Features extraction from fingerprints using frequency ...

Features extraction from fingerprints using frequency domain analysis A. Beghdadi* and M. Deriche** (*) L2TI, Insitut Galilee, Universite Paris 13, France (**) SPRC, QUT, Brisbane, Australia

ABSTRACT This paper presents a new method for feature extraction from fingerprints using the frequency spectrum of greylevel images. The Fourier transform spectrum is analysed with respect to both radial and angular frequencies. The profiles of integrated radial and angular spectrum are used for extracting directional and coarseness measures of the spatial features distribution. The proposed technique does not need pre-processing as in classical fingerprints analysis methods. Furthermore, it does not require tuning of any parameter as in the others techniques. To illustrate the performance of the method, some synthetic and actual fingerprint images are used.

1

INTRODUCTION

For a long time it has been suggested that fingerprint identification/authentication could be automatically achieved on the basis of some known and established biological principles [1]. With the acceptance of fingerprints as robust personal identification characteristics, many efforts have been devoted to the development of automatic fingerprint identification systems [2]–[6]. This field of research rapidly grew and some sophisticated systems have been proposed recently [7]-[9]. However, all of the existing systems suffer from some major drawbacks. For example, in the technique proposed by Jain et al.[7], many pre treatments are involved, and one has to tune many parameters. The pre-treated images are hence parameter-dependent, moreover, there is no indication on how to adjust automatically these parameters. As a consequence, the identification is very sensitive to the choice of these parameters. Another important point is the effect of acquisition conditions [10]-[11]. In Jain’s method, the shape of the features to be extracted, called minutiae, are very sensitive to the acquisition system and to the pre-treatment such as filtering, thresholding, etc... These drawbacks prompted us to develop a completely different approach where the features extraction process is less sensitive to the image quality and where there is no need for parameter tuning. Furthermore, the proposed method is faster and gives accurate feature localisation. Its efficiency and robustness is demonstrated through applications on synthetic and actual images. To prove the efficiency of our technique, we use raw data without any pretreatment as in previous methods.

2

THE PROPOSED METHOD

Before discussing the proposed method, we will start with some fundamentals notions on Fourier analysis.

We then introduce the basic concept behind the new method for image features extraction. 2.1 Basic notions Let f(x,y) be the grey-level at the pixel location (x,y) and F(u,v) the corresponding discrete Fourier Transfrom. Note that since f(.,.) is a real non-negative signal, it is more convenient to centre the discrete Fourier transform so as to exploit its symmetry properties. The centred discrete Fourier transform of f(.,.) is: é 1 X−1Y −1 æ ux vyöù F( u,v ) = f ( x, y )(−1)x+ y expê− j2π ç + ÷ú (1) å å XY x=0 y=0 è X Y øû ë Where XxY is the image size and u = 0 ,1 ,L , X − 1 ; v = 0 ,1 ,L ,Y − 1 are the spatial frequency indices. Note that the actual spatial frequencies are

wx =

u v , w y = . This transform, X Y

F ( w x , w y ) , can be expressed as: F ( w x , w y ) = ℜ( w x , w y ) + jℑ( w x , w y ) (2) The corresponding frequency magnitude and phase spectrum are given by :

F( wx , w y ) = ℜ2 ( w x , w y ) + ℑ2 ( w x , w y ) (3) and

æ ℑ( w x , w y ) ö ÷ φ ( w x , w y ) = tan −1 çç ÷ ( w , w ) ℜ x y ø è

(4)

and the power spectrum is given by :

P ( w x , w y ) = ℜ 2 ( w x , w y ) + ℑ 2 ( w x , w y ) (5) Given the symmetry properties of the Fourier spectrum, the analysis could be performed on only a half-plane of the spatial frequency domain. Thus, it is convenient to use polar coordinates to analyse the energy distribution in the w x − w y plane. Let θ , r be the polar

(

)

coordinates defined in the frequency plane and taking their values in 0 − π and 0 − R respectively,

[

where

]

[

]

R is the maximum value attained by the radial

frequency index defined by r = u + v . Notice that R corresponds to the maximum radial frequency 2

W = W x2 + W y2

where

2

W x , W y are

the

maximum spatial frequencies. Let us define the frequency spectrum in polar coordinates S ( r ,θ ) and similarly the phase spectrum as ψ ( r ,θ ) . In the following, we will only focus on the frequency spectrum. Let us fix the analysis direction ( θ fixed) and compute the average energy along it.

This quantity is nothing but the angular frequency spectrum given by :

1 R S r ( θ ) = ò S ( r ,θ )dr (6) R 0 Now let us fix r and compute the average energy of components at a distance r from the centre. This yields to the radial frequency spectrum defined by: :

1 πr

π

ò

0

θ = 24 0 ).

π spatial features in the direction θ + . For example, a 2

radial spectrum without peak reveals circularly symmetric energy distribution and thus reflects isotropic texture. Similarly the peaks in Sθ ( r ) reflect coarseness or fine structures. Indeed, peak near the centre reveals coarse structures and a peak far from the centre corresponds to high frequencies structures (fine details). Similar approaches, where specific wedge slices and rings are used, have been formulated for texture analysis [12]. However, the analysis depends on the size of the rings and wedge slices. It is worth noting that the use of wedge slices and rings guarantees immunity to noise. Here, there is no parameter to tune for the analysis and the immunity to noise is hence guaranteed. 2.2 Robustness and accuracy assessment To demonstrate the robustness and accuracy of the proposed angular analysis, we generated an image containing two lines of very close directions (22 and 24 degrees) in a highly noisy background (see fig.1).

= 22 0 and

1.2

S ( r ,θ )dθ (7)

These two signals are very useful for features extraction. The peaks in S r ( θ ) reveal directional

Fig. 1a.Test image

clearly correspond to the two directions ( θ

1

0.8 Average grey-level

Sθ ( r ) =

Figure 1b displays the variations of the mean grey-level along each direction given by the angle θ . It is clearly shown that the technique is very robust and accurate in detecting the directional features. Indeed the two peaks

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Firg. 1b. Angular energy analysis Now, we evaluate experimentally the robustness and accuracy of our method in the frequency domain. An image containing a grid at direction 22.5 deg. superposed on a highly noisy background, is generated. The frequency spectrum is shown on fig. 2.b. The positions of the peaks revealed in fig.2.c clearly correspond to the locations of bright patterns distributed along the expected direction (22.5+90 =112.5 degrees). Their spatial positions are 1/a, 2/a, 3,a…. ,where a is the thickness of the white-black bands, and their energy decreases gradually, as expected for such known patterns, as shown in fig. 2.d.

Fig. 2.a. Noisy image Grid lines at 22.5 deg.

profiles at different scales, one can extract some features which could be used in the computation of a unique description or signature for each fingerprint image.

Fig. 2.b. Frequency spectrum 2. 2

x 10

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Fig. 3.a. Original image

1. 6

r

S (θ)

1. 4 1. 2 1 0. 8 0. 6 0. 4 0. 2

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Fig. 2c. Angular spectrum analysis 12 11 10

Fig. 3.b. Frequency spectrum

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Fig. 2.d. Radial frequency spectrum

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3

RESULTS ON FINGERPRINTS

In what follows, a fingerprint image is considered. The original image and the corresponding frequency spectrum are shown on fig.3.a and 3.b respectively. A visual analysis clearly reveals some the specific spatial characteristics. The angular and radial spectrum analysis, shown in fig.3.c and 3.d respectively, confirm this observation. Indeed, there are three directions and one spatial position corresponding to components of high energy. By analysing the irregularity of these

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θ in degrees

Fig. 3c. Angular frequency spectrum In the following, we will show the discrimination ability of the proposed analysis on a set of randomly chosen fingerprints. For this set of fingerprints, the frequency spectrum analysis reveals three different profiles. Notice that, at the horizontal and vertical directions, all angular frequency spectrum exhibit the same sharp

transition. This is proper to 2D-Fourrier spectrum of any digital image and is due to its finite support. From the irregularity of these profiles, one can capture a unique signature corresponding to the spatial organisation of the given fingerprint structure. This is being currently investigated. 20

θ

S (r)

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5 REFERENCES [1] M. Trauring , “Automatic comparison of fingerridge patterns”, Nature, vol.197, Mar. 1963, pp.938-940. [2] E. Kaymaz, S. Mitra , “Analysis and matching of degraded and noisy fingerprints”, Proceedings-ofthe-SPIE --The-International-Society-for-OpticalEngineering. vol.1771; 1993; p.498-509 [3] A-K. Jain, L. Hong; S. Pankanti, R. Bolle, “ An identity-authentication system using fingerprints” Proceedings-of-the-IEEE. vol.85, no.9; Sept. 1997; p.1365-88.

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Fig. 3.d. Radial frequency spectrum 2.5 2 1.5

Sr (θ)

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Fig. 4. Angular frequency spectrum of 3 fingerprints

4 CONCLUSION AND PERSPECTIVES These preliminary results show the robustness and accuracy of the proposed method in extracting directional features from textures images and especially fingerprints. This method doesn’t require any preprocessing nor parameter tuning. The next step is to extract from each profile a unique signature. This initial analysis showed that this goal could be achieved with the obtained signatures.

[4] A. R. Roddy and J. D. Stosz, “Finger featuresStatistical analysis and system performance estimates”, Proceedings of IEEE, Vol.85, No.9, Sept.1997, pp.1390-1421. [5] K. Karu and A-K. Jain, “ Fingerprint classification “, Pattern-Recognition. vol.29, no.3; March 1996; p.389-404 [6] S. Kasaei, M. Deriche and B. Boashash, “Fingerprint feature extraction using blockdirection on reconstructed images “,, TENCON '97 Brisbane - Australia. Proceedings of IEEE TENCON '97. [7] A. Jain, L. Hong, R. Bolle, “On-line fingerprint verification”, IEEE-Trans. Pattern-Anal. Machine Intell. Vol.19, no.4; April 1997, p.302-14. [8] A.K. Jain, S. Prabhakar S. Chen, “ Combining multiple matchers for a high security fingerprint verification system “, Pattern-Recognition-Letters. vol.20, no.11-13; Nov. 1999; p.1371-9. [9] A.K. Jain, S. Prabhakar L. Hong, S. Pankanti, “ Filterbank-based fingerprint matching “, IEEE Trans. Image Processing. vol.9, no.5; May 2000; p.846-59. [10] Q. Xiao, H. Raafat, “ Fingerprint image postprocessing: a combined statistical and structural approach “, Pattern-Recognition. vol.24, no.10; 1991; p.985-92. [11] B-G. Sherlock, D.M. Monro , K. Millard, “ Algorithm for enhancing fingerprint images “, Electronics-Letters. vol.28, no.18; 27 Aug. 1992; p.1720-1 [12] F. Tomita and S. Tsuji, “Computer analysis of visual textures “, Kluwer, Norwell, MA, 1990.