PRL_Yang

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 Published by Elsevier Science B.V.

Keywords: Fingerprints; Enhancement; Traditional Gabor filter; Modified Gabor filter; Parameter selection; Low pass filter; Band pass

filter

1. Introduction

Fingerprint recognition is being widely appliedin 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. OGorman and Nickerson(1989) and Mehtre (1993) performed fingerprint

image 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 Published by Elsevier Science B.V.doi:10.1016/S0167-8655(03)00005-9

Pattern Recognition Letters xxx (2003) xxxxxx

www.elsevier.com/locate/patrec

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mail to: [email protected]

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 TGFs 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 MGFs 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.

2 J. Yang et al. / Pattern Recognition Letters xxx (2003) xxxxxx

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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 spatialfrequency-

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 x; y is defined as

Gx; y exp

x x02

2r2x y y0

2

2r2y

!

exp2piu0x x0 v0y y0 1

where x0; y0 specify the location in the image,u0; v0 specifying modulation that has spatialfrequency x0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiu20 v20

pand orientation h0

arctanv0=u0, 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):

gx; y; T ;/ exp

12

x2/r2x

"

y2/r2y

#!cos

2px/T

2

x/ x cos/ y sin/ 3

y/ x sin/ y cos/ 4

where / is the orientation of the derived Gaborfilter, and T is the period of the sinusoidal planewave.

If we decompose formula (2) into two ortho-

gonal parts, one parallel and the other perpendi-cular to the orientation /, the following formulacan be deduced:

gx; y; T ;/ hxx; T ;/ hyy;/

exp (

x2/2r2x

!cos

2px/T

)

exp (

y2/2r2y

!)5

The first part hx behaves as a 1-D Gabor functionwhich 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

hhx0 6 0). Its band pass property is related withthe rx. If rx is too small, the band pass filter de-generates into a low pass function (indicated by its

Fourier representation hhx0 0). On the otherhand, if rx is appropriately large, hx can be ap-proximately regarded as an admissible motherwavelet (indicated by its Fourier representation

hhx0 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 xxx (2003) xxxxxx 3

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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 localorientation is represented as low frequency com-

ponents, see Fig. 1(b)). Thereby, the TGF method

may lose some useful original information.

To overcome the TGFs drawbacks mentionedabove, we replace the cosine function cosx; T informula (2) and (5) with another periodic function

F x; T1; T2 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 belowthe x-axis consist of another cosinusoidal func-tional curve with different period T2. F x; T1; T2 isextended periodically and elaborated mathemati-

cally as follows:

F x;T1;T2 f x

xT1=2 T2=2

T1=2 T2=2

6

Fig. 2. The TGF and its response represented in spatial and frequency domain.


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f x

cos 2pxT1

06x6T1=4

cos 2pxT1=4T2=4T2

T1=4< x< T1=4T2=2

cos 2pxT1=2T2=2T1

T1=4T2=26x6T1=2T2=2

8>>>>>>>>>:

7

where btc floort means the largest integer notlarger than t.

From the above definition, F x; T1; T2 is a pe-riodic even-symmetric oscillator with the period

T1 T2=2, and it becomes a true cosinusoidalfunction when T1 T2. Then, our MGF can bespecified by modulating the periodic function

F x; T1; T2 by a 2-D anisotropic Gaussian func-tion. So, formula (5) is turned into

Fig. 3. The periodic function F x; T1; T2. The parts above thex-axis consist of a cosinusoidal functional curve with period T1,and those below the x-axis consist of another cosinusoidalfunctional curve with different period T2.

Fig. 4. Our MGF and its response represented in spatial and frequency domain.


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g0x; y; T1; T2;/ h0xx; T1; T2;/ h0yy;/

exp (

x2/2r2x

!F x/; T1; T2

)

exp (

y2/2r2y

!)8

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 andry of the 2-D Gaussian function, the period T ofthe assumed sinusoidal plane wave and the con-

volution mask size 2N 1 2N 1. Honget 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 pixel

x; y in each block.3. Estimate the local orientation of each block us-

ing the following formula:

hi;j

12tan1

PiW =2uiW =2

PjW =2vjW =2 2Gxu;vGyu;vPiW =2

uiW =2PjW =2

vjW =2 G2xu;vG2yu;v

!

9Then, hi; j is regularized into the range of p=2to p=2. Finally, the parameter / of the TGF ischosen as the orientation of each block.

However, their block-wise scheme is coarse and

cannot obtain fine orientation field, which tends tocorrupt the TGFs 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 pixelis 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=2 T2=2 in our MGF corre-sponds to T in the TGF that is depicted as theridge distance by Hong et al. (1998) and they be-

come the same when T1 T2. Further investigatingthe formula (8), we learn that the zero crossings of

g0 are merely determined by the oscillator F x; T1;T2. Accordingly, we specify T1 and T2 as double


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of the local ridge width and valley width. The

determination of T1 and T2 is detailed as follows.Let Ii; j denote an arbitrary pixel to be filtered

currently whose neighborhoods have the ridge

width Wr and valley width Wv. Firstly, a method isapplied to roughly determine whether Ii; j is lo-cated on a ridge or valley. If Ii; j belongs to aridge then T1 is set as 2Wr and T2 as 2Wv. Other-wise, if Ii; j is on a valley then T1 is set as 2Wvand T2 as 2Wr (see Fig. 5). The selection of T1and T2 ensures that the centric pixels on eachridges 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 valleywidth 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 valleywidth Wv

Accurate estimation of the ridge width and

valley width is in fact a difficult task. We follow

Hongs method of computing ridge frequency toobtain them. Firstly, the fingerprint image is di-

vided into blocks of size w w (w 16). For eachblock centered at pixel Ii; j, an oriented windowof size l w (l 32) is built and an x-signaturesignal is computed. Here, the x-signature is theaverage signal of projection of all the intensities in

the oriented window along the Ii; j 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 resortto 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 x; T1; T2 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.


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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 associatedto 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 x; T1; T2 depends on the characteristics of cur-rent pixels neighborhoods, and hence differentpixel corresponds to different F x; T1; T2. 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 m 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 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 the2-D Gaussian function along the x-axis and ryalong the y-axis. rx and ry control the spatialfrequency 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 moreimportant 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, theband pass associated with low pass filters will

evolve into a pure low pass one due to the over-domination of the Gaussian function in h0xx; T1;T2, 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 ofgreat 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 areexamined:

R T1=40

exp x22r2x

cos 2pxT1

dxR T1=4T2=2

T1=4exp x2

2r2x

cos 2pxT1=4T2=4T2

dx

Q

10


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Z 3T1=4T2=2T1=4T2=2

exp

x

2

2r2x

cos 2px T1=2 T2=2T1

dx 0 11

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 thearea proportion between the central dominant

component (near the origin, above the x-axis) andits two close sidelobes (below the x-axis) in thefactor 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), sinceother sidelobes far away from the origin are sup-

pressed. To achieve a uniform enhancement, Q isspecified 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 inour experiments are listed in Table 1 (Q 1:2).From Table 1, T2 is subdivided into a smaller rangewhen 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 coefficientmatrix. 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

2N 1 2N 1 (N 5 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 2Ww 1 2Wh 1 for our MGF whichvaries according to T1 and T2. Here, 2Ww 1 isset as T2=2 T1=2 T2=2 orthogonal to the localorientation (see Fig. 6). Actually, T2=2 T1=2T2=2 means Wv Wr Wv or Wr Wv Wr. Basedon 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 passproperty 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 theglobal 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 spatialdomain. The central dominant component and its close side-

lobes are marked.

Table 1

Some rxs adopted in our experiments corresponding to differentT1 and T2

T1 T2 rx

4 4; 12 1.54 14; 18 1.64 20; 28 1.86 1.8

8 2.5

10 2.7

12 3.0

14 3.5

16 4.0


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value 5.0 corresponding to ry specified in theprevious subsection.

4. Implementation

In the whole process of image enhancement, the

MGFs 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.


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algorithm, only coefficients of the MGF with the

orientation / 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 / 0. As a result,our MGF enhancement achieves high efficiency,

although we resort to multi-rx, multi-convolutionmask 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 op-

tical live-scanned equipment 400 376,FVC2000 DB2 364 256 (touched sensor), data-base at the University of Bologna 256 256 andNIST 512 512 (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=2 T1=2 T2=2 in the MGF is gen-erally larger than the convolution mask width

2N 1 in the TGF for our tested images (seeTable 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%


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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 Hongs 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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Table 3

Comparison of time cost of fingerprint image enhancement

(based on P4 1.3 GHz, 128 M RAM PC)

Image reso-

lution (pixel)

TGF (N 5,ry 4:0) rx

Average time cost (s)

TGF MGF

224 288 1.8 0.90 0.92256 256 1.8 0.94 1.01364 256 2.0 1.13 1.22400 376 2.2 1.76 1.89


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ARTICLE IN PRESS

A modified Gabor filter design method for fingerprint image enhancementIntroductionTraditional Gabor filter and modified Gabor filterParameter selectionOrientation phi of modified Gabor filterPeriods T1 and T2Computation of ridge width Wr and valley width WvSegmentation of ridges and valleys

Determination of sigmax and sigmaySelection of convolution mask size

ImplementationExperimental resultsConclusionAcknowledgementsReferences

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