J. Biomedical Science and Engineering, 2009, 2, 656-660
doi: 10.4236/jbise.2009.28096 Published Online December 2009 (http://www.SciRP.org/journal/jbise/
JBiSE
).
Published Online December 2009 in SciRes. http://www.scirp.org/journal/jbise
Fingerprint image segmentation using modified fuzzy c-means
algorithm
Jia-Yin Kang1, Cheng-Long Gong1, Wen-Juan Zhang2
1School of Electronics Engineering, Huaihai Institute of Technology, Lianyungang, China;
2School of Computer Engineering, Huaihai Institute of Technology, Lianyungang, China.
Received 16 July 2009; revised 31 August 2009; accepted 1 September 2009.
ABSTRACT
Fingerprint segmentation is a crucial step in finger-
print recognition system, and determines the results
of fingerprint analysis and recognition. This paper
proposes an efficient approach for fingerprint seg-
mentation based on modified fuzzy c-means (FCM).
The proposed method is realized by modifying the
objective function in the Szilagyi’s algorithm via in-
troducing histogram-based weight. Experimental re-
sults show that the proposed approach has an effi-
cient performance while segmenting both original
fingerprint image and fingerprint images corrupted
by different type of noises.
Keywords: Fingerprint; Segmentation; Fuzzy C-means;
Histogram; Robustness
1. INTRODUCTION
Fingerprint segmentation is an important issue in finger-
print recognition system. A fingerprint image usually has
to be segmented to remove uninterested regions before
some other steps such as enhancement and minutiae detec-
tion so that the image processing will consume less CPU
time. A fingerprint image generally consists of different
regions: non-ridge regions, high quality ridge regions, and
low quality ridge regions. Fingerprint segmentation is usu-
ally to identify non-ridge regions and unrecoverable low
quality ridge regions and exclude them as background [1].
Most segmentation methods are block-wised ones which
divide the fingerprint image into un-overlapped blocks and
decide on the type (background and foreground) of each
block. Some other methods are pixel-wised ones which
determine the type of each pixel. Fingerprint segmentation
typically computes the feature (or feature vector) of each
element, block or pixel, and then determines the element’s
type based on the feature (vector). The features used in
fingerprint segmentation mainly include statistical features
of pixel intensity, directional image and ridge projection
signal et al.
Fuzzy c-means (FCM) clustering algorithm, an unsu-
pervised clustering technique, has been widely used in
image segmentation since it was proposed [2,3]. Com-
pared with hard c-means algorithm [4], FCM is able to
preserve more information from the original image.
However, for one thing, it is noise-sensitive for not tak-
ing into account the spatial information [5]; for another,
it is supposed that each feature date has the same contri-
bution to classifying results [6]. To solve the first problem,
recently, many researchers proposed the algorithms ac-
counting for spatial information via modifying the ob-
jective function of standard FCM algorithm [5,7,8]. To
solve the second problem, Li et al. [6] proposed a modi-
fied clustering algorithm via introducing feature weight
of the data.
Generally, fingerprint image is gray level image and is
inevitably corrupted by noise during acquisition. Con-
sequently, data feature of the fingerprint is the pixel’s
gray value. From the gray level histogram of the finger-
print image, it is easily known that the occurrence fre-
quencies of the different gray levels are usually different.
Therefore, different gray level pixel has different con-
tribution to clustering results.
In this paper, we propose a modified algorithm for noisy
fingerprint image segmentation. The proposed approach is
based on modified fuzzy c-means which is robust to noise.
Our method achieves more desirable performance com-
pared to standard FCM and Szilagyi modified FCM in [8].
The paper is organized as follows. In Subsection 2.1,
standard FCM clustering algorithm is described. Subsec-
tion 2.2 presents the proposed modified FCM algorithm
to segment the fingerprint. In Section 3, the experimental
results are presented. Finally, Section 4 gives our con-
clusions and discussions.
2. METHODOLOGY
2.1. Standard FCM Algorithm
The FCM algorithm assigns pixels to each category by
using fuzzy memberships.

J. Y. Kang et al. / J. Biomedical Science and Engineering 2 (2009) 656-660 657
SciRes Copyright © 2009 JBiSE
Let denotes an image
with
{,1,2, ,|}
d
ii
Xxi Nx 
N
pixels to be partitioned into classes, where
c
i
x
represents features data. The algorithm is an iterative
optimization that minimizes the objective function de-
fined as follows [3]:
2
11
cN
m
mkii
ki
k
J
uxv



(1)
with the following constraints:
11
{[0,1]| 1,,0,
cN
ki kiki
ki
uuiuN



}k
(2)
where represents the membership of pixel
ki
ui
x
in the
cluster, is the class center; || denotes the
Euclidean distance, is a weighting exponent on
each fuzzy membership. The parameter controls the
fuzziness of the resulting partition. The membership
functions and cluster centers are updated by the follow-
ing expressions:
th
kk
vth
k
1m
||
m
2/( 1)
1
1
()
ki c
ik m
lil
uxv
xv





(3)
and
1
1
N
m
ki i
i
kN
m
ki
i
ux
v
u





(4)
In implementation, matrix V is randomly initialized,
and then U and V are updated through an iterative proc-
ess using Eq.s 3 and 4 respectively.
2.2. Modified FCM Algorithm
Szilagyi et al.proposed a fast FCM clustering algorithm,
EnFCM [8], which is used for gray level image segmen-
tation. The algorithm accounts for pixel spatial informa-
tion. Before the algorithm implementation, a linearly-
weighted sum image

, composed by original image
and local neighboring average of each pixel in original
image , was calculated as follows:
1()
1i
ii
jN
R
j
x
x
N






(5)
where i

is the gray value of the pixel in the image
th
i

. stands for the set of neighbors falling into a local
window around i
i
N
x
, ad n
R
N iits cardinality. The pa-
rameter a n the second term controls the effect of the
penalty. In essence, the addition of the second term in
Eq.5, equivalently, formulates a spatial constraint and
aims at keeping continuity on neighboring pixel values
around
s
i
i
x
. Accordingly, the modified objective func-
tion was described as follows:
2
11
q c
m
slkll
kl
k
J
uv 



(6)
where {,1,2, ,}
ll
 q


 is the data set rearranging
from he image

defined in Eq.5 according to gray
level. {}(1,2, ,
k
Vvk)c


{ }
kl
Uu
represents the prototype
of the cluster,
th
k(1,2, ,,1,2, ,)k cl q


represents the fuzzy membership of gray value l with
respect to cluster . denotes the number of the gray level
of the given image which is generally much smaller than
.
kq
Nl

is the number of the pixels having the gray value
equal to l, where 1, 2,,lq

. Naturally, 1
q
l
lN



.
Similar to the standard FCM algorithm, under the
constraints that 11
c
kl
ku 


for any l, minimize
s
J
de-
fined in Eq.6. Specifically, taking the first derivatives of
s
J
with respect to and , and zeroing them, re-
spectively, two necessary but not sufficient conditions
for
kl
uk
v
s
J
will be obtained as follows:
2/( 1)
2/( 1)
1
()
()
m
lk
kl cm
lr
r
v
u
v







 (7)
1
1
qm
lkll
l
kqm
lkl
l
u
v
u






 (8)
Obviously, in Eq.6, gray level was viewed as the clas-
sified data. Hence, the number of classified data only
depends on gray level, and doesn’t enlarge with the in-
creasing of image size. However, Eq.6 doesn’t take dif-
ferent gray level which has different influence on classi-
fying results into consideration, i.e., Eq.6 considers that
every gray level has the same contribution to the classi-
fying results. Actually, according to the gray level histo-
gram of the fingerprint image, it is clear that the occur-
rence frequencies of different gray level are different.
Therefore, different gray level has different contribution
to clustering results. Based on above analysis, we modi-
fied the objective function in Eq.6 as follows:
2
11
q c
m
sllkll
kl
k
J
wu v 



(9)
where is the weighting coefficient of
l
w(1,2,,)
llq

,
and can be computed via histogram as follows:
,0,1,
l
l
wl
N

,q
(10)
where q denotes the number of the gray level of the
given image. l

is the number of the pixels having the

658 J. Y. Kang et al. / J. Biomedical Science and Engineering 2 (2009) 656-660
SciRes Copyright © 2009
q
JBiSE
gray value equal to l, where . Naturally,
1, 2,,l
1
q
l
l
N


, , i.e., can be
viewed as the occurrence probability of each gray level.
Hence, from Eq.10, it is known that the weighting coef-
ficient of each gray level can be given by the normalized
image histogram.
11
q
l
lw 
(1,2, l
wl
c
k
,q
1u 
)
Similarly, under the constraints that 1
kl


u
for
any l, minimize Js defined in Eq.9. Specifically, taking
the first derivatives of Js with respect to and ,
and zeroing them, respectively, two necessary but not
sufficient conditions for Js will be obtained as follows:
kl k
v
2/( 1)
2/( 1)
m
m

1
kl c
r
u
 ()
()
lk
lr
v
v 





 (11)
1
1
qm
ll
m
kl
llk
l
q
ll
l
wu
wu
k
v


1/
l
wq
1cN 
,2,,)c





l
w
1m
(12)
From Eq.12, it is known that the function of weight-
ing coefficient lies in adjusting the clustering center.
Eq.9 will degenerated to Eq.6 while .
The modified FCM algorithm (spatially weighting
FCM clustering algorithm, called SWFCM) can be
summarized as follows:
Step 1: Fix and 2; then select ini-
tial class prototypes ; set
(1
k
vk 0

 to a
very small value.
Step 2: Compute the new image

in terms of Eq.5
in advance.
Repeat:
Step 3: Compute/modify kl

with by
Eq.s 11 and 12.
k
v
kl
Step 4: Update with the modified
k
v

by
Eq. 12.
Until (||
new old
VV


2ma
)
3. RESULTS AND DISCUSSIONS
In the following experiments, we first execute the three
segmentation algorithms, FCM, EnFCM and SWFCM
on an original fingerprint image in Subsection 3.1. Then
perform the three segmentation algorithms on noisy fin-
gerprint images corrupted, respectively, by Gaussian noise
and salt and pepper noise to investigate the robustness of
the algorithms in Subsection 3.2. Finally, the Subsection
3.3 gives the corresponding quantitative comparisons for
the segmenting results presented in Subsection 3.1 and
3.2. In all the following experiments, we set the parame-
ters , , , .
2c55
10  
3.1. Results on Original Fingerprint Image
To compare the segmenting performances of the above
three algorithms, FCM, EnFCM and SWFCM, we apply
these algorithms to an original test fingerprint image as
shown in Figure 1(a) with the size of pixels,
and the corresponding segmenting results are, respec-
tively, displayed in Figures 1(b,c,d).
300 300
As shown in Figure 1, it is clear that our proposed
algorithm performs more visually significant than other
two methods do. More detailed quantified comparison
according to execution time and iteration step are given
in the next subsection.
3.2. Results on Fingerprint Images Corrupted
by Noises
To examine the above three algorithms’ robustness to noise,
we apply the three algorithms on fingerprint images cor-
rupted by noises. Figure 2(a) is the original image with
no noise and Figures 2(b) and 2(c) are the same images
corrupted, respectively, by the Gaussian noise
(0, 0.05




d
) and the salt and pepper noise with
noisy density 0.02

. The segmenting results on Figures
2(a) and 2(b) are shown in Figures 3 and 4, respectively.
(a) (b)
(c) (d)
Figure 1. Fingerprint image segmentation. (a) Original
fingerprint image; (b) Fingerprint segmentation result
using FCM; (c) Fingerprint segmentation result using
EnFCM; (d) Fingerprint segmentation result using
SWFCM.
(a) (b) (c)
Figure 2. Fingerprint image. (a) Original image; (b) The im-
age corrupted by Gaussian noise; (c) The image corrupted by
salt and pepper noise.

J. Y. Kang et al. / J. Biomedical Science and Engineering 2 (2009) 656-660 659
SciRes Copyright © 2009 JBiSE
Figure 3. Segmenting results on fingerprint image corrupted
by Gaussian noise. (a) Fingerprint segmentation result using
FCM (b) Fingerprint segmentation result using EnFCM (c)
Fingerprint segmentation result using SWFCM.
Figure 4. Segmenting results on fingerprint image corrupted
by salt and pepper noise. (a) Fingerprint segmentation result
using FCM; (b) Fingerprint segmentation result using EnFCM;
(c) Fingerprint segmentation result using SWFCM.
Both from Figures 3 and 4, We can visually see that
FCM is influenced by the Gaussian noise and the salt
and pepper noise to different extents, respectively, which
indicate that FCM algorithm lacks enough robustness to
both the Gaussian noise and the salt and pepper noise,
while EnFCM and SWFCM can basically eliminate the
effect of the noises. Although the segmenting results
using EnFCM and SWFCM are visually almost same,
more detailed quantified comparison according to exe-
cution time, iteration step and signal-to-noise ratio (SNR)
are needed to further investigate in the next subsection.
3.3. Quantitative Segmenting Results Comparisons
We tabulate quantitative segmenting comparisons in Tables
1,2,3 of the above three algorithms for Figures 1,3,4,
respectively.
From Tables 1,2,3, we can obviously see that the it-
eration step of SWFCM is less than that of FCM and
EnFCM. Furthermore, the execution time (CPU: 2 GHz,
Memory: 1GHz, Operating system: windows XP, Soft
ware: Matlab 7.0) of SWFCM is reduced compared with
FCM and EnFCM due to both the less iterations and
only dependence on the number of the gray-level (256)
rather than the image size itself (300 ).
q
N300
Table 1. Comparison scores of three methods corresponding to
Figure 1.
Algorithm T N
FCM 5.123 35
EnFCM 3.841 28
SWFCM 3.077 23
Table 2. Comparison scores of three methods corresponding to
Figure 3.
Algorithm T N SNR
FCM 3.198 17 28.075
EnFCM 2.573 13 28.591
SWFCM 1.967 11 31.308
Table 3. Comparison scores of three methods corresponding to
Figure 4.
Algorithm T N SNR
FCM 3.130 14 22.157
EnFCM 2.217 8 24.972
SWFCM 1.048 4 27.872
Note: In the above three tables, T stands for execution time with the
unit of second; N stands for iteration step.
From Tables 2 and 3, we can also see that the SNR of
SWFCM is less than that of FCM and EnFCM. From
this results, it can be concluded that the newly-proposed
algorithm give rise to better denoising performance than
both FCM and EnFCM algorithms.
4. CONCLUSIONS
In this paper, an automatic modified FCM clustering
algorithm for fingerprint segmentation was proposed.
The proposed algorithm is realized by modifying the
objective function in the Szilagyi’s algorithm via intro-
ducing the gray histogram-based weighting. Experimen-
tal results show that proposed method can dramatically
speed up FCM, and can achieve better denoising per-
formance compared with EnFCM. Therefore, the pro-
posed approach will be promising in real fingerprint
recognition system, in which the fingerprint images are
contaminated by noises heavily.
5. ACKNOWLEDGMENTS
The authors would like to address appreciations to anonymous review-
ers for their valuable comments and suggestions to improve the pres-
entation of this paper. This work was supported by the Jiangsu Post-
doctoral Science Foundation (Grant No. 0901077C), the HHIT Science
Foundation (Grant No. Z2008035) and Postdoctoral Science Founda-
tion of China (Grant No. 20090451167).
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