a modified gabor filter design method for fingerprint image enhancement
TRANSCRIPT
A modified Gabor filter design method for fingerprintimage enhancement
Jianwei Yang, Lifeng Liu, Tianzi Jiang *, Yong Fan *
National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, P.O. Box 2728,
Beijing 100080, PR China
Received 17 June 2002; received in revised form 8 January 2003
Abstract
Fingerprint image enhancement is an essential preprocessing step in fingerprint recognition applications. In this
paper, we propose a novel filter design method for fingerprint image enhancement, primarily inspired from the tra-
ditional Gabor filter (TGF). The previous fingerprint image enhancement methods based on TGF banks have some
drawbacks in their image-dependent parameter selection strategy, which leads to artifacts in some cases. To address this
issue, we develop an improved version of the TGF, called the modified Gabor filter (MGF). Its parameter selection
scheme is image-independent. The remarkable advantages of our MGF over the TGF consist in preserving fingerprint
image structure and achieving image enhancement consistency. Experimental results indicate that the proposed MGF
enhancement algorithm can reduce the FRR of a fingerprint matcher by approximately 2% at a FAR of 0.01%.
� 2003 Elsevier Science B.V. All rights reserved.
Keywords: Fingerprints; Enhancement; Traditional Gabor filter; Modified Gabor filter; Parameter selection; Low pass filter; Band pass
filter
1. Introduction
Fingerprint recognition is being widely applied
in the personal identification for the purpose of
high degree of security. However, some fingerprint
images captured in variant applications are poor in
quality, which corrupts the accuracy of fingerprint
recognition. Consequently, fingerprint image en-
hancement is usually the first step in most auto-matic fingerprint identification systems (AFISs).
There have existed a variety of research activi-
ties along the stream of reducing noises and in-
creasing the contrast between ridges and valleys
in the gray-scale fingerprint images. Some ap-
proaches are implemented in spatial domain, others
in frequency domain. O�Gorman and Nickerson
(1989) and Mehtre (1993) performed fingerprintimage enhancement based on directional filters;
Maio and Maltoni (1998) employed neural
network in minutiae filtering; Almansa and
Lindeberg (2000) enhanced them in scale space;
*Corresponding authors. Tel.: +86-10-8261-4469; fax: +86-
10-6255-1993.
E-mail addresses: [email protected] (J. Yang), lfliu@
nlpr.ia.ac.cn (L. Liu), [email protected] (T. Jiang), yfan@
nlpr.ia.ac.cn (Y. Fan).
0167-8655/03/$ - see front matter � 2003 Elsevier Science B.V. All rights reserved.
doi:10.1016/S0167-8655(03)00005-9
Pattern Recognition Letters 24 (2003) 1805–1817
www.elsevier.com/locate/patrec
Greenberg et al. (2000) and Jiang (2001) resorted
to an anisotropic filter and an oriented low pass
filter to suppress noises respectively. In contrast
with the above methods in spatial domain, Sher-
lock et al. (1994), Willis and Myers (2000) and
Kamei and Mizoguchi (1995) denoised fingerprintimages in frequency domain. There are advantages
and disadvantages of analysis merely in spatial
domain or frequency domain. As is well known,
the Gabor filter is a very useful tool for texture
analysis in both domains and hence combines the
advantages of both filters. Considering their fre-
quency-selective and orientation-selective proper-
ties and optimal joint resolution in both domains,Hong et al. (1998) made use of Gabor filter banks
to enhance fingerprint images and reported to
achieve good performance.
In their algorithm, called the traditional Gabor
filter (TGF) method in this paper, Hong et al.
assumed that the parallel ridges and valleys exhibit
some ideal sinusoidal-shaped plane waves associ-
ated with some noises. In other words, the 1-Dsignal orthogonal to the local orientation is ap-
proximately a digital sinusoidal wave. Then, the
TGF is tuned to the corresponding local orienta-
tion and ridge frequency (reciprocal of ridge dis-
tance) in order to remove noises and preserve the
genuine ridge and valley structures. Unfortunately,
their prior sinusoidal plane wave assumption is
inaccurate because the signal orthogonal to the
local orientation in practice does not consist of
an ideal digital sinusoidal plane wave in some
fingerprint images or some regions (see Fig. 1).
Moreover, the TGF�s parameter selection in theirmethod (such as the standard deviation of the
Gaussian function) is empirical. This implemen-
tation implies the disadvantage of image-depen-
dence. In some cases, it could unexpectedly result
in inconsistent image enhancement, which is
baneful to the following steps.
In order to overcome its shortcomings, we
improve the TGF to the modified Gabor filter(MGF) by discarding the inaccurate prior sinu-
soidal plane wave assumption. Our MGF�s pa-
rameters are deliberately specified through some
principles instead of experience and an image-
independent parameter selection scheme is ap-
plied. Experimental results illustrate that our
MGF could achieve better performance than the
TGF.The rest of this paper is organized as follows. In
Section 2, we briefly introduce the TGF and our
MGF, and meanwhile highlight our motivation of
extending the TGF to the MGF. Section 3 is de-
voted to the parameter selection of our MGF.
Implementation is detailed in Section 4. Experi-
Fig. 1. A fingerprint image and corresponding ridge and valley topography. The top-right region can be approximately treated as a
sinusoidal plane wave, but never the bottom-left.
1806 J. Yang et al. / Pattern Recognition Letters 24 (2003) 1805–1817
mental results are shown in Section 5. In Section 5
we made some conclusions.
2. Traditional Gabor filter and modified Gabor filter
The Gabor function has been recognized as a
very useful tool in computer vision and image
processing, especially for texture analysis, due to
its optimal localization properties in both spatial
and frequency domain. There are lots of papers
published on its applications since Gabor (1946)
proposed the 1-D Gabor function. The family of
2-D Gabor filters was originally presented byDaugman (1980) as a framework for understand-
ing the orientation-selective and spatial–frequency-
selective receptive field properties of neurons in the
brains� visual cortex, and then was further mathe-
matically elaborated (Daugman, 1985).
The 2-D Gabor function is a harmonic oscil-
lator, composed of a sinusoidal plane wave of a
particular frequency and orientation, within aGaussian envelope. A complex 2-D Gabor filter
over the image domain ðx; yÞ is defined as
Gðx; yÞ ¼ exp
� ðx� x0Þ2
2r2x
� ðy � y0Þ2
2r2y
!
� expð�2piðu0ðx� x0Þ þ v0ðy � y0ÞÞÞ ð1Þ
where ðx0; y0Þ specify the location in the image,
ðu0; v0Þ specifying modulation that has spatial–
frequency x0 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiu20 þ v20
pand orientation h0 ¼
arctanðv0=u0Þ, and rx and ry are the standard de-
viations of the Gaussian envelope respectively
along x-axis and y-axis. Derived from formula (1)
by elaborately selecting above parameters, the
even-symmetric real component of the original 2-D Gabor filer can be obtained, which is adopted in
(Jain and Farrokhnia, 1991; Hong et al., 1998):
gðx; y; T ;/Þ ¼ exp
� 1
2
x2/r2x
"þ
y2/r2y
#!cos
2px/
T
� �
ð2Þ
x/ ¼ x cos/ þ y sin/ ð3Þ
y/ ¼ �x sin/ þ y cos/ ð4Þ
where / is the orientation of the derived Gabor
filter, and T is the period of the sinusoidal plane
wave.
If we decompose formula (2) into two ortho-
gonal parts, one parallel and the other perpendi-cular to the orientation /, the following formula
can be deduced:
gðx; y; T ;/Þ ¼ hxðx; T ;/Þ � hyðy;/Þ
¼ exp
(�
x2/2r2
x
!cos
2px/
T
� �)
� exp
(�
y2/2r2
y
!)ð5Þ
The first part hx behaves as a 1-D Gabor function
which is a band pass filter, and the second one hyrepresents a Gaussian function which is a low pass
filter. Therefore, a 2-D even-symmetric Gabor fil-
ter (TGF) performs a low pass filtering along
the orientation / and a band pass filtering or-
thogonal to its orientation /. The band pass andlow pass properties along the two orthogonal
orientations are very beneficial to enhancing fin-
gerprint images, since these images usually show a
periodic alternation between ridges and valleys
orthogonal to the local orientation and parallel
exhibit an approximate continuity along the local
orientation.
It should be pointed out that hx in formula (5)could be treated as a non-admissible mother
wavelet (indicated by its Fourier representation
hhxð0Þ 6¼ 0). Its band pass property is related with
the rx. If rx is too small, the band pass filter de-
generates into a low pass function (indicated by its
Fourier representation hhxð0Þ 0). On the other
hand, if rx is appropriately large, hx can be ap-
proximately regarded as an admissible motherwavelet (indicated by its Fourier representa-
tion hhxð0Þ 0) with good band pass property (see
Fig. 2).
For the purpose of enhancing fingerprint images
by the TGF, Hong et al. (1998) assumed that ridges
and valleys show a sinusoidal plane wave pattern
and specified the parameter T in formula (2) or (5)
as the distance between two successive ridges.However, in practice this prior assumption is in-
accurate. In Fig. 1, the ridge and valley structures
J. Yang et al. / Pattern Recognition Letters 24 (2003) 1805–1817 1807
in the top-right region can be roughly regarded as a
sinusoidal plane wave pattern, but never those in
the bottom-left region. In that case, the TGF
method fails. This phenomenon can be explicitly
explained in frequency domain. Although a band
pass filter can enlarge the signal of a particular
frequency and suppress others, the preferred fre-
quency cannot be accurately specified in somecases. In other words, the ridge and valley pattern
like the bottom-left region of Fig. 1 is not com-
posed of a sinusoidal plane wave of only a partic-
ular frequency but a periodic one whose Fourier
extension contains different frequency harmonics.
The TGF cannot pass the entire harmonics except
the signal of a particular frequency. However, the
low frequency components usually contain usefultexture information (e.g. slow variation of intensi-
ties near ridges� centers orthogonal to the local
orientation is represented as low frequency com-
ponents, see Fig. 1(b)). Thereby, the TGF method
may lose some useful original information.
To overcome the TGF�s drawbacks mentioned
above, we replace the cosine function cosðx; T Þ informula (2) and (5) with another periodic function
F ðx; T1; T2Þ to construct our MGF. It is incorpo-
rated with two cosinusoidal functional curves with
different periods T1 and T2 (see Fig. 3). The partsabove the x-axis consist of a cosinusoidal func-
tional curve with a period T1 and the ones below
the x-axis consist of another cosinusoidal func-
tional curve with different period T2. F ðx; T1; T2Þ isextended periodically and elaborated mathemati-
cally as follows:
F ðx;T1;T2Þ ¼ f x�
� xT1=2þ T2=2
� �� ðT1=2þ T2=2Þ
�ð6Þ
Fig. 2. The TGF and its response represented in spatial and frequency domain.
1808 J. Yang et al. / Pattern Recognition Letters 24 (2003) 1805–1817
f ðxÞ
¼
cos 2pxT1
�06x6T1=4
�cos 2pðx�T1=4�T2=4ÞT2
�T1=4< x< T1=4þT2=2
cos 2pðx�T1=2�T2=2ÞT1
�T1=4þT2=26x6T1=2þT2=2
8>>>>><>>>>>:
ð7Þ
where btc ¼ floorðtÞ means the largest integer not
larger than t.From the above definition, F ðx; T1; T2Þ is a pe-
riodic even-symmetric oscillator with the period
ðT1 þ T2Þ=2, and it becomes a �true� cosinusoidalfunction when T1 ¼ T2. Then, our MGF can bespecified by modulating the periodic function
F ðx; T1; T2Þ by a 2-D anisotropic Gaussian func-
tion. So, formula (5) is turned into
Fig. 3. The periodic function F ðx; T1; T2Þ. The parts above the
x-axis consist of a cosinusoidal functional curve with period T1,and those below the x-axis consist of another cosinusoidal
functional curve with different period T2.
Fig. 4. Our MGF and its response represented in spatial and frequency domain.
J. Yang et al. / Pattern Recognition Letters 24 (2003) 1805–1817 1809
g0ðx; y; T1; T2;/Þ ¼ h0xðx; T1; T2;/Þ � h0yðy;/Þ
¼ exp
(�
x2/2r2
x
!F ðx/; T1; T2Þ
)
� exp
(�
y2/2r2
y
!)ð8Þ
The frequency representation of the MGF is nolonger a band pass filter passing only one central
frequency component, but a band pass filter as-
sociated with a bank of low pass filters (see Fig. 4).
The associated low pass filters are beneficial to
passing the useful low frequency components.
Therefore, our MGF can more straightforwardly
express the texture characteristics of fingerprint
images than the TGF.
3. Parameter selection
Parameter selection plays a crucial role in the
use of the TGF and has long been a research focus
in the field of image processing. However, the
computation of filter coefficients is very complex(Bovick et al., 1990). For texture analysis, some
principles of parameter selection are proposed (e.g.
Jain and Farrokhnia, 1991; Clausi and Jernigan,
2000) based on comparison between the output
of the human visual system and the Gabor filter
response. Responsible for the specific finger-
print image enhancement, parameter selection also
needs to be explored. In the TGF, there are fiveparameters to be specified, including the Gabor
filter orientation /, the standard deviations rx and
ry of the 2-D Gaussian function, the period T of
the assumed sinusoidal plane wave and the con-
volution mask size ð2N þ 1Þ � ð2N þ 1Þ. Hong
et al. specified them based on the empirical data.
In our MGF, the period T is decomposed into T1and T2, and most of the parameters including theconvolution mask size are specified adaptively.
3.1. Orientation / of modified Gabor filter
Hong et al. (1998) firstly utilized a least mean
square estimation method to compute the orien-
tation field of fingerprint images block-wisely. The
steps are as follows:
1. Divide the input fingerprint image into blocks
of size W � W .
2. Compute the gradients Gx and Gy at each pixelðx; yÞ in each block.
3. Estimate the local orientation of each block
using the following formula:
hði;jÞ
¼ 1
2tan�1
PiþW =2u¼i�W =2
PjþW =2v¼j�W =2 2Gxðu;vÞGyðu;vÞPiþW =2
u¼i�W =2
PjþW =2v¼j�W =2 ðG2
xðu;vÞ�G2yðu;vÞÞ
!
ð9ÞThen, hði; jÞ is regularized into the range of �p=2to þp=2. Finally, the parameter / of the TGF is
chosen as the orientation of each block.
However, their block-wise scheme is coarse and
cannot obtain fine orientation field, which tends tocorrupt the TGF�s performance. In order to esti-
mate the orientation field more accurately, we ex-
tend their method into a pixel-wise one. For each
pixel, a block with size W � W centered at the pixel
is referred to, so the orientation of each pixel can
be estimated by the formula (9). To reduce the
computational cost, a sliding window technique is
employed (Yang et al., 2002). For an image, theorientation of the MGF is tuned to the orientation
at current pixel, and thus a low pass filtering along
the orientation and a band pass associated with
low pass filtering orthogonal to the orientation are
performed.
It needs to be emphasized that a step of
smoothing the orientation field by a low pass filter
is necessary since sometimes the orientation field isdistorted by noises.
3.2. Periods T1 and T2
Examining the formulas (5)–(8), we draw the
conclusion that T1=2þ T2=2 in our MGF corre-
sponds to T in the TGF that is depicted as the
ridge distance by Hong et al. (1998) and they be-
come the same when T1 ¼ T2. Further investigatingthe formula (8), we learn that the zero crossings of
g0 are merely determined by the oscillator F ðx; T1;T2Þ. Accordingly, we specify T1 and T2 as double
1810 J. Yang et al. / Pattern Recognition Letters 24 (2003) 1805–1817
of the local ridge width and valley width. The
determination of T1 and T2 is detailed as follows.
Let Iði; jÞ denote an arbitrary pixel to be filtered
currently whose neighborhoods have the ridge
width Wr and valley width Wv. Firstly, a method is
applied to roughly determine whether Iði; jÞ is lo-cated on a ridge or valley. If Iði; jÞ belongs to a
ridge then T1 is set as 2Wr and T2 as 2Wv. Other-
wise, if Iði; jÞ is on a valley then T1 is set as 2Wv
and T2 as 2Wr (see Fig. 5). The selection of T1and T2 ensures that the centric pixels on each
ridges and valleys are given the heaviest weights
in the later convolution phase, which benefits to
enhance the contrast between ridges and valleys.To this end, there are two prerequisites to be
solved:
1. How to compute the ridge width Wr and valley
width Wv.
2. How to determine whether a pixel is on a ridge
or valley, i.e. segmentation of ridges and val-
leys.
Before addressing the two issues, a step of
smoothing the fingerprint image is necessary be-
cause it may be filled with noises such as holes on
ridges and peaks on valleys. We utilize 1-D direc-
tional Gaussian filter at each pixel along its ori-
entation to remove the noises.
3.2.1. Computation of ridge width Wr and valley
width Wv
Accurate estimation of the ridge width and
valley width is in fact a difficult task. We follow
Hong�s method of computing ridge frequency toobtain them. Firstly, the fingerprint image is di-
vided into blocks of size w� w (w ¼ 16). For each
block centered at pixel Iði; jÞ, an oriented window
of size l� w (l ¼ 32) is built and an x-signaturesignal is computed. Here, the x-signature is the
average signal of projection of all the intensities in
the oriented window along the Iði; jÞ orientation
(please refer to Hong et al. (1998) for more detailsabout the x-signature). The shape of the x-signa-ture signal is similar to Fig. 1(a) or (b). Its first and
second order derivatives indicate the ridge width
and valley width. Inaccurate ridge width and val-
ley width could lead to inter-block non-uniform
image enhancement, since the estimation proce-
dure is block-wise not pixel-wise. To compute
the ridge width and valley width from the dis-crete signal x-signature more accurately, we resort
to a fitting method to acquire the first and second
order derivatives. Based on the trade-off between
accuracy and efficiency, the discrete Chebyshev
polynomials introduced by Haralick (1984) and
Tico and Kuosmanen (1999) are employed to
perform the fitting. The zero crossings of the sec-
ond order derivatives and magnitude of the first
Fig. 5. The curve of F ðx; T1; T2Þ corresponding to different period T1 and T2. Pixel Pa is located on a ridge, so T1 is set as the double ofridge width 2Wr and T2 as the double of valley width 2Wv. Pixel Pb is on a valley, so T1 is set as 2Wv and T2 as 2Wr.
J. Yang et al. / Pattern Recognition Letters 24 (2003) 1805–1817 1811
order derivatives are together taken into account
to determine the ridge width and valley width.
In other words, the distance between two zero
crossings of the second order derivatives is re-
garded as the ridge width or valley width if the
magnitude of the corresponding first order deriv-ative is larger than a threshold. Then, the signs
of the second order derivatives specify whether it
is ridge or valley. Thereby, the information of
ridge width Wr and valley width Wv is associated
to each block. In application, ridge width and
valley width fall into a certain interval. If ex-
ceeding the interval, they are replaced by the mean
of those available in neighboring eight blocks.
3.2.2. Segmentation of ridges and valleys
As mentioned above, the functional form of
F ðx; T1; T2Þ depends on the characteristics of cur-
rent pixel�s neighborhoods, and hence different
pixel corresponds to different F ðx; T1; T2Þ. For thispurpose, a previous step of determining whether
the pixel is located on a ridge or valley is necessary.In our algorithm, we adopt a local threshold
method to roughly segment ridges and valleys.
Firstly, the mean m and standard deviation s ofintensities in each block that is divided in the
previous phase of estimating ridge width and val-
ley width are calculated. Secondly, for each block
a local threshold thres ¼ mþ d � s is selected. Fi-
nally, each pixel at the block is classified into twocategories of ridge or valley by comparing its in-
tensity with thres (d ¼ 0:2 in our experiments).
Generally speaking, this segmentation method
is rough and some pixels may be misclassified due
to the existence of noises. But in our experiments,
the performance is acceptable after Gaussian di-
rectional smoothing. For more accurate segmen-
tation, the gradient at each pixel can also beapplied by topography methods (e.g. Wang and
Pavlidis, 1993; Haralick et al., 1983).
3.3. Determination of rx and ry
In the MGF, rx is the standard deviation of the
2-D Gaussian function along the x-axis and ry
along the y-axis. rx and ry control the spatial–frequency bandwidth of the MGF response. The
larger they are, the wider bandwidth is expected.
However, too wide bandwidth can unexpectedly
enlarge the noises, and too narrow bandwidth
tends to suppress some useful signals.
The value of ry determines the smoothing de-
gree along the local orientation. Too large ry canblur the minutiae. In our algorithms, ry is empir-
ically set as 4.0.
Compared with ry , rx inherently plays a more
important role for the enhancement performance
and needs to be specified carefully. It influences the
degree of contrast enhancement between ridges
and valleys. This selection involves a trade-off. If
rx is too large, the factor h0x in formula (5) will havemore high frequency components and even un-
stably oscillate near the origin, which leads to ar-
tifacts. On the other hand, if rx is too small, the
band pass associated with low pass filters will
evolve into a �pure� low pass one due to the over-
domination of the Gaussian function in h0xðx; T1;T2Þ, which results in blurring edges (boundaries)
between ridges and valleys. Hong et al. (1998)empirically selected rx as 4.0 and Greenberg et al.
(2000) specified it as 3.0 for his experimental im-
ages. Both of their parameter selections depend on
specific image database. It is known that the in-
fluence of rx on the performance is related with T1and T2 (only T in the TGF). If T1 and T2 are of
great variation in a fingerprint image, a constant
rx could result in a non-uniform enhancement,even in some regions there is no enough enhance-
ment but in others artifacts occurs.
The inconsistency of inter-block enhance-
ment implied that ridges and valleys in differ-
ent blocks are given non-uniform weights by filter
masks, since the filtering procedure is a convo-
lution between images and filter masks. To
avoid the inconsistency, the MGF mask is as-signed to each block by involving the local char-
acteristics, T1 and T2. The following constraints are
examined:
R T1=40
exp � x2
2r2x
�cos 2px
T1
�dxR T1=4þT2=2
T1=4exp � x2
2r2x
�cos 2pðx�T1=4�T2=4Þ
T2
�dx
¼ Q
ð10Þ
1812 J. Yang et al. / Pattern Recognition Letters 24 (2003) 1805–1817
Z 3T1=4þT2=2
T1=4þT2=2exp
�� x2
2r2x
�
� cos2pðx� T1=2� T2=2Þ
T1
� �dx 0 ð11Þ
Given a fixed Q, rx corresponding to certain T1 andT2 can be obtained by a numeric resolving method.
Therefore, constraints (10) and (11) provide a link
between the rx and T1 and T2, that is, a link be-
tween rx and each block. Here, Q represents the
area proportion between the central dominant
component (near the origin, above the x-axis) andits two close sidelobes (below the x-axis) in the
factor h0x (see Fig. 6). Moreover, constraints (10)
and (11) ensure that a MGF is a stable oscillator
near the origin (Q > 1, in the application), since
other sidelobes far away from the origin are sup-
pressed. To achieve a uniform enhancement, Q is
specified as a global one. To speed up the filtering,
the rxs corresponding to different T1 and T2 arecomputed off-line since the ridge width and valley
width are in a certain interval. Some rxs adopted in
our experiments are listed in Table 1 (Q ¼ 1:2).From Table 1, T2 is subdivided into a smaller range
when T1 is small.
3.4. Selection of convolution mask size
The implementation of enhancing fingerprint
images by the MGF or TGF is a convolution be-
tween an image and a part of filters� coefficient
matrix. The convolution mask size influences the
performance of filtering and computational cost.
Too large mask size tends to burden the en-
hancement processing and meanwhile bring anunstable factor when the area of the central
dominant component is less than the sum of that
of its two close sidelobes. But if it is too small, the
MGF or TGF collapses into a 2-D low pass filter
and the advantage of the band pass filter will be
lost. Hong et al. (1998) set the mask size as
ð2N þ 1Þ � ð2N þ 1Þ (N ¼ 5Þ from his experience.
However, it is illogical that the mask size is stillconstant when the width of ridges and valleys
varies. In contrast, we select the convolution mask
size as ð2Ww þ 1Þ � ð2Wh þ 1Þ for our MGF which
varies according to T1 and T2. Here, ð2Ww þ 1Þ is
set as ðT2=2þ T1=2þ T2=2Þ orthogonal to the local
orientation (see Fig. 6). Actually, T2=2þ T1=2þT2=2 means Wv þ Wr þ Wv or Wr þ Wv þ Wr. Based
on the formulas (10) and (11), this selection en-sures the area of the central dominant is larger
than the sum of that of its two close sidelobes
(represented by Q > 1). Thereby, the band pass
property is exerted and meanwhile both instability
and truncation errors are avoided.
From the above discussions, the convolution
mask size is integrated with the T1, T2 and rx by the
global parameter Q to achieve consistent en-hancement. Moreover, Wh is selected as a constant
Fig. 6. The response of the factor h0x in formula (8) in spatial
domain. The central dominant component and its close side-
lobes are marked.
Table 1
Some rxs adopted in our experiments corresponding to different
T1 and T2
T1 T2 rx
4 ½4; 12� 1.5
4 ½14; 18� 1.6
4 ½20; 28� 1.8
6 – 1.8
8 – 2.5
10 – 2.7
12 – 3.0
14 – 3.5
16 – 4.0
J. Yang et al. / Pattern Recognition Letters 24 (2003) 1805–1817 1813
value 5.0 corresponding to ry specified in the
previous subsection.
4. Implementation
In the whole process of image enhancement, theMGF�s design is completed based on the analysis
in frequency domain, and images are enhanced in
spatial domain. Meanwhile, the coefficients of the
Gaussian directional filter and MGF are com-
pleted off-line for speedup. In the TGF, Gabor
filter banks with different orientations are em-
ployed and their coefficients are computed re-spectively. This entails a number of filters. In our
Fig. 7. Enhancement results corresponding to the fingerprint images of Fig. 8. The first two columns are the results using the TGF with
different rx; ry . The third column is the results by our MGF.
1814 J. Yang et al. / Pattern Recognition Letters 24 (2003) 1805–1817
algorithm, only coefficients of the MGF with the
orientation / ¼ 0 are computed and image rota-
tion is implemented instead of computing the
multi-directional MGFs. That is, MGF banks with
different rxs corresponding to different T1 and T2are completed in advance. Then, image blocks withthe same size as that of the convolution mask are
rotated to the MGF orientation / ¼ 0. As a result,
our MGF enhancement achieves high efficiency,
although we resort to multi-rx, multi-convolution
mask technique.
5. Experimental results
We test the efficiency and robustness of our
algorithm using some fingerprint images, which
consist of our image database captured by an
optical live-scanned equipment ð400� 376Þ,FVC2000 DB2 ð364� 256Þ (touched sensor), data-
base at the University of Bologna ð256� 256Þ andNIST ð512� 512Þ (National Institute of Standardand Technology) series fingerprint image database.
The parameters of our MGF are uniform to all the
images to validate our image-independent param-
eter selection scheme. Our experimental results
demonstrate that our MGF is more powerful in
fingerprint image enhancement than the TGF.
Some experimental results are illustrated in Fig. 7
corresponding to the original images in Fig. 8.The experimental results reveal that the difficult
task in parameter selection of the TGF has been
resolved in our MGF. The spurious ridges and
valleys are avoided and uniform enhancement
performance is achieved. We also performed the
feature extraction and feature matching (Ratha
et al., 1996) on a combined fingerprint image
database from our database, FVC 2000 DB2 and
the database at University of Bologna. The fin-gerprint matcher reported by Ratha et al. (1996) is
a widely applied method. It employed the Hough
transform to align two minutia sets. From the
experimental results, our MGF makes the feature
extraction more reliable and feature matching
more accurate (see Table 2). Further investigating
our approaches and experiments, we learn that the
slightly higher computational cost of the MGFprimarily results from its larger convolution mask
size, since T2=2þ T1=2þ T2=2 in the MGF is gen-
erally larger than the convolution mask width
2N þ 1 in the TGF for our tested images (see
Table 3). To achieve fast speed in large images,
convolution implementations in spatial domain
can be substituted by the multiplications in fre-
quency domain.
Fig. 8. Some fingerprint images in our experiments. (a) is captured from an optical equipment. (b) is f23 of NIST-4. (c) is f09 of
NIST-4.
Table 2
Fingerprint matching performance under the enhanced images
by the TGF and MGF
Filter FAR
FRR
0.01% 0.05% 0.1% 0.15% 1%
TGF 5.9% 5.3% 4.3% 3.9% 3.1%
MGF 3.5% 3.1% 2.9% 2.9% 2.8%
J. Yang et al. / Pattern Recognition Letters 24 (2003) 1805–1817 1815
6. Conclusion
In this paper, a MGF has been proposed for
fingerprint image enhancement. The modification
of the TGF can make the MGF more accurate in
preserving the fingerprint image topography. And
a new scheme of adaptive parameter selection for
the MGF is discussed. This scheme leads to theimage-independent advantage in the MGF. Al-
though there are still some intermedial parameters
determined by experience, a step of image nor-
malization can compensate the drawback.
However, some problems need to be solved in
the future. A common problem of the MGF and
TGF is that both fail when image regions are
contaminated with heavy noises. In that case, theorientation field can hardly be estimated and ac-
curate computation of ridge width and valley
width is prohibitively difficult. Therefore, a step of
segmenting these unrecoverable regions from the
original image is necessary, which has been ex-
plored in Hong�s work to some extent.
Acknowledgements
The authors are highly grateful to the anony-
mous reviewers for their significant and construc-
tive critiques and suggestions, which improve the
paper very much. This work was partially sup-
ported by Hundred Talents Programs of the Chi-
nese Academy of Sciences, the Natural ScienceFoundation of China, Grant No. 60172056 and
697908001, and Watchdata Digital Company. We
acknowledge that the experiments in this research
are conducted on the fingerprint database from the
NIST, University of Bologna and FVC2000. We
would also like to give thanks to our colleagues in
National Laboratory of Pattern Recognition for
their stimulated discussions and comments on our
work.
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