Adaptive Initialization of Cluster Centers using Ant Colony
Optimization: Application to Medical Images
B. S. Harish
1
, S. V. Aruna Kumar
1
, Francesco Masulli
2
and Stefano Rovetta
2
1
Department of Information Science and Engineering, Sri Jayachamarajendra College of Engineering,
Mysuru, Karnataka, India
2
Department of Informatics, Bio Engineering, Robotics and System Engineering(DIBRIS),
University of Genova, Genova, Italy
Keywords:
Segmentation, Clustering, Fuzzy C Means, Ant Colony Optimization, RSKFCM.
Abstract:
Segmentation is a fundamental preprocessing step in medical imaging for diagnosis and surgical operations
planning. The popular Fuzzy C-Means clustering algorithm perform well in the absence of noise, but it is non
robust to noise as it makes use of the Euclidean distance and does not exploit the spatial information of the
image. These limitations can be addressed by using the Robust Spatial Kernel FCM (RSKFCM) algorithm
that takes advantage of the spatial information and uses a Gaussian kernel function to calculate the distance
between the center and data points. Though RSKFCM gives a good result, the main drawback of this method
is the inability of obtaining good minima for the objective function as it happens for many other clustering
algorithms. To improve the efficiency of RSKFCM method, in this paper, we proposed the Ant Colony Op-
timization algorithm based RSKFCM (ACORSKFCM). By using the Ant Colony Optimization, RSKFCM
initializes the cluster centers and reaches good minima of the objective function. Experimental results carried
out on the standard medical datasets like Brain, Lungs, Liver and Breast images. The results show that the
proposed approach outperforms many other FCM variants.
1 INTRODUCTION
Clustering is an unsupervised learning process in
which data objects are assigned into a set of dis-
joint group so that, objects in the same group are
similar among them and different from the objects
from the other groups. Clustering algorithms can be
categorized into two groups: hierarchical and parti-
tional. Hierarchical algorithms recursively find nested
clusters either in a top-down (divisive) or bottom up
(agglomerative) fashion (Jain et al., 1999). In con-
trast, partitional algorithms find all the clusters simul-
taneously as a partition of the data and do not im-
pose a hierarchical structure. There are two popu-
lar partitional clustering algorithms: K-Means (KM)
(Ng et al., 2006; Chen et al., 1998) and Fuzzy C-
Means (FCM) clustering (Wang et al., 2006; Hadjah-
madi et al., 2008). Most hierarchical algorithms have
quadratic or higher complexity in the number of infor-
mation periods and consequently are not suited for big
data sets, where as partitional algorithms often have
less complexity.
Clustering methods have received significant at-
tention among the researchers due to their wide ap-
plicability in many disciplines like object recogni-
tion, geographical imaging, medical image process-
ing etc. (Jain et al., 1999). Segmentation plays a vital
role in medical image processing. In literature, many
clustering algorithms are used to solve the medical
image segmentation problem (Chen and Zhang, 2004;
Chuang et al., 2006; Aruna Kumar and Harish, 2014).
In crisp clustering methods, like K-Means, data are
divided into a number of clusters where data elements
belong to exactly one cluster. But images must be
considered fuzzy due to the uncertainty present in
them in terms of region/boundaries and non-uniform
intensity variations. Modeling images using fuzzy
sets allows us to keep the uncertainty of belonging
using a membership function. Thus, fuzzy clustering
methods turn out to be well suited for the segmenta-
tion of medical images.
In the last few years, variants of FCM cluster-
ing algorithms have been introduced by different re-
searchers by pointing out various problems concern-
ing the usage of the spatial information and the dis-
tance computation. (Ahmed et al., 2002) proposed a
modified FCM (FCM S) by incorporating spatial con-
straints into objective function. However, the way in
Harish, B., Kumar, S., Masulli, F. and Rovetta, S.
Adaptive Initialization of Cluster Centers using Ant Colony Optimization: Application to Medical Images.
DOI: 10.5220/0006210905910598
In Proceedings of the 6th International Conference on Pattern Recognition Applications and Methods (ICPRAM 2017), pages 591-598
ISBN: 978-989-758-222-6
Copyright
c
 2017 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
591

which they incorporate the neighboring information
limits their application to single-feature inputs. To re-
duce the computational time of FCM S, (Chen and
Zhang, 2004) proposed two variants (FCM S1 and
FCM S2) of FCM S algorithm. These two algorithms
introduced the extra mean and median-filtered im-
age, respectively, which can be computed in advance,
to replace the neighborhood term of FCM S. Thus,
the execution times of both FCM S1 and FCM S2
are considerably reduced. (Chuang et al., 2006) pro-
posed a robust spatial FCM (SFCM) method which
incorporates the spatial information into membership
function for clustering. (Van Lung and Kim, 2009)
proposed a Generalized Spatial Fuzzy C-Means (GS-
FCM) algorithm for medical images. This method
utilizes both given pixel attributes and the spatial lo-
cal information which is weighted correspondingly to
neighbor elements based on their distance attributes.
(Aruna Kumar and Harish, 2014) proposed a Ro-
bust Spatial Kernel FCM (RSKFCM). This method
considers the properties of local neighborhood pix-
els and uses the kernel distance function to measure
the distance between pixels and cluster centers. The
RSKFCM method works effectively for medical im-
age segmentation. However, the performance of the
RSKFCM depends on the initialization of the clus-
ter centers. Random initialization of the cluster cen-
ters makes the algorithm often to fall into the lo-
cal optimal solution. Spectral clustering is another
clustering method, which is used for many applica-
tions such as image segmentation, community detec-
tion and database clustering (Kuo et al., 2014; Archip
et al., 2005). The main challenge of this method is to
create appropriate laplacian.
Nature-inspired methods like Particle Swarm Op-
timization (PSO), Ant Colony Optimization (ACO)
techniques where successfully employed to solve the
cluster initialization problem over the recent years.
ACO has been applied successfully to numerous op-
timization problems. The successful applications of
ACO attracted many researchers. Compared to other
heuristic optimization algorithms, discretion and par-
allel nature of ACO are well appropriated in cluster-
ing, because ACO searches smartly and utilizes char-
acteristics such as positive feedback, robustness and
distributed computing. (Zhang et al., 2011; Yu et al.,
2012; Han and Shi, 2007). (Yu et al., 2012) proposed
an adaptive Ant Colony Optimization based fuzzy
clustering algorithm. This method uses Ant Colony
Optimization to initialize the cluster centers. (Han
and Shi, 2007) developed an improved ACO method
which reduces the computation time by improving the
heuristic function and initialization of the clustering
centers.
In this paper, to overcome cluster initialization
problem of RSKFCM, we employed ant colony op-
timization to initialize the cluster centers. We tested
our proposed method on medical images from differ-
ent modalities including MRI Brain images, CT scan
of Lung tumor images, CT scan of Liver images and
MRI Breast images. Finally, the performance of the
proposed method is evaluated using four cluster va-
lidity functions.
The rest of the paper is organized as follows: Sec-
tion 2 present the background information regard-
ing RSKFCM and Ant colony Optimization. Sec-
tion 3 presents proposed method. Experimental setup,
dataset used for experimentation and results are pre-
sented in section 4. Conclusion are drawn in section
5.
2 BACKGROUND
2.1 Robust Spatial Kernel FCM
(RSKFCM)
The technique of fuzzy clustering has become very
important in the application of image segmentation.
This is due to the large role of uncertainty and im-
precision in the images. Traditional Fuzzy C-Means
(FCM) leads to its non robust result mainly due to:
not utilizing the spatial information in the image and
use of Euclidean distance. To overcome these prob-
lems, (Aruna Kumar and Harish, 2015) proposed Ro-
bust Spatial Kernel FCM (RSKFCM). RSKFCM con-
sider the spatial information and uses Gaussian kernel
function to calculate the distance between the center
and data points. RSKFCM incorporates the spatial
function into membership function of the traditional
FCM. The Spatial function is defined as follows:
s
i j
=
∑
k∈NK(x
j
)
u
ik
(1)
where NK(x
j
) represents a square window centered
at pixel x
j
in the spatial domain. This spatial func-
tion represents the probability that pixel x
j
belongs to
i
th
cluster. The spatial function is incorporated into
membership function as follows:
w
i j
=
u
p
i j
s
q
i j
c
∑
k=1
u
p
k j
s
q
k j
(2)
where p and q are parameters controlling the rela-
tive importance of both functions. (Aruna Kumar
and Harish, 2014) incorporated the kernel function
to robust spatial method to improve the performance
ICPRAM 2017 - 6th International Conference on Pattern Recognition Applications and Methods
592

and proposed Robust Spatial Kernel Fuzzy C-Means
(RSKFCM). The individual stages of Robust Spatial
Kernel Fuzzy C-Means (RSKFCM) are described in
Algorithm 1.
Data: Image Data
Result: Segmented Image
Initialize cluster centers, ε, m
repeat
Compute all membership values u
i j
of each
pixel against centers as:
u
i j
=
1
c
∑
k=1




x
j
−v
i
x
j
−v
k




1
m−1
(3)
Compute the new membership value w
i j
using equation 2
Calculate the objective function J as
follows:
J = 2
c
∑
i=1
N
∑
j=1
w
m
i j
(1 − K (x
j
, v
i
)) (4)
Calculate new cluster center values v
i
v
i
=
N
∑
j=1
w
m
i j
K (x
j
, v
i
)x
j
N
∑
j=1
w
m
i j
K (x
j
, v
i
)
(5)
until
{
J(i) − J(i − 1)
}
< ε;
Algorithm 1: Robust Spatial Kernel Fuzzy C-Means
(RSKFCM).
2.2 Ant Colony Optimization (ACO)
Ant Colony Optimization (ACO) is an evolutionary
algorithm which is inspired by the food searching
behavior of ants. ACO approach was proposed
by (Dorigo et al., 1996). Ants are social insects
exhibiting great organization and construction ability
by the colony behaviors. One of the most important
and fascinating is their food searching behavior. The
ants find the shortest path between a food source
and their nest with the help of pheromone trails.
While walking from their nest to the food source,
ants deposit a chemical called pheromone. While
searching a food source, ants move randomly, but
when they encounter a pheromone trail, they decide
whether or not to follow that path based on the
amount of pheromone deposited. If they select that
path, they deposit their own pheromone on the path,
which reinforces that path. The probability that an
ant chooses one path over another is based on the
amount of pheromone on that path.
In ACO, the construction of the path and updating the
pheromone are the main steps. Let path (i,j) denotes
the path which connects node i to j. Each ant going
from node i to j has pheromone ς
i j
on path (i, j). In
the construction of a path solution, the ant chooses its
path based on the following probability:
p
i, j
=
ς
α
i j
(t)ζ
β
i j
(t)
∑
s∈S
ς
α
i j
(t)ζ
β
i j
(t)
, j ∈ S (6)
ς
i j
=
(
1 if d
i j
< r,
0 if otherwise,
(7)
where ζ
i j
(t) =
r
d
i j
, denotes heuristic information
at time t and d
i j
is the distance between i and j,
and ς
i j
(t) denotes the pheromone concentration on
path (i, j) at time t. The control parameters α and β
explain the relative importance of pheromone versus
the heuristic value, r is the radius of the cluster, and
S =
D
s
d
i j
≤ r, s = 1, 2, ..., N
E
is set of feasible nodes.
After all ants have finished path construction, the
quantity of pheromone is updated according to the
following equation:
ς
i j
(t + 1) = ρ ς
i j
(t) +
N
∑
k=1
∆ς
k
i j
(8)
where ρ is the evaporation rate of pheromone, N is the
number of ants, and ∆ς
k
i j
is the amount of increased
pheromone laid on path (i, j) by the k
th
ant.
3 PROPOSED METHOD
The iterative optimization of RSKFCM is essentially
a local searching method, which is likely to fall onto
a local minima and very sensitive to the initialization
of cluster centers. Usually, cluster centers are initial-
ized randomly based on some experience. The clus-
tering results mainly depends on initial cluster cen-
ters. To address this problem, in this paper we are
employing ACO method for cluster initialization. In
Ant Colony Optimization, the solution space is mod-
eled as a graph representation. On the graph each ant
moves from one node to another node and deposit the
pheromone on the path traversed.
To segment an image, it is necessary to identify
the features. In this paper, we have taken gray val-
ues of the pixels as features. In proposed method, we
assumed each pixel as ants and cluster center as food
sources. At each iteration step, an ant randomly select
ungrouped pixel and adds a new node to its partial so-
lution by considering both pheromone and heuristic
Adaptive Initialization of Cluster Centers using Ant Colony Optimization: Application to Medical Images
593

information. The node with stronger pheromone at-
tracts ants. Here the heuristic information indicates
the desirability of assigning a pixel to particular clus-
ter. This heuristic information is obtained by comput-
ing the inverse distance from cluster center to ants.
The pixel which has highest heuristic value would be
more likely to be selected by ants.
The proposed ACORSKFCM consists of two
steps. In the first step, cluster centers are initialized
using ACO. ACO is applied to find the optimal clus-
ter centers in three steps: initialization, construction
and updating process. In initialization process c pix-
els are assigned randomly on the input image as clus-
ter centers. The initial value of pheromone ς
0
is set
to be a constant value. In construction process, for
each ant i in input image calculate the distance be-
tween cluster center and ant as d
i j
= K(X
i
,V
j
), where,
K(X
i
,V
j
) is the kernel distance metric. If d
i j
then set
p
i j
= 1, otherwise if d
i j
≤ r then calculate the p
i j
us-
ing equation (6). If p
i j
≥ λ, assign the ant i to A
j
and
update the pheromone information using equation (8)
and update the cluster centers as V
j
=
1
A
j
∑
j∈A
j
x
j
. This
process is repeated until the successive difference be-
tween cluster centers is less than or same as stopping
threshold. In second step RSKFCM method is ap-
plied to segment the given input image. RSKFCM
uses the cluster centers found in the first step. The
membership value is calculated for each pixel against
the centers using equation 2. Next the cluster centers
are updated using the equation 5. This process is re-
peated until the successive difference between cluster
center is less than an assigned threshold ε (stopping
criteria). The proposed algorithm (ACORSKFCM) is
described in Algorithm 2.
4 EXPERIMENTAL VALIDATION
This section presents an experimental validation of
the proposed method.
4.1 Evaluation Metrics
The performance of the proposed method is eval-
uated using cluster validity indices. These indices
help to validate whether clustering method accurately
presents the structure of the data set or not. Wide va-
rieties of cluster validity indices are proposed in the
literature. In this paper we have used four widely
used cluster validity functions, namely the Partition
Coefficient (V
pc
), the Partition Entropy (V
pe
), the
Fukuyama-Sugeno function (V
f s
), and the Xie-Beni
function (V
xb
).
Data: Image Data
Result: Segmented Image
Initialize cluster center V
j
, α, β, ρ, ε, r
A
j
is the ant set that contains the member of
cluster V
j
t = 0
repeat
t= t+1
For each ant i in Input image, calculate
distance between ant and cluster center as:
d
i j
= K(X
i
,V
j
)
If d
i j
= 0 then set p
i j
= 1, otherwise if
d
i j
≤ r then calculate the p
i j
using the
equation 6
If p
i j
≥ λ, assign the ant i to A
j
and update
the pheromone information using equation
8
Update the cluster centers using the
following equation:
V
j
=
1
|A
j
|
∑
j∈A
j
x
j
until
{
V (t) −V (t − 1)
}
< ε;
Use these cluster centers as initial cluster
centers and perform RSKFCM algorithm to
segment the input image
Algorithm 2: Proposed Method (ACORSKFCM).
(Bezdek, 2013) proposed the Partition Coefficient
(V
pc
) and the Partition Entropy (V
pe
) which uses only
the membership values to evaluate the cluster validity:
V
pc
(U) =
1
n
n
∑
j=1
c
∑
i=1
u
m
i j
(9)
V
pe
(U) =
1
n
n
∑
j=1
c
∑
i=1
u
m
i j
log u
i j
(10)
The value of V
pc
varies between [
1
c
, 1] where c
indicates the number of clusters. The value of V
pe
ranges between [0, log
a
c] where c is the number of
cluster and a is the base of the logarithm. When V
pc
is maximal or V
pe
is minimal, the optimal clusters are
achieved.
The Fukuyama-Sugeno function (V
f s
) (Fukuyama
and Sugeno, 1989) which is given by:
V
f s
(U,V ; X) =
c
∑
i=1
n
∑
j=1
u
m
i j



x
j
− v
i


2
−
k
v
i
− v
k
2

(11)
where
−
v
=
1
c
c
∑
i=1
v
i
. V
f s
uses both the membership in-
formation and input data. When V
f s
value is mini-
mum, the better clustering results are achieved.
ICPRAM 2017 - 6th International Conference on Pattern Recognition Applications and Methods
594

The Xie-Beni function (V
xb
) function, which was
initially proposed by Xie-Beni (XB) in (Xie and Beni,
1991) and modified by Pal and Bezdek in (Pal and
Bezdek, 1995), is defined as:
V
xb
(U) =
c
∑
i=1
n
∑
j=1
u
m
i j


x
j
− v
i


2
n

min
i6=k
n
k
v
i
− v
k
k
2
o

(12)
In V
xb
the numerator indicates the compactness of the
fuzzy partition and denominator indicates the strength
of the separation between clusters. When V
xb
mini-
mal, the best clustering result is achieved.
4.2 Dataset
In order to demonstrate the effectiveness of the pro-
posed method, we conducted experiments and eval-
uated the performance on medical images from dif-
ferent modalities including MRI Brain images, CT
scan of Lung images, CT scan of Liver images and
MRI Breast images. The MRI image of the brain
chosen for the experiment is available in three bands:
T1-weighted, proton density (pd)-weighted and T2-
weighted. The normal brain images are obtained from
Brain-web database (Brainweb). In this paper, we
have used the transversal slice map, the slice thick-
ness is 1 mm and the size is 217 x 181 pixels. We
have choosen the lung, liver, breast datasets from
(Aruna Kumar and Harish, 2015). Dataset consists
of 50 different lung images, 30 different liver images
and 50 MRI breast images.
4.3 Experimental Setup and Results
To evaluate the performance of the proposed algo-
rithm, we have compared our proposed method with
other three cluster initialization methods, namely ran-
dom initialization, k-means ++ based initialization
(Arthur and Vassilvitskii, 2007), and genetic algo-
rithm based initialization (Aruna Kumar et al., 2015).
We combined these initialization methods with FCM
variants, namely FCM, Kernel FCM, Spatial FCM,
RSKFCM. Table 1 gives the description of these al-
gorithms.
In the experimental comparison, for all the algo-
rithms we used a fuzziness coefficient m = 2, a neigh-
boring window size of 3 × 3, p = 1 and q = 1 for the
spatial function s
i j
, and a stopping criterion that stops
the iterations when the largest difference between all
cluster centers and their updated values are smaller
than ε = 10
−5
or the maximum iteration number of
100 has been achieved.
Table 1: Description of the algorithms considered for com-
parison.
Method Description
FCM 1 Random Fuzzy c-means (FCM)
KFCM 1 Random Kernel FCM
SFCM 1 Random Spatial FCM
RSKFCM 1 Random Robust Spatial Kernel FCM
FCM 2 K-means++ based Fuzzy c-means (FCM)
KFCM 2 K-means++ Kernel FCM
SFCM 2 K-means++ Spatial FCM
RSKFCM 2 K-means++ Robust Spatial Kernel FCM
GAFCM Genetic algorithm based FCM
GAKFCM Genetic algorithm based Kernel FCM
GASFCM Genetic algorithm based Spatial FCM
GARSKFCM Genetic algorithm based Robust Spatial
Kernel FCM
ACOFCM Ant colony based FCM
ACOKFCM Ant colony based Kernel FCM
ACOSFCM Ant colony based Spatial FCM
ACORSKFCM Ant colony based Robust Spatial Kernel
FCM
In literature, many researches and experiments
have revealed some basic properties of the ACO pa-
rameters. In the proposed method, α, β, ρ, λ are
the major parameters. α and β are two parameters
which controls the pheromone concentration and the
heuristic value. λ indicates the minimum probability
for pixel classification. When α is set to zero, ACO
turns into greedy randomized search algorithm. When
α is set to, too large value, ACO will become less
optimized. Large value of the λ leads to increase in
computation time and prevents many pixels from be-
ing clustered. In order to prevent from stagnation, ρ
should be assigned to less than 1. In this paper, we
set the parameters as follows: α = 1, β = 2, ρ = 0.9,
λ = 0.35, r = 20, as suggested in (Yu et al., 2012).
We initialized GA parameters as follows: population
size s = 150, crossover probability p
c
= 0.25, mu-
tation probability p
m
= 0.05, number of generation
g = 300, as suggested in (Aruna Kumar et al., 2015).
We implemented and simulated all the algorithms
with Matlab
R
R2013a.
Figure 1-4 shows the segmentation result on med-
ical images. Table 2, Table 3 , Table 4 and Table 5
compare the performance of all the methods with our
proposed method on Brain, Lung, Liver and Breast
images.
4.4 Time Complexity
The computational complexity of the segmentation
method is a major concern for real-time data handling.
The time complexity of ACO is approximately O(n
2
).
Adaptive Initialization of Cluster Centers using Ant Colony Optimization: Application to Medical Images
595

Figure 1: Segmentation results of Brain image with 4 clus-
ters using proposed method.
Figure 2: Segmentation results of Lung image with 3 clus-
ters using proposed method.
For the RSKFCM algorithm, during each iteration,
the system calculates the distance from each pixel to
every cluster center using the Gaussian Kernel met-
ric. After calculating distance, the system computes
the new membership function using equation 2. If w
is window size, then to calculate the new membership
value, the system needs to perform 2w
2
sum and 2w
2
multiplication operations. Assuming that each oper-
ation is equally dominant, the membership calcula-
tion takes O

4w
2

. Therefore, the time complexity
of RSKFCM for each pixel is O

c
2
d
2
w
2

, where d is
the input image dimension, c is the number of clus-
ter. If the total number of pixels in the image is n, the
time complexity of RSKFCM is O

nc
2
d
2
w
2
i

, where
i is the total number of iterations. Therefore the time
complexity of our proposed method is:
T
M
= O

nc
2
d
2
w
2
i + n
2

' O(n
2
) (13)
4.5 Discussion
Table 2- 5 shows the comparison of cluster validity in-
dices of the proposed method with other methods. For
any good clustering results the values of V
pc
should
be maximum and V
pe
, V
f s
, V
xb
should be minimum.
According to comparison made between the proposed
method and other initialization method, the proposed
Figure 3: Segmentation results of Liver image with 3 clus-
ters using proposed method.
Figure 4: Segmentation results of breast image with 3 clus-
ters using proposed method.
method shows the better results due to high conver-
gence ability of the ACO. The result of the proposed
method mainly depends on the ρ that is evaporation
rate of pheromone. The larger value of ρ results in
low segmentation accuracy. The time complexity of
the proposed method is O(n
2
).
5 CONCLUSION
Fuzzy clustering is a popular clustering method which
as wide varieties of applications including medical
image segmentation. Fuzzy clustering algorithm is
sensitive to initialization and easily trapped in local
minima. The cluster center initialization plays a vi-
tal role in fuzzy clustering and its variants. Ran-
dom initialization of cluster centers does not guaran-
tee the unique clustering results. To overcome this
problem, in this paper we presented a cluster center
initialization method based on Ant Colony Optimiza-
tion (ACO). Ant Colony Optimization is an evolu-
ICPRAM 2017 - 6th International Conference on Pattern Recognition Applications and Methods
596

Table 2: Performance Comparison for Brain images.
Method V
pc
V
pe
V
xb
V
fs
[1 · 10
−3
] [−1 · 10
6
]
FCM 1 0.856 0.275 50.94 317.67
KFCM 1 0.846 0.299 51.82 315.54
SFCM 1 0.932 0.115 52.82 334.14
RSKFCM 1 0.944 0.114 46.93 366.65
FCM 2 0.677 0.620 36.32 170.42
KFCM 2 0.761 0.459 42.73 227.31
SFCM 2 0.886 0.234 38.11 262.45
RSKFCM 2 0.914 0.161 24.14 288.89
GAFCM 0.706 0.513 46.93 123.28
GAKFCM 0.858 0.304 31.59 129.83
GASFCM 0.858 0.139 23.41 130.58
GARSKFCM 0.942 0.099 18.97 132.68
ACOFCM 0.843 0.306 55.86 309.74
ACOKFCM 0.925 0.443 52.49 334.15
ACOSFCM 0.942 0.105 32.71 357.26
Proposed Method 0.960 0.065 16.76 386.73
Table 3: Performance Comparison for Lung images.
Method V
pc
V
pe
V
xb
V
fs
[1 · 10
−3
] [−1 · 10
6
]
FCM 1 0.934 0.122 38.05 127.79
KFCM 1 0.934 0.126 35.65 129.83
SFCM 1 0.962 0.056 35.90 130.86
RSKFCM 1 0.974 0.045 31.00 132.68
FCM 2 0.887 0.217 59.17 178.91
KFCM 2 0.930 0.131 42.28 144.67
SFCM 2 0.849 0.304 32.84 281.26
RSKFCM 2 0.927 0.129 29.17 269.71
GAFCM 0.911 0.171 56.01 141.39
GAKFCM 0.931 0.124 41.90 154.68
GASFCM 0.943 0.081 44.71 168.18
GARSKFCM 0.964 0.067 43.26 190.34
ACOFCM 0.906 0.182 40.63 264.39
ACOKFCM 0.945 0.064 46.71 269.37
ACOSFCM 0.964 0.023 26.37 347.38
Proposed Method 0.986 0.013 26.37 347.38
tionary method which can be applied to solve various
function optimization problems. Experiments are per-
formed on medical images from different modalities.
The proposed method is compared with the Random
initialization, K-means++ based initialization and Ge-
netic algorithm based initialization. The experimental
results show that the proposed hybrid method is effi-
cient in terms of cluster validity metrics.
Table 4: Performance Comparison for Liver images.
Method V
pc
V
pe
V
xb
V
fs
[1 · 10
−3
] [−1 · 10
6
]
FCM 1 0.910 0.177 32.69 253.68
KFCM 1 0.900 0.198 31.61 251.27
SFCM 1 0.951 0.069 31.05 264.11
RSKFCM 1 0.963 0.065 30.07 267.56
FCM 2 0.657 0.592 70.43 159.74
KFCM 2 0.822 0.326 45.71 241.71
SFCM 2 0.932 0.139 29.74 248.70
RSKFCM 2 0.943 0.104 24.07 264.75
GAFCM 0.892 0.201 55.51 210.56
GAKFCM 0.901 0.198 45.77 224.51
GASFCM 0.931 0.153 42.30 230.16
GARSKFCM 0.952 0.081 40.67 250.17
ACOFCM 0.932 0.127 36.21 127.10
ACOKFCM 0.953 0.046 39.13 230.10
ACOSFCM 0.961 0.049 31.12 192.42
Proposed Method 0.984 0.025 29.64 286.72
Table 5: Performance Comparison for Breast images.
Method V
pc
V
pe
V
xb
V
fs
[1 · 10
−3
] [−1 · 10
6
]
FCM 1 0.910 0.159 47.75 161.92
KFCM 1 0.904 0.172 55.13 157.77
SFCM 1 0.964 0.062 40.09 129.86
RSKFCM 1 0.967 0.057 34.97 166.14
FCM 2 0.774 0.395 49.06 121.74
KFCM 2 0.878 0.241 28.75 124.76
SFCM 2 0.794 0.373 30.72 138.27
RSKFCM 2 0.825 0.312 24.73 141.97
GAFCM 0.913 0.174 40.08 138.76
GAKFCM 0.910 0.102 37.47 139.29
GASFCM 0.921 0.079 35.46 140.13
GARSKFCM 0.942 0.064 31.63 150.39
ACOFCM 0.892 0.185 44.72 134.39
ACOKFCM 0.948 0.089 39.64 137.27
ACOSFCM 0.949 0.087 30.23 140.78
Proposed Method 0.984 0.071 26.71 165.71
REFERENCES
Ahmed, M. N., Yamany, S. M., Mohamed, N., Farag, A. A.,
and Moriarty, T. (2002). A modified fuzzy c-means
algorithm for bias field estimation and segmentation
of mri data. Medical Imaging, IEEE Transactions on,
21(3):193–199.
Archip, N., Rohling, R., Cooperberg, P., Tahmasebpour, H.,
and Warfield, S. K. (2005). Spectral clustering al-
gorithms for ultrasound image segmentation. In In-
ternational Conference on Medical Image Computing
Adaptive Initialization of Cluster Centers using Ant Colony Optimization: Application to Medical Images
597

and Computer-Assisted Intervention, pages 862–869.
Springer.
Arthur, D. and Vassilvitskii, S. (2007). k-means++: The
advantages of careful seeding. In Proceedings of the
eighteenth annual ACM-SIAM symposium on Discrete
algorithms, pages 1027–1035. Society for Industrial
and Applied Mathematics.
Aruna Kumar, S. V. and Harish, B. S. (2014). Segmenting
mri brain images using novel robust spatial kernel fcm
(rskfcm). Eighth International Conference on Image
and Signal Processing, pages 38–44.
Aruna Kumar, S. V. and Harish, B. S. (2015). Segment-
ing medical images using computational intelligence
technique. International Journal of Information Pro-
cessing, 9(1):48–56.
Aruna Kumar, S. V., Harish, B. S., and Guru, D. S. (2015).
Segmenting mri brain images using evolutionary com-
putation technique. In Cognitive Computing and In-
formation Processing (CCIP), International Confer-
ence on, pages 1–6.
Bezdek, J. C. (2013). Pattern recognition with fuzzy objec-
tive function algorithms. Springer Science & Business
Media.
Brainweb. http://brainweb.bic.mni.mcgill.ca/brainweb/.
Chen, C. W., Luo, J., and Parker, K. J. (1998). Im-
age segmentation via adaptive k-mean clustering
and knowledge-based morphological operations with
biomedical applications. IEEE Transactions on Image
Processing, 7(12):1673–1683.
Chen, S. and Zhang, D. (2004). Robust image segmenta-
tion using fcm with spatial constraints based on new
kernel-induced distance measure. Systems, Man, and
Cybernetics, Part B: Cybernetics, IEEE Transactions
on, 34(4):1907–1916.
Chuang, K.-S., Tzeng, H.-L., Chen, S., Wu, J., and Chen,
T.-J. (2006). Fuzzy c-means clustering with spatial
information for image segmentation. computerized
medical imaging and graphics, 30(1):9–15.
Dorigo, M., Maniezzo, V., and Colorni, A. (1996). Ant sys-
tem: optimization by a colony of cooperating agents.
Systems, Man, and Cybernetics, Part B: Cybernetics,
IEEE Transactions on, 26(1):29–41.
Fukuyama, Y. and Sugeno, M. (1989). A new method of
choosing the number of clusters for fuzzy c-means
method. In Proceedings of Fifth Fuzzy Systems Symp,
pages 247–250.
Hadjahmadi, A. H., Homayounpour, M. M., and Ahadi,
S. M. (2008). Robust weighted fuzzy c-means clus-
tering. In IEEE International Conference on Fuzzy
Systems(IEEE World Congress on Computational In-
telligence), pages 305–311. IEEE.
Han, Y. and Shi, P. (2007). An improved ant colony al-
gorithm for fuzzy clustering in image segmentation.
Neurocomputing, 70(4):665–671.
Jain, A. K., Murty, M. N., and Flynn, P. J. (1999). Data
clustering: a review. ACM computing surveys (CSUR),
31(3):264–323.
Kuo, C.-T., Walker, P. B., Carmichael, O., and Davidson, I.
(2014). Spectral clustering for medical imaging. In
2014 IEEE International Conference on Data Mining,
pages 887–892. IEEE.
Ng, H., Ong, S., Foong, K., Goh, P., and Nowinski, W.
(2006). Medical image segmentation using k-means
clustering and improved watershed algorithm. In
IEEE Southwest Symposium on Image Analysis and
Interpretation, pages 61–65. IEEE.
Pal, N. R. and Bezdek, J. C. (1995). On cluster validity
for the fuzzy c-means model. IEEE Transactions on
Fuzzy systems, 3(3):370–379.
Van Lung, H. and Kim, J.-M. (2009). A generalized spatial
fuzzy c-means algorithm for medical image segmenta-
tion. In Fuzzy Systems, 2009. FUZZ-IEEE 2009. IEEE
International Conference on, pages 409–414. IEEE.
Wang, W., Zhang, Y., Li, Y., and Zhang, X. (2006). The
global fuzzy c-means clustering algorithm. In The
Sixth World Congress on Intelligent Control and Au-
tomation, volume 1, pages 3604–3607. IEEE.
Xie, X. L. and Beni, G. (1991). A validity measure for fuzzy
clustering. IEEE Transactions on pattern analysis and
machine intelligence, 13(8):841–847.
Yu, J., Lee, S.-H., and Jeon, M. (2012). An adaptive aco-
based fuzzy clustering algorithm for noisy image seg-
mentation. International Journal of Innovative Com-
puting Information and Control, 8(6):3907–3918.
Zhang, J., Zhang, X., and Zhang, J. (2011). Image segmen-
tation method based on improved genetic algorithm
and fuzzy clustering. Advanced Materials Research,
143:379–383.
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