Image Segmentation Based on Bio-Inspired Optimization Algorithms

Abstract

This chapter addresses the issue of image segmentation by clustering in the domain of image processing. Fuzzy C-Means is a widely adopted clustering algorithm. Bio-inspired optimization algorithms are optimal methods inspired by the principles or behaviors of biology. For the purpose of reinforcing the global search capability of FCM, five Bio-Inspired Optimization Algorithms (BIOA) including Biogeography- Based Optimization (BBO), Artificial Fish School Algorithm (AFSA), Artificial Bees Colony (ABC), Particle Swarm Optimization (PSO), and Bacterial Foraging Algorithm (BFA) are used to optimize the objective criterion function, which is interrelated to centroids in FCM. The optimized FCMs by the five algorithms are used for image segmentation, respectively. They have different effects on the results.

Full text

Image Segmentation Based on Bio-
Inspired Optimization Algorithms
Hongwei Mo
Automation college, Harbin Engineering University, China
Lifang Xu
Engineering Training Center,Harbin Engineering University, China
Mengjiao Geng
Automation college, Harbin Engineering University, China
ABSTRACT
This paper addresses the issue of image segmentation by clustering in the domain of image processing.
Fuzzy C-Means is a widely adopted clustering algorithm. Bio- inspired optimization algorithms are
optimal methods inspired by the principles or behaviors of biology. For the purpose to reinforce the
global search capability of FCM, five bio-inspired optimization algorithms(BIOA) including
Biogeography Based Optimization(BBO),Artificial Fish School Algorithm(AFSA), Artificial Bees
Colony(ABC),Particle Swarm Optimization(PSO) and Bacterial Foraging Algorithm(BFA)are used to
optimize the objective criterion function which is interrelated to centroids in FCM. And the optimized
FCMs by the five algorithms are used to image segmentation, respectively.They have different effects on
the results.
INTRODUCTION
Image segmentation is one of the central problems in computer vision and pattern recognition. It refers to
the process of assigning a label to every pixel in an image such that pixels with the same label share
certain visual characteristics. The result of image segmentation is a set of segments (sets of pixels) that
collectively cover the entire image. Pixels in the same region are similar with respect to some
characteristics or computed properties, such as color, intensity, and texture. Adjacent regions are
significantly different with respect to the same characteristics. The goal of segmentation is to simplify
and/or change the representation of an image into something that is more meaningful and easier to
analyze (Shapiro & Stockman, 2001).
There are many general-purpose approaches available for image segmentation such as threshold methods
(Mardia & Hainsworth, 1988), edge-based methods (Perona & Malik, 1990), region-based methods
(Hijjatoleslami & Kitter, 1998), and graph-based methods (Felzenszwalb & Huttenlocher, 2004). In
contrast to the heuristic nature of these methods, one would formalize an objective criterion for evaluating
a given segmentation. This would allow us to formulate the segmentation problem as an optimization
problem. The objective function that one would seek to optimize is the interclass variance that is used in
cluster analysis. An optimizer can lead to efficient solutions for optimal segmentation. But the objective
function is usually not a monotone chain, therefore the problem is general NP-hard. Following this way,
some clustering methods have been applied to solve image segmentation problems.
Clustering techniques represent the non-supervised pattern classification in groups (Jain et al., 1999).
Considering the image context, the clusters correspond to some semantic meaning in the image, which is,
objects. Among the many methods for data analysis through clustering and unsupervised image
segmentation is: Nearest Neighbor Clustering, Fuzzy C-Means (FCM) clustering and Artificial Neural
Networks for Clustering (Jain et al., 1999). Such bio and social-inspired methods try to solve the related
problems using knowledge found in the way nature solves problems. Social inspired approaches intend to
solve problems considering that an initial and previously defined weak solution can lead the whole

population to find a better or a best so far solution.
Among them, the most successful image segmentation algorithm into homogeneous regions is fuzzy
c-means algorithm (Bezdek, 1981). There are a lot of visual applications reporting the use of fuzzy
c-means, e.g. in medical image analysis, soil structure analysis, satellite imagery (Felzenszwalb &
Huttenlocher, 2004; Hijjatoleslami & Kitter, 1998; Mardia & Hainsworth, 1988; Perona & Malik, 1990).
Many variations of approaches have been introduced over last 20 years, and image segmentation remains
an open-solution problem. As global optimization techniques, evolutionary algorithms (EAs) are likely to
be good tools for image segmentation task. In the past two decades, EAs have been applied to image
segmentation with promising results (Andrey, 1999; Bhandarkar & Zhang, 1999; Bhanu et al., 1995;
Gong et al., 2008; Koppen et al., 2003; Maulik, 2009; Melkemi et al., 2006; Veenman et al., 2003). These
algorithms exploited the metaphor of natural evolution in the context of image segmentation.
The original FCM algorithm, due to its drawbacks such as poor ability of global searching, easy sticking
at local optimal solution, is often improved by combining with other optimal algorithm and then used in
image segmentation. In this paper, we adopt five bio-inspired optimization algorithms to search the center
of cluster for FCM. The paper is organized as follows. At first, the FCM and image segmentation are
introduced respectively. Second, BBO, AFSA,ABC, PSO and BFOA are introduced. Third, the hybrid
clustering methods of the five BIOAs and FCM are tested on some standard images from the USC-SIPI
Image Database and the simulation results are analyzed. At last, the conclusions are drawn.
BACKGROUND
Recently there has been an increase in the presence of bio-inspired optimization algorithms(BIOA) of
image segmentation. Most of them focus on searching the right center of cluster for FCM. Yang et al.
(2007) proposed a FCM based on Ant Colony Algorithm. Tian et al. (2008) applied the FCM optimized
by PSO to segment SAR images and its experimental results on the MSTAR dataset had demonstrated
that the proposed method was capable of effectively segmenting SAR images and achieving better results
than the improved FCM (IFCM) algorithm. Yang et al. (2008) had proposed a three-level tree model
which was inspired from the ants’ self-assembling behavior to make the clustering structure more
adaptive for image segmentation. In order to increase the segmentation precision of brain tissues in MR
images to solve some problems existing in the present genetic fuzzy clustering algorithm, Nie, et al. (2008)
had proposed an improved genetic fuzzy clustering algorithm. Experiment results showed that higher
segmentation accuracy was obtained using the proposed segmentation method comparing with the fast
FCM algorithm and the conventional genetic fuzzy clustering algorithm. Zeng et al. (2008) directly
unified GA in the magnetic resonance images (MRI) segmentation and the global optimum in MRI
segmentation was obtained. Swagatam, et al.(2010) had presented a modified differential evolution (DE)
algorithm for clustering the pixels of an image in the gray-scale intensity space in their paper and
extensive comparison results has indicated that the proposed algorithm has an edge over a few
state-of-the-art algorithms for automatic multi-class image segmentation. Sowmya et al. (2011) had used
a competitive neural network (CNN) and fuzzy clustering techniques to segment color images.
In Sathya(2011), MBF algorithm for solving the multilevel thresholding for image segmentation is
proposed. The proposed method considers the two objective functions of the Kapur’s and Otsu’s methods.
The feasibility of the proposed method is demonstrated for fourteen different images and compared with
BF, PSO and GA methods. The results show that the proposed MBF algorithm can significantly
outperform the other evolutionary techniques, on the basis of the solution quality, stability and
computation efficiency.
In Sathya(2011), the authors propose a new optimization approach to solve multilevel thresholding using
the adaptive bacterial foraging (ABF)technique.
Balasubramani(2013) used Artificial Bee Colony Algorithm to improve the efficieny of FCM on
abnormal brain image.
IMAGE SEGMENTATION AND FCM

The State-of-the-art
In general, image segmentation techniques can be classified in:
a. Threshold-based techniques: are generally used for gray level images. A threshold
value T is defined to split the image in two parts: foreground and background based on pixel value
b. Histogram-based techniques: the histogram of all the pixels is calculated, and
according to peaks and valleys different clusters are formed
c. Edge detection techniques: first and second order derivatives are used for detection of edges. Edges
are divided in two categories: intensity edges and texture edges
d. Region-based techniques: uses region growing and region splitting-merging procedures. Region
growing procedure groups pixels or sub regions into large regions based on predefined criteria. Region
split-merge divides image into disjoint regions and then either merge and/or split to satisfy prerequisite
constraints
e. Watershed Transformation techniques: considered to be more stable than the previous techniques, it
considers the gradient magnitude of an image (GMI) as a topographic surface. Pixels having the highest
GMI correspond to watershed lines, which represent region boundaries.
In summary, image features may contain concepts (definitions of things) and relations between concepts.
This chapter is located in this context of optimization techniques. We present some new techniques to
solve clustering and image segmentation problems and discussion about experiments and results.
The FCM
Clustering is the most popular method for medical image segmentation, with fuzzyc-means(FCM)
clustering and expectation– maximization(EM)algorithms being the typical methods. A common
disadvantage of EM algorithms is that the intensity distribution of brain images is modeled as a normal
distribution,which is not the fact for noisy images. FCM is a kind of simple mechanical clustering method
based on exploring minimum value of the objective function (Wu & Yang, 2002). The objective function
proposed by Dunn is called the clustering criterion function, namely error squares function. Historically,
FCM clustering algorithm introduced by Bezdek(Bezdek,1981) is based on minimizing an objective
function, with respect to the fuzzy membership and set of cluster centroids. It has the drawback of
increase insensitivity of the membership function to noise. If image contains noise or is affected by
artifacts, their presence can change the pixel intensities, which will result in an improper segmentation.
Let
],,,[ 21 n
xxxX 
be the n dimension sample space. The criterion function is shown by (1):

 
 c
i
N
kA
ik
m
ik xVUXJ 1 1
2
)(),;(

(1)
where
n
ic RvvvvV  ],,,,[ 21 
, V is the clustering center.
The Euclidean distance between data set
k
x
and clustering center
i

is
)()(
2
2ik
T
ik
A
ikikA xAxxD


(2)
where
ik

is the membership function that the
th
i
sample belongs to
th
k
clustering center. It is define
by equation (3)
Nkci
DD
c
j
m
jkAikA
ik  


1,1,
)/(
1
1
)1/(2

(3)
FCM is described as follows:
Step1: Select
0e
, initialize clustering centre
0

, let
1g
.
Step2: Calculate the fuzzy matrix
g
U
based on equation (3).
Step3: If

i
and
r
make
1)( g
ir

and
rk 
, then let
0)( g
ir

.
Step4: Update the clustering center following equation (4):

ci
x
N
k
m
ik
N
kk
m
ik
i 


1,
1
1



(4)
Step5: If
e
kk  )1()(

, stop iteration, else let
1 gg
and return to step 1.
BIO-INSPIRED OPTIMIZATION ALGORITHMS
Biogeograpy Based Optimization
BBO is a new population-based optimization algorithm(Simon,2008), which mimics how animals migrate
from one habitat to another, how new species arise, and how species become extinct. These biological
behaviors are modeled into search methods for optimization. In BBO, the variables that characterize
habitability are called suitability index variables (SIVs), which are similar to genes of genetic algorithms
(GAs). Each individual is considered as a habitat with a habitat suitability index (HSI), which is similar to
the fitness of GAs. A good solution is analogous to a habitat with a high HSI and shares its good SIVs
with low HSI solution. Low HSI solutions accept a lot of new features from high HSI solutions to raise
their quality.
The main feature of BBO which differs from the other EAs lies in its migration strategy or migration
operation. In BBO, each individual has its own emigration rate and immigration rate, which are the
functions of the number of species in the habitat. Mathematically, the concept of emigration and
immigration can be represented by a probabilistic model. Suppose that the number of an individual’s
species is
k
(
max
1,2,...,kS
where
max
S
is the maximum number of species), and then immigration
rate
k

and emigration rate
k

can be calculated as:
max
(1 )
kk
IS


(5)
max
kEk
S


(6)
where
I
and
E
are the maximum possible immigration and emigration rate, respectively.
If a given solution is selected to be modified, its immigration rate

is used to probabilistically decide
whether or not to modify each SIV in that solution. If a given SIV in a given solution
i
X
is selected to
be modified, the emigration rates

of the other solutions is used to probabilistically decide which
solution
j
X
should migrate a randomly selected SIV to the solution
i
S
. Migration is written as
   
ij
X SIV X SIV
(7)
After migration is completed, mutation is used to increase the diversity of the population to get better
solutions. Mutation changes a habitat’s SIV randomly based on mutation rate, just as in other EAs.
Suppose that
N
is the size of the population
P
,
T
is the iteration generation and
max
g
is maximum
number of generation, the pseudo-code of BBO is given in Algorithm 1.
Algorithm 1  BBO algorithm
Initialize parameters:
N
,
max
g
Evaluate the fitness for each habitat in population
P
While
max
Tg
do
For each habitat do
Map the HSI to number of species k,

and

according to (6) and

(7)
Probabilistically choose the immigration habitat based on

If immigrating then
Probabilistically choose the emigration habitat based on

   
ij
X SIV X SIV
End if
End for
Probabilistically decide whether to mutate each habitat in population
P
Evaluate the fitness for each habitat in population
P
T
=
T
+1
End while
Artificial Fish School Algorithm
The models imitate the fish swarm series of behavior in nature which can be defined as(Rocha,2011):
1. Random behavior
2. Searching behavior
3. Swarming behavior
4. Chasing behavior
5. Leaping behavior
The next behavior of artificial fish depends on its current state and environmental state. Random behavior
can be presented as the initialization phase of the algorithm. The crucial step in the AFS algorithms is a
“visual scope”. A basic biological behavior of any animal is to discover a region with more food, by
vision or sense. Depending on the current position of the individual in the population,marked as
in
xR
,
three possible situations may occur:
1. When the “visual scope” is empty, and there are no other individuals in its neighborhood to follow,
individual
i
x
moves randomly searching for a better region
2. When the “visual scope” is crowded, the xi individual has difficulty to follow any particular individual,
and searches for a better region choosing randomly another location from the “visual scope”.
3. When the “visual scope” is not crowded, the xi individual can choose between two option: to swarm
moving towards the central or to chase moving towards the best location. The condition that determines
the crowd issue of xi individual in the ‘visual scope’ is given in Eq. 8:
i
np
m


(8)
where
(0,1]


is the crowd parameter,
m
is the number of individuals in the population and
i
np
is
the number of individuals in the “visual scope”. In the searching behavior phase, an individual is
randomly chosen in the “visual scope” of
i
x
and a movement towards it is carried out if it improves
current
i
x
location. Otherwise, the individual
i
x
moves randomly. The swarming behavior is
characterized by a movement towards the central point in the “visual scope” of
i
x
. The swarming
behavior is progressive stage that is activated only if the central point has a better function value than the
current
i
x
. Otherwise, the point
i
x
follows the searching behavior. The chasing behavior presents a
movement towards the point that has the last function value
min
x
. The swarm and chase behavior can be
considered as local search. Leaping behavior solves the problem when the best objective function value in
the population does not change for a certain number of iterations. In this case the algorithm selects
random individual from the population. This process empowers algorithm for obtaining better results in
solving numerous problems.

Artificial Bee Colony Optimization
As mentioned before, Karaboga (2005) developed an algorithm based on the behavior of honey bees,
called ABC. The ABC pseudo code is shown next:
1.Initialize food sources
2. Repeat
3. Each employed goes to a food source in its memory
3a. Determines a neighbor source
3b. Evaluates nectar
3c. Return to hive and dances
4. Each onlooker watches the dance
4a. Chooses one of the sources, considering the intensity of dance
4b. Goes to the food source selected
4c. Determines a neighbor source
4d. Evaluates nectar
5. The food sources abandoned are determined
Abandoned food sources are replaced by new ones discovered by scouts
6. The best food source until this iteration is saved
7. Go to step 2 until a certain criteria is reached.
The initial food sources are randomly initialized, by the formula:
,_ ()( _ _ )
k
i j j j j
x x low rand x high x low  
(9)
1,2,..., ; 1,2,..., ; 0
fs
j D i N k  
being considered that
_j
x high
and
_j
x low
are the upper and lower limits where the function to optimize
is defined;
fs
N
is the number of food sources,
D
states for dimensions and
k
is the actual iteration.
Next in the algorithm, each employed bee is sent to a randomly selected food source and a neighbor is
determined.
Both, the source in memory and the modified one are evaluated; the bee memorizes the new position and
forgets the old one. Later, employed bees return the hive and dances; and onlooker bees will choose a
food source to exploit according to a probability’s function:
1
fs
i
iN
j
j
fit
qfit


(10)
where
i
fit
represents the fitness of solution
i
,evaluated by the employed
i
,calculated by:
1( ) 0
( ) 1
1 ( ( ))
i
i
i
i
if f x
fx
fit
abs f x elsewhere





(11)
Later, again a neighbor is determined by the onlooker, both food sources are evaluated and the best is
memorized. Finally, one scout is generated at the end of each iteration in order to explore for new food
sources. The cycle is repeated both until a minima distance is reached or a maximum iterations number.
Particle Swarm Optimization
Particle Swarm Optimization (PSO) was created as a general purpose optimizer in 1995, when Kennedy
and Eberhart joined their efforts in order to simulate the social behavior of some species; those efforts
evolved until the simulation became a general purpose optimizer whose main idea lies behind the
individuals in a swarm (Kennedy & Eberhart, 1995). In this work we have used a modification of Clerc’s
PSO (Clerc,1999), where a constriction parameter is used. In that PSO version, the two main governing
equations are:
1( 1 () ( _ ) 2 () ( _ ))
k k k k
i k i i i i
v v c rand p best x c rand g best x

         
(12)

11k k k
i i i
x v x


(13)
In the first part of the algorithm, the particles’ positions and velocities are randomly initialized:
,_ ()( _ _ )
k
i j j j j
x x low rand x high x low  
(14)
,_ ()( _ _ )
k
i j j j j
v v low rand v high v low  
(15)
1,2,..., ; 1,2,..., ; 0
p
j D i N k  
Considering
()rand
is a uniformly distributed random number,
_j
x high
and
_j
v high
are the
superior limits that positions and velocities can reach;
_j
x low
and
_j
v low
are the respective inferior
limits, and
p
N
states the particle’s number. The next part deals with knowing
_i
p best
known as the
best particle found at
i
-th position until iteration
k
,and
_g best
represents the best global particle
found so far, considering all the population. Once the aforementioned values are found, velocities and
position of all particles are actualized by using Eq. (13), taking into account that
k

is the constriction
parameter as proposed in Wei and Kangling (2008), modified with:
k

=
0max
exp k
N






(16)
Usually
1 2 2cc
. It is important to notice that the dynamic constriction parameter is a slightly
difference to the original Clerc’s algorithm, in which the constriction parameter is static. In this case,
0

is an initial constriction value,

is a control value,
k
is the actual iteration and
max
N
represents the
maximum number of iterations.
Bacterial Foraging Optimization Algorithm
Passino (2002) proposed a new kind of bionic algorithm-- Bacteria Foraging Optimization Algorithm
(BFOA) which is based on the behavior that E. coli engulfs food in human's intestinal. In this algorithm,
each individual in the colony is independent. They continuously change direction and step length to find
out the local point with the most abundant food in the search space which is equivalent to the optimal
solution in algorithm. Meanwhile, in order to enhance the searching accuracy, this algorithm contains
replication and elimination processes to find the global optimal solution. Besides very strong global
search ability, BFOA also has fine local search capability (Chu et al., 2008).The basic procedures of
BFOA are demonstrated as follows:
Step 1： Initialization
n
,
S
,
C
N
,
S
N
,
re
N
,
ed
N
,
ed
P
,
)(iC
),2,1( Si 
are the main parameters, where
n
: Dimension of the search space,
S
: The number of bacteria in the colony,
C
N
: Chemotactic steps,
S
N
: Swim steps,
re
N
: Reproductive steps,
ed
N
: Elimination and dispersal steps,
ed
P
: Probability of elimination,
)(iC
: Run-length unit.
Step 2: Elimination-dispersal loop:
1 ll
.
Step 3: Reproduction loop:
1 kk
.
Step 4: Chemotaxis loop:
1 jj
.

a) For
Si ,2,1
, take a chemotactic step for bacterium
i
as follows.
b) Compute fitness function,
),,,( lkjiF
.
c) Let
),,,( lkjiFMlast 
to save this value since we may find a better value via a swim.
d) Tumble: Generate a random vector
n
Ri  )(
with each element
)(im
,
1,2,mn
, a
random number in
]1,1[
.
e) Move: Let
)()(
)(
)(),,(),,1( ii
i
iClkjlkj T
ii




(17)
This results in a step of size
)(iC
in the direction of the tumble for bacterium
i
.
f) Compute
),,,( lkjiF
with
),,1( lkj
i

.
g) Swim:
(i) Let
0m
(counter for swim length).
(ii) While
S
Nm 
• Let
1 mm
.
• If
last
FlkjiF  ),,1,(
, let
),,1,( lkjiFFlast 
, then anther step of size in this
same direction will be taken as (5) and use the new generated
),,1( lkj
i

to compute
the new
),,1,( lkjiF 
.
• Else let
S
Nm 
.
h) Go to next bacterium
1i
.if
Si 
, go to sub-step b) to process the next bacterium.
Step 5: If
C
Nj 
, go to step 3. In this case, continue chemotaxis since the life of the bacteria is not
over.
Step 6: Reproduction
For the given
k
and
l
, and for each
Si ,2,1
, let:



1
1),,,(
c
N
j
i
health lkjiFF
(18)
be the health of the bacteria. Sort bacteria in order of ascending values (
health
F
).
The
r
S
bacteria with the highest Fhealth values die and the other
r
S
bacteria with the best values split
and the copies are placed at the same location as their parent.
Step 7: If
re
Nk 
，go to step 2. In this case the number of specified reproduction steps is not
reached and start the next generation in the chemotactic loop.
Step 8: Elimination–dispersal. For
Si ,2,1
, with probability
ed
P
, eliminate and disperse each
bacterium, which results in keeping the number of bacteria in the population constant. To do this, if a
bacterium is eliminated, simply disperse one to a random location on the optimization domain. If
ed
Nl 
, then go to step 2, otherwise ends.
In the BFOA, run-length unit is the size of the step taken in each swim or tumble. In order to use it to
solve the problem of clustering, the run-length is changed to be adaptive. Here, we define
)(iC
as
follows:
),(**00001.0)1,( jiCMlastjiC 
(19)
where
i
represents the
th
i
bacterium,
j
the
th
j
chemotaxis,
Mlast
the fitness value of the
th
i
bacterium in
th
j
chemotaxis.

BF-FCM Algorithm
In this section, for example, we combine BFOA and FCM to implement clustering. We use BFOA to
optimize clustering criterion function of FCM algorithm.
The clustering criterion function in FCM algorithm is taken as the fitness function
),,,( lkjiF
in
BF-FCM. That is,
),,,( lkjiF
=

 
 c
i
N
kA
ik
m
ik xVUXJ 1 1
2
)(),;(

(20)
The main steps of BF-FCM are:
Step1: According to the clustering category number
c
, set the bacteria number as its 10 times,
which is
cS  10
.
Step2: Select
0e
, initialize clustering center
0

based on equation (4), let
1g
.
Step3: Initialize parameters
n
,
S
,
C
N
,
S
N
,
re
N
,
ed
N
,
ed
P
,
)(iC
Step4: Calculate fuzzy matrix
g
U
according to the equation (3).
Step5: Compute the minimum value of the fitness function.
Step6: If
e
kk  )1()(

, stop iteration, else let
1 gg
and return to step 1.
Step7: After the iteration in step 6, take the position of bacteria as the cluster centers. Then start
clustering by FCM.
Step8: When FCM finishes clustering, then BF-FCM ends.
IMAGE SEGMENTATION EXPERIMENTS
Experiments Evaluation
The experiments rely on evaluate numerical results of clustering algorithms based on BBO, AFSA, ABC,
PSO and BFOA. We define the following algorithms variations:
a. BBO-FCM
b.AFSA-FCM
c.ABC-FCM
d.PSO-FCM
e.BFOA-FCM
In order to evaluate the effectiveness of clustering, Cluster Validation Indexes(CVI) was used to obtain
numerical results including Partition Coefficient (PC), Classification Entropy (PE), Separation (S),
Separation Coefficient (SC), Xie and Beni index (XB). These indexes are shown as the following:
Partition Coefficient (PC): PC is used to measure the overlap between classes. It is defined by
2
11
1
( ) ( )
cN
ij
ij
PC c N



(21)
where
ij

is the membership of data point
j
in category
i
.
Partition Entropy (PE): PE measures the fuzzy degree of the category and its definition is as follows:

 
 c
i
N
jijij
N
cPE 1 1 )log(
1
)(

(22)
Separation and Compactness (SC): What SC measures is the firmness sum between categories.








c
ic
kiki
N
jij
m
ij
N
x
cSC 1
1
2
1
2
)(
)(


(23)
Separation index (S): On contrary to SC, the minimize distance is employs by S to classify data and it is
defined by
2
,
1 1
2
2
min
)(
)(
ikki
c
i
N
jijij
N
x
cS






 
(24)
Xie and Beni index (XB): XB is a validation function proposed by Xie and Beni and it is defined by:
2
,
1 1
2
min
)(
)(
ijki
c
i
N
jij
m
ij
xN
x
cXB






 
(25)
For a review on CVI refer to (El-Melegy et al., 2007).
Parameters Settings
For general comparison purpose, we don’t consider the effect of different parameters settings on the
performance of image segmentation. We use the common parameters settings as follows:
BBO Settings: For BBO, we use the following parameters: habitat modification probability is 1,
immigration probability bounds per gene are [0,1] , step size for numerical integration of probabilities,
maximum immigration and migration rates for each island are 1 , and mutation probability is 0.
AFSA Settings: The main parameters are maximal try_number=100, sense distance=4000, crowd factor

=0.618, swimming step=300.
ABC Settings: Limit=100, which is a control parameter in order to abandon the food source.
PSO Settings: In our experiments cognitive and social components are both set to 2. Inertia weight, which
determines how the previous velocity of the particle influences the velocity in the next iteration, is 0.8.
The parameters of BF-FCM are given in Table1. The number of clustering center of BF-FCM is the same
as that of FCM. Amongst these parameters,
e
is the convergence indicator.
Table 1 The parameters of BF-FCM
The procedure of image segmentation of BIOA-FCM is described as follows:
Step1: Selecting an image, and turn it into gray image
Step2: Calculate roughness according to equation (14).
Step3: Construct two-dimensional features data sets based on gray value and roughness
Step4: Initialize parameters of BIOA-FCM, and run it.
Step5: Display image segmentation results after this algorithm is finished.
Experiments Results
The dataset used in image segmentation experiments was obtained from the USC-SIPI Image Database
(http://sipi.usc.edu/database/). They are Lena, Baboon,Woman, Peppers, Milkdrop,Camera, Bridge and
Airplane.
For comparison purposes experiments were taken for classical Fuzzy C-means and the other five
BIOA-FCMs, considering 100 rounds – with maximum 100 iterations each.
Tables 1 and Figure 1 to 16 present quantitative and qualitative image segmentation results, respectively.
For these datasets there is no ground truth (no true labels). Thus, the evaluation about how
measure/approach has the best result need to be made through quantitative and qualitative results. Best
quantitative results are bolded in tables.
Figure 1,3,5,7,9,11,13 and 15 show qualitative results for FCM and the other five BIOA-FCMs,
respectively. Figure 2,4,6,8,10,12,14,16 show the equipotential lines for the images.

Figure 1 Qualitative image segmentation results for Lena image
Figure 2 Equipotential lines for Lena
The number of clusters of Lena is 6. From the results in Figure1, it can be seen that BF-FCM has the best
results. From the results in Figure 2, it can seen that the clustering centers of ABC-FCM and PSO-FCM
fall into local optimum.
Figure 3 Qualitative image segmentation results for baboon image
Figure 4 Equipotential lines for Baboon
The number of clusters of Baboon is 4. From the results in Figure 3, it can be seen that the six algorithms
obtain similar results. From the results in Figure 4, it can be seen that the clustering centers of ABC-FCM
are close to each other.
Figure 5 Qualitative image segmentation results for Woman image
Figure 6 Equipotential lines for Woman
The number of clusters of Woman is 5. BBO-FCM,AFSA-FCM and ABC-FCM can identify woman
and background. ABC-FCM falls into local optimum.
Figure 7 Qualitative image segmentation results for Peppers image
Figure 8 Equipotential lines for Peppers
The number of clusters of Peppers is 5. From the Figure 7, it can be seen that BBO-FCM can identify the
peppers with similar gray value. And the type lines of peppers are also continuously. The results of the
other algorithms are not as good as that of BBO-FCM. From Figure 8, it can be seen that ABC-FCM falls
into local optimum again.
Figure 9 Qualitative image segmentation results for Milkdrop image
Figure 10 Equipotential lines for Milkdrop
The number of clusters of Milkdrop is 4. From Figure 9, It can be seen that BBO-FCM separate all the
milk drops with clear type. The edges of these drops are very clear. ABC-FCM separates the inverted
images and inner loop of milk drops. From Figure 10, it can be seen the PSO-FCM,AFSA-FCM,
BF-FCM and FCM obtain similar clustering centers.
Figure 11 Qualitative image segmentation results for Camera image
Figure 12 Equipotential lines for Camera
The number of clusters of camera is 4. From Figure 11, it can be seen that none of the algorithms identify
the camera and background successfully. But BF-FCM has relative better results than the other algorithms.
From Figure 12, it can be seen that all the algorithms didn’t identify correctly any of the classes.
Figure 13 Qualitative image segmentation results for Bridge image
Figure 14 Equipotential lines for Bridge
The number of clusters of bridge is 4. From Figure 13 and Figure 14, it can be seen that PSO-FCM has
the worst results. The other algorithms have similar results. ABC-FCM falls into local optimum.
Figure 15 Qualitative image segmentation results for Plane image
Figure 16 Equipotential lines for Plane
The number of clusters of plane is 3. From Figure 15 and Figure 16, it can be seen that all the algorithms
cannot obtain good results. FCM and ABC-FCM have worse results than the other algorithms.
Basically, BBO-FCM shows better results on all the images since it can search the clustering centers
accurately. ABC-FCM is easy to fall into local optimum in the experiments.
Table 2 CVI results for FCM and BIOA-FCMs
According to results from Table 1,for Lena, BBO-FCM got best results considering XB and CE for Lena.
But it has smaller PC value. PSO has bigger PC value so PSO-FCM can separate the image simply and
clearly in Fig.1. For Baboon, BBO-FCM doesn’t have the best results considering all the measures. XB of
FCM is bigger and S of FCM is smaller, so it cannot identify different classes clearly. For Woman image,
FCM has the worst value of XB index and S index. BBO-FCM has smaller CE and XB. So BBO-FCM
can identify the detail of the woman. For Pepper image, all the algorithms have similar indices.
BBO-FCM has the best results in Fig .7 qualitatively. So it is necessary to justify the results subjectively
when the quantitative and qualitative evaluation are not consistent. For Milldrop, Camera,Bridge and
Plane, all of them are difficult to separate the classes. The classical FCM has similar evaluation values for

the four images. It has big XB value and small S value. So it cannot identify single class from the total
classes. For the other BIOA-FCMs, BBO-FCM has one or two better indices than the other algorithms.
FUTURE RESEARCH DIRECTIONS
For the image segmentation, it only takes gray scale images into account and adopts gray value and
roughness as features for segmentation. In future research, it is necessary to testify it on color images and
consider the other image characteristics, like texture, region and borders in future research. And we will
apply more nature inspired computing methods on image segmentation in order to show whether and how
the nature inspired computing methods can be adaptively applied to what kinds of images.
CONCLUSION
In this chapter, we proposes five hybrid algorithms, AFS-FCM,BBO_FCM,BF-FCM, ABC-FCM,
PSO-FCM, which are bio-inspired optimization algorithms combined with the standard FCM. These new
approaches aim at optimizing the cluster criterion function directly related to the cluster centers of FCM
to improve the quality of clustering. Two kinds of experiments are conducted. Qualitative and quantitative
results are obtained in order to evaluate the clustering effectiveness. All the experiments results are
compared to those obtained by standard FCM and quantitative and qualitative analysis shows that the
BBO-FCM have relative better performance than ABC-FCM,AFS-FCM,PSO-FCM and FCM on the
images used in the chapter.
ACKNOWLEDGMENTS
This work is partially supported by the National Natural Science Foundation of China under Grant
No.61075113, the Excellent Youth Foundation of Heilongjiang Province of China under Grant No.
JC201212, the Fundamental Research Funds for the Central Universities No.HEUCFZ1209 and Harbin
Excellent Discipline Leader,No.2012RFXXG073.
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Table 1 The parameters of BF-FCM
Parameters
Values
n
2
c
9
e
0.000001
S
90
C
N
50
S
N
4
re
N
4
ed
N
2
ed
P
0.25

Lena(original image)
FCM BBO-FCM AFSA-FCM
ABC-FCM PSO-FCM BF-FCM
Figure1 Qualitative image segmentation results for Lena image

FCM BBO-FCM
AFSA-FCM ABC-FCM
PSO-FCM BF-FCM
Figure 2 Equipotential lines for Lena

Baboon(original image)
FCM BBO-FCM AFSA-FCM
ABC-FCM PSO-FCM BF-FCM
Figure 3 Qualitative image segmentation results for baboon image

FCM BBO-BBO
AFSA-FCM ABC-BBO
PSO-FCM BF-FCM
Figure 4 Equipotential lines for Baboon

Woman(original image)
FCM BBO-FCM AFSA-FCM
ABC-FCM PSO-FCM BF-FCM
Figure 5 Qualitative image segmentation results for Woman image

FCM BBO-FCM
AFSA-FCM ABC-FCM
PSO-FCM BF-FCM
Figure 6 Equipotential lines for Woman

Peppers(original image)
FCM BBO-FCM AFSA-FCM
ABC-FCM PSO-FCM BF-FCM
Figure 7 Qualitative image segmentation results for Peppers image
FCM BBO-FCM

AFSA-FCM ABC-FCM
BBO-FCM BF-FCM
Figure 8 Equipotential lines for Peppers
Milktrop(original image)

FCM BBO-FCM AFSA-FCM
ABC-FCM PSO-FCM BF-FCM
Figure 9 Qualitative image segmentation results for Milkdrop image
FCM BBO-FCM

AFSA-FCM ABC-FCM
PSO-FCM BF-FCM
Figure 10 Equipotential lines for Milkdrop
Camera(original image)

FCM BBO-FCM AFSA-FCM
ABC-FCM PSO-FCM BF-FCM
Figure 11 Qualitative image segmentation results for Camera image
FCM BBO-FCM

AFSA-FCM ABC-FCM
PSO-FCM BF-FCM
Figure 12 Equipotential lines for Camera
Bridge(original image)
FCM BBO-FCM AFSA-FCM

ABC-FCM PSO-FCM BF-FCM
Figure 13 Qualitative image segmentation results for Bridge image
FCM BBO-FCM
AFSA-FCM ABC-FCM

PSO-FCM BF-FCM
Figure 14 Equipotential lines for Bridge
Plane(original image)

FCM BBO-FCM AFSA-FCM
ABC-FCM PSO-FCM BF-FCM
Figure 15 Qualitative image segmentation results for Plane image
FCM BBO-FCM
AFSA-FCM ABC-FCM

PSO-FCM BF-FCM
Figure 16 Equipotential lines for Plane
Table 2 CVI results for FCM and BIOA-FCMs
Images
C
CVI
FCM
BBO-FCM
AFSA-FCM
ABC-FCM
PSO-FCM
BF-FCM
Lena
6
SC
XB
CE
S
PC
1.0684
24.0430
0.9850
1.0742e-004
0.5316
1.2735
2.5015e-011
8.5050e-005
0.2792
2.4880e-011
2.2694
0.3532
2.0446
0.5505
0.3345
0.5670
0.8996
1.3544
0.1458
0.0608
5.3410
0.3839
2.0900
1.4035
0.3925
1.0684
24.0430
0.9850
1.0742e-004
0.5316
Baboon
4
SC
XB
CE
S
PC
1.6070
21.4599
0.8059
1.2310e-004
0.5787
2.3520
0.1404
1.3955
0.6720
0.1277
0.9615
1.7361
1.2642
0.2963
1.0262
1.3006
1.7443
1.2428
0.3898
0.1397
2.0409
0.0068
0.4557
0.6082
0.0066
1.6070
21.4599
0.8059
1.2310e-004
0.5787
Woman
5
SC
XB
CE
1.0935
21.3590
0.8125
2.0527
1.7466e-004
0.0673
3.3291
7.3913e-009
1.5325
1.0265
0.0829
1.1775
1.0960
0.7431
1.1352
1.0935
21.3590
0.8125

S
PC
1.0990e-004
0.5971
0.6389
1.3606e-004
1.2594
0.1623
0.2468
0.1735
0.2729
0.2775
1.0990e-004
0.5971
Peppers
5
SC
XB
CE
S
PC
1.0958
40.9849
0.8200
3.7783e-05
0.6001
2.3896
0.0802
1.1923
0.6942
0.0600
1.6854
0.0077
0.5067
0.4192
0.0072
2.1809
1.4853e-008
0.0018
0.5278
8.8651e-009
1.5536
0.1991
1.4625
0.4581
0.1393
1.0977
25.3268
1.4625
7.4988e-05
0.1393
Milkdrop
4
SC
XB
CE
S
PC
0.8783
32.0841
0.5669
6.3765e-005
0.7067
2.2456
0.0376
1.0485
0.7221
0.0906
2.1409
0.0092
0.4935
0.7398
0.0088
2.7977
0.4249
0.5706
1.0784
0.2413
1.3039
0.4699
0.9533
0.2913
0.2349
0.8783
32.0841
0.5669
6.3765e-05
0.7067
Camera
4
SC
XB
CE
S
PC
0.6968
27.6367
0.4384
7.0817e-005
0.7797
2.0697
0.2346
1.3535
0.6152
0.2141
0.2741
3.9648
0.1371
0.1061
3.7258
2.6505
0.0011
0.5452
0.8594
1.8678
2.0099
0.4228
1.4608
0.6512
0.4219
0.6654
35.0630
1.4608
1.7243e-05
0.4219
bridge
4
SC
XB
CE
S
PC
2.0561
31.1346
0.8622
1.5511e-004
0.5439
0.3657
4.6177
0.1074
0.1337
1.0463e-004
1.0919
1.6310
0.8393
0.3467
0.0408
7.5019
0.0465
1.1978
2.7663
0.1151
2.2020
0.3462
1.2324
0.6170
0.1602
2.0561
31.1346
0.8622
1.5511e-004
0.5439
Plane
3
SC
XB
CE
1.1305
35.0280
0.4030
1.6043
0.6743
1.0634
0.9088
0.2734
0.8401
1.2301
1.4699
0.7791
1.4111
0.4936
1.4306
1.1305
35.0280
0.4030

S
PC
9.8403e-005
0.7768
0.6294
0.6578
0.2610
0.2441
0.5571
1.4033
0.4654
0.3932
9.8403e-005
0.7768
Clustering: Clustering techniques represent the non-supervised pattern classification in groups
Fuzzy C-means(FCM): FCM is a kind of simple mechanical clustering method based on exploring
minimum value of the objective function
Image Segmentation: Image segmentation is one of the central problems in computer vision and pattern
recognition. It refers to the process of assigning a label to every pixel in an image such that pixels with
the same label share certain visual characteristics.
Bio-inspired Optimization Algorithms(BIOA): it means the optimization approaches inspired by the
principles of biology or biologic behaviors in nature.
Cluster Validation Indexes (CVI): Cluster Validation Indexes are the criteria in order to evaluate the
effectiveness of clustering.
Biogeograpy Based Optimization(BBO):BBO is a new population-based optimization algorithm, which
mimics how animals migrate from one habitat to another, how new species arise, and how species become
extinct.
Bacteria Foraging Optimization Algorithm (BFOA) : BFOA is a kind of BIOA based on the behavior that
E. coli engulfs food in human's intestinal.
Keywords: Bio-inspired Optimization Algorithm, Image Segmentation, Clustering, Fuzzy C-Means,
Biogeography Based Optimization(BBO),Artificial Fish School Algorithm(AFSA), Artificial Bees
Colony(ABC),Particle Swarm Optimization(PSO) and Bacterial Foraging Algorithm(BFA).