J. Biomedical Science and Engineering, 2011, 4, 100-104
doi: 10.4236/jbise.2011.42014 Published Online February 2011 (http://www.SciRP.org/journal/jbise/
JBiSE
).
Published Online February 2011 in SciRes. http://www.scirp.org/journal/JBiSE
Automatic segmentation of brain tissue based on improved
fuzzy c means clustering algorithm
Zhuang Miao1, X i a o m e i Li n2, Chengcheng Liu2
1Department of neurosurgery, China-Japan Union Hospital, Jilin University, Jilin, China;
2Institute of electrical and electronic engineering, Changchun University of Technology, Changchun, China
Received 9 November 2010; 12 November 2010; 23 November 2010.
ABSTRACT
In medical images, exist often a lot of no ise; the noise
will seriously affect the accuracy of the segmentation
results. The traditional standard fuzzy c-means(FCM)
algorithm in image segmentation do not taken into
account the relationship the adjacent pixels, which
leads to the standard fuzzy c-means(FCM) algorithm
is very sensitive to noise in the image. Proposed im-
proved fuzzy c-means(FCM) algorithm, taking both
the local and non-local information into the standard
fuzzy c-means(FCM) clustering algorithm. The ex-
periment results can show that the improved algo-
rithm can achieve better effect than other methods of
brain tissue segmentatio n.
Keywords: Local Information; Non-local Mean; Brain
Tissue Segmentation
1. INTRODUCTION
Image segmentation is the key technology in image
processing and analysis .In the medical field, with the
imaging technology development and medical imaging
application success in the clinical, image segmentation is
playing an increasingly larger role. On the MRI (mag-
netic resonance imaging) brain images in the white mat-
ter (WM), brain gray matter (GM) and cerebrospinal
fluid (CSF) such as the organizational structure of the
correct segmentation in medical applications is of great
significance. However, there is a lot of noise; the noise
will seriously affect the accuracy of the segmentation
results. The traditional standard FCM algorithm in image
segmentation do not taken into account the relationship
adjacent pixels, which leads to the standard FCM algo-
rithm is very sensitive to noise in the image. Although
some noise in the image can be removed in split before
use of smoothing filters and other methods of, but in
most cases, this approach is unwise, because some of the
details in the image and edge information and noise may
also be removed together by some standard filters. In
order to reduce image noise affect to image and better
for the partition of the segmented image, here we pro-
pose a new algorithm in this chapter, in the proposed
new algorithm, take both the local and non-local infor-
mation into the standard FCM clustering algorithm.
Non-local means algorithm (NL Means), who by
Buades and other peoples as image denoising algorithm
first proposed [1,2]. This algorithm attempts to use the
image height of the redundant information to complete
the work of digital image denoising, in other words, for
each pixel in the image, we can find a lot of images with
which had the same structure of adjacent domains sam-
ples, then we are dealing with these redundant pixels to
be weighted average of the sample. Experimental results
show that non-local means algorithm can successfully
remove the image noise at the same time save the image
in the more complete boundary information. However, in
medical images, the boundary between different organi-
zations is often blurred, and the details of the image,
redundant information is not always present. In order to
protect the image of the fine structure and details of the
information and made them not be destroyed, in the use
of non-local means algorithm at the same time, local
information should also be considered.
2. AUTOMATIC SEGMENTATION ASED
ON IMPROVED FUZZY C MEANS
CLUSTERING ALGORITHM
2.1. Improved Fuzzy C Means Clustering
Algorithm Distance Function
Through the standard FCM algorithm, we can see the
final result is determined by the value of the data of the
degree of membership, and degree of membership of
data is determined by the distance function .Therefore,
we can make conclusions, and the key in the FCM is the
distance that data and cluster center .The proposed algo-

Z. Miao et al. / J. Biomedical Science and Engineering 4 (2011) 100-104 101

2
rithm in this chapter, we will distance function in the
standard FCM rewritten as
 
22
,1 ,,
j
ijljijnlj
Dxvdxvd xv   i
(1)
Among them, is the distance by the impact of lo-
cal information, nl has been affected by the dis-
tancenon-local information,
l
dd
j

is used to control the
proportion parameters between these two diatances, the
valur range is [0,1]. For a pixel i
x
, i is selected with
fixed-size local neighborhood structure, if the k
N
x
in the
i is very close to a pixel gray value of, the center
pixel then i
N
x
should be affected largely by it, Other-
wise, its impact should be very small to i
x
. According
to the above description, the distance formula affected
by the local neighborhood information is:




2
2
,,
,,
kj
kj
lkj ki
xN
lji
lkj
xN
wxxd xv
dxv wxx




 (2)
Where, is the weightin in the neighbor-
hood of each pixel,defined as:

,
lkj
wxx


2
2
,
kj
xx
lkj
wxx e



 (3)
Formula (3) is the variance of pixel gray value in the
neighborhoo d , use it to control the bending degree
of curve.
i
N
All the distance dnl affected by the non-local informa-
tion is the weighted average in all pixel input image I,
calculated as:
 

22
,,
k
nlj inlkjki
xl
dxv wxxdxv



,
(4)
Among them, the weighted values is
determined by

,
nl k j
wxx
j
x
, k
x
the similarity of pixels to 2

.
Generally speaking, ,
nl
w


,
nl k j
wxx satisfy the fol-
lowing conditions:

0,
nl k j
wxx1
,

,
k
nl k j
xl
wxx


2.2. Improved Fuzzy C Means Clustering
Algorithm Weight
The similarity of Pixel k
x
and
j
x
is determined by
the gray value the degree of similarity the vector


k
vN
and


j
vN of, the two the similarity of vectors is de-
scribed as a weighted Euclidean distance, among them a
is a Standard deviation of the Gaussian kernel function,
and meet a > 0 If a pixel structure of the neighborhood
with similar structure to the gray neighborhood
j
x
Then the pixel is relatively large weight, that should be a
relatively large impact
j
x
. Weight is calculated as:


1
,
nlkj kj
j

,
x
xUxx
Zx
 (5)
Among them


kj
x,Ux is the similarity of the expo-
nential form,


j
Z
x for the regularization constraints

 
2
2,
2
,
kj
a
vN vN
h
kj
xUx e


(6)

 
2
2,
2
kj
a
vN vN
h
jk
 Zx e


(7)
Parameter h is the control parameter, which controls the
degree of exponential decline, the same, and also control
the recession of the Euclidean distance weight function.
For convenience of calculation, for the search similar to
neighborhood structure is often limited to a program
called “search window”, use i. For example, in [3]
experiments, the size of neighborhood is defined as the 7
×7 square, the search window size is set to 21 × 21.

To determine the parameters
j
i

in the formula (1),
proposed called “sorting means algorithm” approach in
here. This algorithm and Garnett and other peoples [4]
proposed statistical method is very similar to ROAD.
Suppose
j
x
is the pixels we have to consider, the size
of the search window i

is S × S, for each pixel in
the search window, by the formula (6) to calculate the
index of similarity, and then descending order of their
values, then the pixelsthe balance parameter
j
x
is de-
fined as:

1,
1
m
j
ikj
Uxx
m
 
i
 (8)
Among them, Ui ranking in the search window is the
U-value of i first big, m value is defined as m = S - 1.
3. EXPERIMENTAL RESULTS
In this section, the improved FCM algorithm is applied
to synthetic square image, include simulated brain im-
ages and real brain images, and results were compared
with the expansion of the standard FCM algorithm. In
experiments, additional brain tissue (such as the cerebral
cortex, fat, etc.) has been removed before the split.
3.1. MRI Images
Here, we will apply the proposed algorithm in this paper
in the T1 magnetic resonance brain image data. We also
split the image into three categories, namely, white mat-
ter (WM), gray matter (GM) and cerebrospinal fluid
(CSF), in the experiment, we do not consider the back-
ground pixels. As opposed to synthetic square image, the
brain images are much more complex, so in order to
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opyright © 2011 SciRes. JBiSE

Z. Miao et al. / J. Biomedical Science and Engineering 4 (2011) 100-104 102
save the image in detail, we set the parameters h = 500,
the neighborhood size Nj = 3 × 3, the search window size
Ωi = 7 × 7.
Figure 1(a) contains a 9% noise images of brain
slices, using the standard FCM, FCMSI, IFCM, RFCM
and ASFCM image segmentation algorithm, the results
were as shown in Figure 1(b) to Figure 1(f). Figure 1(g)
is the use of segmentation algorithms proposed in this
paper, after the results. Figure 1(a) The Ground Truth as
shown in Figure 1(h).
To test the proposed algorithm in this paper in dif-
ferent noise levels in the segmentation results, we
conducted the following comparative experiments.
Figures 2(a), (e) and (i) respectively, contain 3%, 5%
and 7% of the noise of the MRI brain images, using
segmentation algorithm proposed in this chapter, the
results are, respectively, Figures 2(b), (f) and (g). These
(a) (b)
(c) (d)
(e) (f)
(g) (h)
Figure 1. MRI brain images of different methods of comparing
the results of Segmentation (a) brain image (z = 70) damaged
by 9% noise, (b) FCM. (c) FCMSI. (d) IFCM. (e) RFCM. (f)
ASFCM. (g) The proposed method in this paper. (h) Ground
Truth.
(a) (b)
(c) (d)
(e) (f)
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Z. Miao et al. / J. Biomedical Science and Engineering 4 (2011) 100-104 103
(g) (h)
(i) (j)
(k) (l)
under differe
sults with the standard FCM segmentation results and
rithms are applied in the differe
no
ing and subjective factors, the
good repeatability. Therefore, automatic segmentation
NCES
B. and Morel, J.M. (2005) A non-local
ge denoising. IEEE Computer Society
Figure 2. Segmentation resultsnt noise levels
compared (a), (e) and (i) contain 3%, respectively, 5% and 7%
of the noise of the image. (b), (f) and (j) are the application of
the segmentation algorithm proposed. (c), (g) and (k) are the
segmentation results. (d), (h) and (l) are Ground Truth.
re
Ground Truth compare the accuracy of our method can
obviously be shown.
Next, the six algont
ise levels of the three-dimensional brain image seg-
mentation; this division is carried out by the order biopsy.
It can be seen, when the image does not contain noise or
low noise level, all the results generated by those algo-
rithm are the same but with the noise level enhanced, in
contrast to several other algorithms, the segmentation
algorithm proposed in this paper.
4. CONCLUSION
Because of time-consum
artificial segmentation of brain MR images results is not
method of brain tissue is needed to complete the Auto-
matic segmentation of MR images. But the morphology
of brain tissue structure for the complex maneuver,
combined with noise, partial volume effect (PVE) and
image bias field (BF) existing the division of their or-
ganization with strong pixel ambiguity and uncertainty,
which makes the fuzzy clustering compared to other
technologies are more widely used in brain MR image
segmentation. In this paper, proposed a modified fuzzy
C means clustering algorithm. In medical images, there
is often a large noise to exist. The noise can seriously
affect the accuracy of the segmentation results. This
method use of non-pixel neighborhood information to
suppress the image of the noise, through a new distance
calculation method to replace Euclidean distance meas-
ure algorithm of the traditional fuzzy C means to achieve
the process of denoising in the during division. Through
a large number of experiments and different algorithms
comparison, proved the validity and correctness of the
algorithm.
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