaptive and Hybrid Method for Image Segmentation Using Multilevel Thresholding
Copyright © 2013 MECS I.J. Image, Graphics and Signal Processing, 2013, 1, 46-57
Algorithm 3
Initialize all parameters (listed in Table 1)
for each particle Xi do
Initialize particle‘s position
Initialize particle‘s velocities stochastically
Initialize pbest
end
Initialize gbest position and Mbest
iter ← 0
while (iter < itermax) do
for each particle Xi do
Update particle velocity
Enforce velocity bounds
Update particle ‗s position
Enforce position bounds
Evaluate particle‘s fitness
Record new pbest value of the particle
end
Record new gbest and Mbest
Select particles that are evolved by SA
for each selected particle Xi do
T ← T0
current_solution ← pbesti
current_fitness ← f itness(current_solution)
while ( T>Tf) do
iterSA ← 0, // iteration of SA algorithm
while (iterSA< iterSAmax) do
Generate neigh_solution
Evaluate neigh_solution‗s fitness
if accept (neigh_solution) then
current_solution ← neigh_solution
end
iterSA←iterSA+1
Update pbesti if improvement
end
TT *


end
end
Update gbest position and Mbest
iter ← iter + 1
end
Segment the image using the optimal number of
thresholds Mbest and the optimal thresholds values given
by gbest.
A. Particle representation
Since in this paper, we have to optimize the threshold
values and the number of thresholds, we have chosen to
represent the particle with both real values and binary
values. The real values are used to select the optimal
threshold values which are updated by Real PSO
algorithm. Binary values are used to select the optimal
number of thresholds using the Binary PSO. The Real
PSO and Binary PSO evolve in parallel contribute in the
evaluation of the fitness function.
In this representation, a binary mask is associated
with each threshold value. The value of this mask
determines whether the threshold value is used in the
thresholding process or not. The initial population
 
Np
XXXXPop ,...,, 321

is made up of Np possible
particles (solutions). For a user-defined maximum
thresholds number Tmax, a single particle Xi is a vector of
Tmax binary masks and Tmax real numbers that represent
the Tmax thresholds values.
For a particle Xi, each probably threshold value
)....1( max
Tjtij 
is associated with a mask
ij

. The
threshold value
ij
t
is taken into account if its
corresponding mask is set to 1 that is:
1 
ij

and
discarded otherwise that is
0 
ij

. Therefore, for each
particle, the total number of masks set to 1 gives the
number of thresholds Mi encoded in it, that is:


max
1
T
jiji
M

For a Tmax thresholds problem, the position of a
particle is formulated as:
 
 
max
21
2121
1 ,1 subject to
1....0 and ,1,0
,,.....,,,,.....,,
max
maxmax
TjNpi
Lttt
tttX
iT
iiij
T
iT
ii
iT
iii





(7)
If after initialization, it is found that no mask could be
set to ―1‖ in a particle (all threshold values are invalid),
one random mask is selected and set to 1. Thus a valid
particle should include at least one mask set to 1 in its
position vector.
Two examples of the particle structure in the
proposed approach are shown on Figure 1.
]225,225,160,45,12,0,1,0,1,0[
  
 valuesthre sholds
fieldmasks
]240,210,100,50,10,1,0,1,0,1[
  
 valuesthresholds
fieldmask
Figure 1. Two examples of the particle structure in the AMT-PSOSA
algorithm.
In the first example, particle Xi represents 3 classes (2
thresholds), and the associated thresholds values are 45
and 225. Thresholds values 12, 160 and 250 are invalid
and not used to thresholding the image.
In the second example, particle Xi represents 4 classes
(3 thresholds), and the associated thresholds values are
10, 100 and 240. Thresholds values 50 and 210 are
invalid and not used to thresholding the image.
The position of each particle is changed using the
following rule: the threshold values are update using
continuous PSO equations whereas the mask field is
changed using equations of Binary PSO. In addition the
velocity of each particle must lie within the interval
[0,1].

A Fully Adaptive and Hybrid Method for Image Segmentation Using Multilevel Thresholding 51
Copyright © 2013 MECS I.J. Image, Graphics and Signal Processing, 2013, 1, 46-57
B. Population initialization
To generate the initial population of particles, we use
in this paper the random generation strategy until all
particles in a population are created. Each individual
particle Xi of the population is initialized by randomly
chosen threshold values within the range [gmin, gmax],
where gmin and gmax are the minimum and the maximum
gray levels in the image, respectively.
),....,1 and 1(
)(*()
max
minmaxmin
Tj,.....Np i
ggrandgtij


(8)
In addition,
 
1 max
TMM ii 
masks are
randomly chosen and their values are set to ―1‖.
C. Fitness evaluation
The fitness of a particle indicates the degree of
goodness of the solution it represents. In this work the
fitness of a particle is computed using the cost function
ACT [36].
Let

and,,, ii
M
be the number of thresholds
encoded in a particle, the probability of the class Ci , the
mean grey level of the class Ci and the total mean grey
level of the image, respectively:
 







1
0
1
1 ,/ ,1
11
L
jj
t
tj
iji
t
tj
ji jpipp
i
i
i

where pj is the normalized probability at level j
Let
222 and , TBw

be the within-class variance, the
between-class variance and the total class variance,
respectively. They are given by the following
expressions:
 
 
 


 










1
0
2
2
0
2
2
0
12
2
,)(
1
L
jjT
M
iiiB
j
M
i
t
tj
iw
pj
pjM i
i



The ACT function proposed by Yen et al. is defined
as follows:
2
2
2/1 ))((log))((*)( MMDiskMF 

(9)
The Disk(M) represents the within-class variance
and is defined as:
)()( 22 MMDisk WT


The first term of F(M) measures the cost incurred by
the discrepancy between the thresholded image and the
original image. The second term measures the cost
resulted from the number of bits used to represent the
thresholded image. In this equation,  is a positive
weighting constant and it is set to 0.8 in this study as
recommended in [36]. The number of thresholds is
determined by counting the number of ―1‖ in the mask
field of the particle position and the corresponding
threshold values are determined accordingly.
The fitness
)(Mfitness
of a particle which
encoded M thresholds is defined as:
)(
1
)( MF
Mfitness 
(10)
When the algorithm converges, the found number of
thresholds M* and the corresponding found thresholds
values are determined by the particle that has the
maximum value of fitness function throughout the entire
run.
D. SA-based local search
As a metaheuristic based method, PSO has a strong
ability in finding the most optimistic result. Meanwhile,
it can be trapped in a local optimum. SA has a strong
ability in finding a local optimistic result, but its ability
in finding the global optimistic result is weak [52].
Combining PSO and SA leads to the combined effect of
two algorithms: the fast convergence of the PSO and its
efficient global search and the efficient local search of
SA and its ability to avoid local minima, which gives
better results.
There are many ways to combine PSO with SA, but
the best one is which take advantage of probability
jumping property of SA without increasing the
computational cost or altering the fast convergence
ability of PSO. In this paper, we apply the jump
property of SA to the process of updating the local best
positions of selected particles in the swarm. Indeed, it
would be helpful for the best particles to jump out the
local minima, and as a result, the whole swarm would
move to better positions. SA algorithm is applied for a
particle if it is selected with an adaptive probability Pe
as in [22]. Let gbest the global best fitness of the current
iteration;
pbest
be the average fitness value of the
population and pbesti be the fitness value of the solution
(particle) to be evolved. The expression of probability,
Pe is given below:
if k
if
)(
)(
4
2











PbestPbest
PbestPbest
Pbestgbest
Pbestgbest
k
P
i
i
i
e
(11)
Here, values of k2 and k4 are kept equal to 0.5 [22].
This adaptive probability helps PSO to avoid getting
stuck at local optimum.
The value of Pe increases when the fitness of the
particle is quite poor. In contrast when the fitness of the
particle is a good solution, Pe will be low.
SA starts with a local best solution pbest of a selected
particle Xi and generates a random neighbor solution
using a heuristic strategy. A valid threshold
ij
t

52 A Fully Adaptive and Hybrid Method for Image Segmentation Using Multilevel Thresholding
Copyright © 2013 MECS I.J. Image, Graphics and Signal Processing, 2013, 1, 46-57
(
1 
ij

)in Xi is chosen to undergo a perturbation
operation with probability equal to 0.2. The threshold
value is then modified as follows:
][ where
)(*
maxmin
minmax
,ggt
ggtt
new
ij
old
ij
new
ij



(12)
where
new
ij
t
and
old
ij
t
represent the new and the old
threshold value.

is a random number between [-1, 1].
Thus the solution encoded by the particle is
reconfigured, although the number of thresholds
belonging to it remains unaltered.
After the SA-based local search is completed, the
gbest of the whole swarm should be updated if a
solution with better quality is found during the local
search.
IV. EXPERIMENTAL RESULTS
In order to assess the ability of the proposed
algorithm to determine the number of thresholds and to
achieve good quality image segmentation, synthetic and
real images (Lena, Pepper, Baboon, Airplane, Hunter
and Cameraman) have been used.
Figures 2 and 3 show these test images along with
their histograms. All real images are of size (512 x 512)
except the Pepper image which is of size (256 x 256).
Experiments have been carried out for several number
of thresholds M ranging from 2 to 5. First experiments
have been conducted to set the control parameters used
in the AMT-PSOSA algorithm. Their values are
gathered in Table 1.
The quality of the thresholded image has been
evaluated using the uniformity measure defined by the
following equation:
Figure 2. Synthetic image and its histogram.
Figure 3. Real test images and their histograms a)Lena; b) Pepper,
c)Mandril, d) Airplane, e) Hunter, f) Cameraman
2
minmax
0
2
)(*
)(
)(*21 ggN
g
MU
M
jRi
ji
j






(13)
Where
M is the number of thresholds,
Rj is the segmented region j,
gi is the grey level of pixel i

j is the mean of grey levels of those pixels in
segmented region j
N is the total number of pixels in the given
image,
gmax is the maximal grey level of the pixels in
the given image,
gmin is the minimum grey level of the pixels in
the given image,
The domain of the uniformity measure is the range
[0,1]. A higher value of uniformity means that the
quality of the thresholded image is better.
d
e
f

A Fully Adaptive and Hybrid Method for Image Segmentation Using Multilevel Thresholding 53
Copyright © 2013 MECS I.J. Image, Graphics and Signal Processing, 2013, 1, 46-57
TABLE 1. PARAMETER SETTINGS FOR AMT-PSOSA
ALGORITHM
Parameters
Values
Population size (Np)
Maximum Inertia weight (wmax)
Minimum Inertia weight (wmin)
Maximum velocity (Vmax)
Minimum velocity (Vmin)
Cognitive coefficient (C1)
Cognitive coefficient (C2)
Maximum number of iterations (itermax )
// parameter values of SA algorithm
Initial temperature (T0)
Final temperature (Tf)
Annealing rate (

)
maximum number of iteration (iterSAmax)
50
0.9
0.4
+1.0
-1.0
1.429
1.429
1000
1000
1
0.99
100
TABLE 2. PARAMETER SETTINGS FOR THE GA AND
DMTBPSO ALGORITHMS.
Parameter set for the GA algorithm
Values
Population size (Np)
Crossover probability (Pc)
Mutation probability (Pm)
Maximum number of iterations
100
0.9
0.1
1000
Parameter set for the DMTBPSO algorithm
Values
Population size (Np)
Pini
Inertia weight (w)
Maximum velocity (Vmax)
Cognitive coefficient (C1)
Cognitive coefficient (C2)
Maximum number of iterations
100
0.5
0.72
255
2
2
1000
To further appreciate the performance of the proposed
method, experimental results from the multilevel
thresholding technique based on the recently developed
automatic multilevel thresholding algorithm DMTBPSO
[38] and on a classical PSO and GA algorithms have
been examined and compared with the proposed method
AMT-PSOSA. In order to make an objective
comparison, the results through an exhaustive search
method are also presented. GA-based method, PSO-
based method and the exhaustive search method use
Otsu‘s criterion as objective function defined below:


 M
kkkOtsu Mf
0
2
)()(

In the following we will refer to them as ES-Otsu,
GA-Otsu, PSO-Otsu and DMTBPSO. Parameter values
of GA and DMTBPSO algorithms are presented in
Table 2. We employ the best possible parameter settings
recommended for DMTBPSO algorithm in [38]. PSO-
Otsu is implemented using the same parameter values of
AMT-PSOSA.
For GA-Otsu, PSO-Otsu and ES-Otsu, the number of
thresholds must be given in advance. In order to
compare them with the proposed AMT-PSOSA, we
must reformulate them in such a way that the number of
thresholds is extracted automatically. As in [7], GA-
Otsu, PSO-Otsu and ES-Otsu are executed in this paper
with varying gradually the number of thresholds. The
optimal threshold number, which optimizes the cost
function ATC defined, is recorded.
The main steps of this algorithm are given in
algorithm 4 below [7].
Algorithm 4
1. M=1
2. Apply the ES-Otsu method or the GA-Otsu method
or PSO-Otsu method using the number M of
thresholds
3. Compute the value of the cost function F(M) by
using the output optimal thresholds values
4. If F(M) is decreased, set M=M+1 and go to step 2
else go to step 5
5. Output the threshold number M* and the optimal
thresholds values obtained from the corresponding
multilevel thresholding method.
Moreover, in order to investigate the effects of the
hybridization of the PSO with SA, we have compared
AMT-PSOSA with a classical PSO based multilevel
thresholding method (AMT-PSO) which uses the same
particle representation scheme and fitness function as
the AMT-PSOSA.
Table 3 summarize the obtained results for the
synthetic and real images using the proposed AMT-
PSOSA algorithm and the other multilevel thresholding
algorithms including the optimal number of thresholds,
the corresponding best ATC function value and the
uniformity measure related to the synthetic image and
the six real test images. Also the computing time of each
algorithm is given for each image. From this table, we
can draw the following conclusions: The computational
time of the exhaustive search method (ES-Otsu) is very
expensive and increases sharply when the number of the
thresholds increases. AMT-PSO and AMT-PSOSA
algorithms provide the same threshold number than GA-
Otsu, PSO-Otsu and ES-Otsu algorithms, for all test
images. The results of AMT-PSO and AMT-PSOSA
algorithms are better than those of DMTBPSO
algorithm. AMT-PSOSA is better that AMT-PSO which
means that performance is greatly improved by the SA-
local search procedure. In most cases, the performance
of the proposed method, evaluated through the optimal
threshold number M*, the cost function F(M) and the
uniformity measure U, are close to those of ES-Otsu.
From computation time view point, the proposed
method gives a reasonable CPU time, even though the
SA-local search is added.

54 A Fully Adaptive and Hybrid Method for Image Segmentation Using Multilevel Thresholding
Copyright © 2013 MECS I.J. Image, Graphics and Signal Processing, 2013, 1, 46-57
TABLE 3. COMPARISON OF PERFORMANCES FOR SYNTHETIC AND REAL TEST IMAGE
Image
Algorithms
M*
Thresholds values
ATC function
Uniformity
CPU time
Synthetic image
ES-Otsu
3
74-126-176
6.353374
0.997436
9.897
GA-Otsu
3
74-126-176
6.353374
0.997436
0.987
PSO-Otsu
3
74-126-176
6.353374
0.997436
0.645
DMTBPSO
3
81-125-171
6.513393
0.997218
1.092
AMT-PSO
3
74-126-176
6.353374
0.997436
0.065
AMT-PSOSA
3
74-126-176
6.353374
0.997436
0.480
Lena
ES-Otsu
4
75-114-145-180
9.948331
0.991877
5571.872
GA-Otsu
4
74-112-145-180
9.948545
0.987776
0.987
PSO-Otsu
4
74-114-145-180
9.948331
0.991877
0.468
DMTBPSO
4
78-117-150-187
10.04973
0.991598
0.428
AMT-PSO
4
73-113-146-185
9.950145
0.991750
0.062
AMT-PSOSA
4
75-114-145-180
9.948331
0.991877
0.420
Pepper
ES-Otsu
4
49-88-129-172
10.742761
0.992231
879.786
GA-Otsu
4
49-87-129-171
10.744781
0.987543
1.045
PSO-Otsu
4
50-88-130-172
10.744231
0.991976
0.749
DMTBPSO
4
52-102-137-168
11.203033
0.991064
0.953
AMT-PSO
4
49-89-128-171
10.746420
0.992161
0.094
AMT-PSOSA
4
50-89-129-172
10.743711
0.992168
0.303
Mandril
ES-Otsu
3
86-124-159
9.599374
0.991805
108.795
GA-Otsu
3
85-123-158
9.600745
0.986334
1.023
PSO-Otsu
3
85-124-158
9.599423
0.990754
0.733
DMTBPSO
3
76-116-155
9.695672
0.991581
0.777
AMT-PSO
3
84-125-161
9.628662
0.990648
0.047
AMT-PSOSA
3
86-124-159
9.599374
0.991805
0.688
Jetplane
ES-Otsu
3
89-141-188
9.367949
0.991605
69.218
GA-Otsu
3
88-140-188
9.377912
0.988023
0.987
PSO-Otsu
3
89-141-188
9.367949
0.991605
0.577
DMTBPSO
3
82-143-176
9.821992
0.990456
0.675
AMT-PSO
3
90-139-186
9.377236
0.991582
0.047
AMT-PSOSA
3
89-141-188
9.367949
0.991605
0.285
Hunter
ES-Otsu
3
71-114-155
9.951925
0.989024
54.102
GA-Otsu
3
71-114-155
9.951925
0.989024
0.923
PSO-Otsu
3
71-114-155
9.951925
0.989024
0.686
DMTBPSO
4
71-114-149-182
10.16450
0.989953
0.767
AMT-PSO
3
71-113-155
9.954443
0.989017
0.047
AMT-PSOSA
3
71-114-155
9.951925
0.989024
0.520
Cameraman
ES-Otsu
3
57-116-154
10.105743
0.992610
113.106
GA-Otsu
3
59-119-156
10.106754
0.987334
1.023
PSO-Otsu
3
57-116-154-
10.105343
0.992610
0.702
DMTBPSO
4
60-110-150-167
10.633063
0.992482
0.876
AMT-PSO
3
55-114-153
10.106912
0.992608
0.063
AMT-PSOSA
3
57-116-154
10.105743
0.992610
0.490
As PSO is a stochastic optimization algorithm, the
stability of the PSO-based strategies has also been
assessed by gathering optimal number of thresholds and
the corresponding objective function F(M) values over
several runs. The variation of the results through different
runs gives an indication of the stability of the used
algorithm which is influenced by its search abilities. The
more results are close to each other, the more stable is the
algorithm. The mean  and standard deviation  are
defined as:
 



 k
ii
k
ii
kk 1
2
11
,



(14)
where k is the number of runs for each stochastic
algorithm (k = 50), i is the best objective value obtained
by the ith run of the algorithm. Higher standard deviation
values show that the algorithm is unstable.

A Fully Adaptive and Hybrid Method for Image Segmentation Using Multilevel Thresholding 55
Copyright © 2013 MECS I.J. Image, Graphics and Signal Processing, 2013, 1, 46-57
TABLE 4. MEAN AND THE STANDARD DEVIATION VALUES OF THE NUMBER OF THRESHOLDS, THE CORRESPONDING
OBJECTIVE VALUES AND THE UNIFORMITY MEASURE THROUGH 50 RUNS OBTAINED BY DIFFERENT OPTIMIZATION
ALGORITHMS
Images
Algorithms
M*
ATC function
Uniformity
mean
deviation
mean
deviation
mean
deviation
Lena
DMTBPSO
4.15
0.589
11.01742
4.7964e-01
0.98969
1.2961e-03
AMT-PSO
3.75
0.046
10.13291
7.4081e-02
0.99103
6.9339e-04
AMT-PSOSA
4
0
9.95813
9.1729e-03
0.99185
1.5489e-05
Pepper
DMTBPSO
5.25
0.433
12.24612
3.5860e-01
0.99039
1.2767e-03
AMT-PSO
3.5
0.049
11.01522
1.1722e-03
0.99101
6.2871e-04
AMT-PSOSA
4
0
10.75325
1.0666e-03
0.99217
2.4848e-05
Mandril
DMTBPSO
4.06
0.661
10.82737
4.7496e-01
0.99084
1.1987e-03
AMT-PSO
3.1
0.030
9.63651
3.0049e-05
0.99168
4.2643e-04
AMT-PSOSA
3
0
9.60531
2.3790e-05
0.99179
1.0138e-05
Jetplane
DMTBPSO
4.05
0.668
10.27023
4.5917e-01
0.99087
1.0525e-03
AMT-PSO
2.95
0.022
9.44559
4.9994e-03
0.99141
1.1638e-04
AMT-PSOSA
3
0
9.37127
3.0340e-03
0.99159
7.4358e-06
Hunter
DMTBPSO
4.15
0.572
10.88537
4.6357e-01
0.98791
1.6340e-03
AMT-PSO
3
0
10.06812
3.0755e-04
0.98871
1.8056e-04
AMT-PSOSA
3
0
9.95374
2.2595e-04
0.98902
6.6696e-06
Cameraman
DMTBPSO
4.9
0.72
11.44428
3.9183e-01
0.99206
1.1916e-03
AMT-PSO
2.9
0.061
10.19008
4.1678e-03
0.99265
2.9348e-04
AMT-PSOSA
3
0
10.10832
4.1132e-03
0.99269
8.0141e-06
The mean and the standard deviation values of the
number of thresholds, the corresponding objective values
and the uniformity measure through 50 runs for
DMBTPSO, AMT-PSO and AMT-PSOSA algorithms
has been recorded in Table 4 for the six real test images.
As shown on the Table 4, the proposed algorithm
achieves mean values that are closest to optimal ones
compared to any of the other strategies. Furthermore, the
achieved standard deviation values indicate the
superiority of AMT-PSOSA over the other algorithms in
terms of stability.
V. CONCLUSION
In this paper, we have proposed a new automatic
multilevel thresholding algorithm based on the
hybridization of the Particle Swarm Optimization with
the Simulated Annealing. The new developed hybrid
technique makes full use of the exploration ability of
PSO and the exploitation ability of SA and offsets the
weaknesses of each. AMT-PSOSA uses both real and
discrete values for the particle representation in order to
determine the appropriate number of thresholds as well as
the optimal threshold values using the ATC function.
Experimental results over synthetic and real test images
show the efficiency of AMT-PSOSA over exhaustive
search method, GA based method, PSO based method
and the recently proposed DMTBPSO algorithm.
ACKNOWLEDGMENT
The authors would like to thank the anonymous
reviewers for their helpful comments.
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OUADFEL Salima, received her state engineer degree,
master degree in computer science from Mentouri
University in Constantine Algeria and she received a PhD
in Computer Science from the University of Batna,
Algeria, in 2007. She is currently an Associate Professor
at the computer science department of Mentouri
University and a researcher at MISC laboratory
Constantine City. Her current research includes natural
inspired metaheuristics and their applications for image
processing.
MESHOUL Souham, received the state engineer degree,
master degree and State doctorate degree in computer
science from Mentouri University in Constantine Algeria.
She is currently an associate professor at the computer
science department and a researcher at MISC laboratory
Constantine City. Her current interests include
computational intelligence and its applications, complex
systems, bioinformatics, pattern recognition and image
analysis and understanding.