1. science
2. computer science
3. artificial intelligence

ISSN 2394-3777 (Print)
ISSN 2394-3785 (Online)
Available online at www.ijartet.com
International Journal of Advanced Research Trends in Engineering and Technology (IJARTET)
Vol. II, Special Issue XXIII, March 2015 in association with
FRANCIS XAVIER ENGINEERING COLLEGE, TIRUNELVELI
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN COMMUNICATION SYSTEMS AND
TECHNOLOGIES (ICRACST’15)
TH
25 MARCH 2015
Reformulated Fuzzy C - means Based Image
Segmentation
1
2
3
S.Rajeswari , K.Thulasi , A.Vijayalakshmi , P.Subbalakshmi
4
U.G. Student, Department of Computer Engineering, PSRR Engineering College, Sivakasi,Tamilnadu India.
Associate Professor, Department of Computer Engineering, PSRR Engineering College,SivakasiTamilnadu,India4
Abstract – Image segmentation deals with partition of
images in to separate constitutes. Fuzzy C-means
(FCM) is a hard clustering algorithm. It uses spatial
information and enhances their insensitiveness to
noise. But it still lacks enough robustness to noise
when the absence of prior knowledge of noise. To
overcome this, Fuzzy Local Information C-means
(FLICM) is introduced. It is independent to noise and
free of parameter selection. Here, Reformulated
Fuzzy Local Information C-means (RFLICM) is
introduced which replaces spatial information by
local coefficient of variation. The local coefficient of
variation exploits more contextual information when
compared to spatial information. Simulations on the
segmentation of synthetic and medical images
demonstrate the robustness and advantages of
RFLICM algorithm. Performances of medical image is
found by means of Segmentation accuracy .
Index Terms - FCM, FLICM, RFLICM, Spatial
information, Segmentation accuracy.
I. INTRODUCTION
Fuzzy clustering plays an important role in solving
problems in the areas of pattern recognition and fuzzy
model identification. A variety of fuzzy clustering
methods have been proposed and most of them are
based upon distance criteria [3]. One widely used
algorithm is the Fuzzy C-Means (FCM) algorithm. It
uses reciprocal distance to compute fuzzy weights.
Fuzzy c-means (FCM) is one of the most promising
fuzzy clustering methods [3]. Clustering, particularly
fuzzy C-means (FCM)-based clustering and its
variants, have been widely used in the task of image
segmentation due to their simplicity and fast
convergence [1] [4], [6] [10] - [12]. By carefully selecting
input features such as pixel color, intensity, texture, or
a weighted combination of these data, the FCM
algorithm can segment images to several regions in
accordance with resulting clusters [1]. In most cases, it
is more flexible than the corresponding hard clustering
algorithms. It is effective for spherical clusters; it does
not perform well for more general clusters. The FCM
algorithm has also been extended to the kernel FCM
algorithm, which yields better performance. However,
for such kernel-based methods, a crucial step is the
combination or selection of the best kernels among an
extensive range of possibilities [3]. Recently, the FCM
and other clustering based image segmentation
approaches use the local spatial information of pixels in
classical clustering procedures[1] [4] [6]. Because of the
local spatial information, the new FCM algorithm has
demonstrated robustness over noises in images [1] [4].
In addition to the incorporation of local spatial
information, the FCM has made an improvement in
their performance. Clustering is performed on the basis
of the gray level histogram of the summed image.
However, this FCM do not directly apply on the
original image. They need some parameters a (or λ) to
control the trade-off between robustness to noise and
effectiveness of preserving the details. The selection of
these parameters is not an easy task, and has to be
made by experience or by using the trial-and-error
257
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ISSN 2394-3777 (Print)
ISSN 2394-3785 (Online)
Available online at www.ijartet.com
International Journal of Advanced Research Trends in Engineering and Technology (IJARTET)
Vol. II, Special Issue XXIII, March 2015 in association with
FRANCIS XAVIER ENGINEERING COLLEGE, TIRUNELVELI
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN COMMUNICATION SYSTEMS AND
TECHNOLOGIES (ICRACST’15)
TH
25 MARCH 2015
method. To overcome the above mentioned problems,
Stelios et al.[5] presents a novel robust fuzzy local
information c-means clustering algorithm (FLICM),
which is free of any parameter selection, as well as
promoting the image segmentation performance. In
FLICM, a novel fuzzy factor is defined to replace the
parameter a used in above algorithms and its variants
[2]. In order to overcome the above mentioned
disadvantages a new factor in Fuzzy C Means objective
function is needed. The new factor should have some
special characteristics such as,
• Incorporate local spatial and local gray level
information in a fuzzy way in order to preserve
robustness and noise insensitiveness.
• Control the influence of the neighborhood pixels
depending on their distance from the central pixel.
• Use the original image avoiding preprocessing steps
that could cause detail missing .
So, Reformulated Fuzzy Local Information C-means
(RFLICM) is proposed, which adopts the local
coefficient of variation to replace the spatial distance as
a local Similarity measure. Furthermore, it presents a
more robust result. Although RFLICM algorithm can
exploit more local context information to estimate the
relationship of pixels in neighbors [3] [7].
II. FLICM (Fuzzy Local Information C-Means)
The conventional FCM algorithm[8] [9] works well on
noise free images, but it is fails to segment images
ruined by noise and other image relics. This algorithm
has the drawback of producing the non-robust result
because of the ignorance of the spatial contextual
information in an image and the use of the non- robust
Euclidean distance. In order to overcome these
problems, a novel robust fuzzy local information cmeans clustering (FLICM) is introduced which
overcomes the problem of parameter selection a and
also promotes the image segmentation performance. It
determines the spatial and gray level relationship that
is free of any parameter selection. The FLICM
algorithm has some attractive characteristics like (a) it
is independent of the type of noise and is free of any
parameter selection. (b) It incorporates both the local
spatial and the local gray level relationship
simultaneously in a fuzzy way. (c) The fuzzy local
constraints are automatically determined; hence there
is no need for any parameter selection. (d) The
clustering performance is enhanced concurrently by
balancing the image details and noise. This is achieved
automatically by using fuzzy local constraints. (e) It
controls the influence of the neighborhood pixels based
on their distance from the central pixel. (f) Uses the
original image avoiding the preprocessing steps which
could cause the missing of the image details [8]. The
objective
function
is
termed
as
J
N
m

c
  [u || x  v
m
.
ki
i 1 k 1
i
k
|| 2 
G
ki
]
(4)
The parameter m is a weighting exponent on each
fuzzy membership and determines the amount of
fuzziness of the resulting classification. Here, we set
m = 2 for the following experiments. The fuzzy factor
G ki is defined mathematically as follow,
G d
N
ki
j
i
1
ij
1  u  || x  v ||
m
1
kj
j
2
k
(5)
where the ith pixel x i is the center of the local window
and the jth pixel x j represents the neighboring pixels
falling in to the window around x i , d ij is the spatial
Euclidean distance between pixels i and j . N i stands
for the set of neighbors in a window around x i . v k
represents the prototype of the center of cluster k, and
u kj represents the fuzzy membership of gray value x j
with respect to the kth cluster.
The two necessary conditions with respect to Uki and Vk
u
ki
1






||  || 
 || x  v || G
x v G
c
j 1
2
i
k
2
i
j
1
m
 1
(6)
ki 


ji 
258
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ISSN 2394-3777 (Print)
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International Journal of Advanced Research Trends in Engineering and Technology (IJARTET)
Vol. II, Special Issue XXIII, March 2015 in association with
FRANCIS XAVIER ENGINEERING COLLEGE, TIRUNELVELI
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN COMMUNICATION SYSTEMS AND
TECHNOLOGIES (ICRACST’15)
TH
25 MARCH 2015
N
v
k


m
ki
u
i 1
N

u
i1
x
m
ki

jN i
i
(7)
u
u

b=b+1 and go to step 4.
The advantage of the FLICM algorithm is that the
objective function is automatically determined even in
the absence of prior noise knowledge.
III. RFLICM (Modified Fuzzy Local Information
C-Means)
Reformulated Fuzzy Local Information c-means
clustering (RFLICM) algorithm, which implements the
local coefficient of variation to replace the local spatial
distance as a local similarity measure. In accordance
with the fuzzy factor G ki , it is conditional that the
local gray level information and spatial information
in G ki are represented by the gray-level difference and
spatial distance respectively. The local spatial
relationship changes adaptively according to spatial
distances from the central pixel. The local coefficient of
variation is defined as,
c
u

var  x 
x2
(8)
Where varx  and x are the intensity variance and the
mean in a local window of the image, respectively.

2  min  


*1 

G ki 
The FLICM algorithm is given as follows:
1)Set the number c of the cluster prototypes,
fuzzification factor m and the stopping condition ε.
2) Initialize randomly the fuzzy partition matrix.
3) Set the loop counter b=0.
4) Calculate the cluster prototypes using (6).
5) Compute the membership values using (7).
b 
b 1 

< ε then stop, otherwise, set
6) If max
1


j Ni
u
m
 ||
kj 
j

,

u 

2
c c c c
u
/
x v
j
k
u
|| 2 , if
/
2
j  
u


j
c c
u
u
1

2  min  


* 1 

u
m
 ||
kj 
j

,

u 

2
c c c c
u
/
x v
j
k
u
|| 2 , if
/
(9)
2
j  
u


j
c c
u
u
Where Cu represents the local coefficient of variation of
central pixel. c uj represents the j th local coefficient of
variation in neighbours, c u is the mean value of c uj
that is located in a local window. The fuzzy factor G’ki
balances the membership value of the central pixel by
considering the local coefficient of variation and the
gray level of the neighbouring pixels. When there is a
difference between the results of the local coefficient of
variation that are obtained by the neighbouring pixels
are different, the weightings added to the neighbouring
pixel in G’ki will be increased to suppress the influence
of outlier, which is expected to be more robust [8].
The RFLICM algorithm is given as follows:
1) Set the number c of the cluster prototypes,
fuzzification factor m and the stopping condition ε.
2) Initialize randomly the fuzzy partition matrix.
3) Set the loop counter b=0.
4) Calculate the cluster prototypes using (6).
5) Compute the membership values using (7).
b 
b 1 

< ε then stop, otherwise, set
6) If max
u
u

b=b+1 and go to step 4.
RFLICM algorithm can exploit more local context
information to estimate the relationship of pixels in
neighbors.
V. RESULTS AND DISCUSSION
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International Journal of Advanced Research Trends in Engineering and Technology (IJARTET)
Vol. II, Special Issue XXIII, March 2015 in association with
FRANCIS XAVIER ENGINEERING COLLEGE, TIRUNELVELI
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN COMMUNICATION SYSTEMS AND
TECHNOLOGIES (ICRACST’15)
TH
25 MARCH 2015
In this section the algorithms were run on a computer
system. All the programs were written in mat lab and
run under Windows XP (64 bit) operating system. Both
the images consist of 256 × 256 pixels and include two
classes with two intensity value taken as 20 and 120, as
shown in Fig. 1(a). The number of clusters is 2. The
algorithms (FLICM, and RFLICM) are tested on the
images corrupted by Salt & Pepper noise. In our
numerical experiments, we generally choose ε = 0.001
[8]. Also the RFLICM algorithm is compared with
FLICM. The RFLICM algorithm can detect the clusters
of an image overcoming the disadvantages of the FCM
based clustering techniques.The below are the
simulation results for Brain tumour image using the
Clustering techniques like FLICM,RFLICM.
(a)
Fig. 1. Segmentation results on the Brain tumour
image corrupted by Salt & Pepper noise (15%). (a)
Original image. (b) Noisy image. (c) Enhanced
Image.(d) FLICM result.
(a)
(b)
(c)
(d)
(b)
Fig. 2. Segmentation results on the Brain tumour
image corrupted by Salt & Pepper noise (15%). (a)
Original image. (b) Noisy image. (c) Enhanced Image.
(d) RFLICM result.
(c)
(d)
260
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Available online at www.ijartet.com
International Journal of Advanced Research Trends in Engineering and Technology (IJARTET)
Vol. II, Special Issue XXIII, March 2015 in association with
FRANCIS XAVIER ENGINEERING COLLEGE, TIRUNELVELI
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN COMMUNICATION SYSTEMS AND
TECHNOLOGIES (ICRACST’15)
TH
25 MARCH 2015
VI. PERFORMANCE MEASURES
FCM based clustering techniques are compared by
means of Segmentation accuracy. It can be defined as
the number of correctly classified pixels divided by
total number of pixels. FLICM, RFLICM Algorithms
are compared by means of
features like SA
Segmentation accuracy deals with how well the image
is segmented. From the tabulation it is clearly found
that RFLICM is the best when compared with FLICM.
SA=
number of classified pixels
Total number of pixels
Table.1.Comparison of Segmentation accuracy, PSNR
for Brain tumour Image
Algorithm
FLICM
RFLICM
Segmentation Accuracy
93.18
97.07
VII. CONCLUSION
In this paper FCM based clustering techniques are used
to identify the tumor in the human brain.FCM has
some limitations, that is, it wrongly classifies the noisy
pixels in the medical images and has incorrect
membership and improper segmentation for noisy
images. To overcome that, FLICM with fuzzy factor is
introduced which includes spatial and gray level
information. Here, RFLICM (Reformulated Fuzzy Local
Information C-Means) Algorithm is used which
replaces spatial information by local coefficient of
variation can exploit more contextual information.
Features like Segmentation Accuracy is calculated
using Matlab coding and the above two algorithms are
compared. Simulation results show that the RFLICM
Algorithm gives better results. The results were
tabulated and compared.
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Vol. II, Special Issue XXIII, March 2015 in association with
FRANCIS XAVIER ENGINEERING COLLEGE, TIRUNELVELI
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN COMMUNICATION SYSTEMS AND
TECHNOLOGIES (ICRACST’15)
TH
25 MARCH 2015
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