Fingerprint Orientation Image Estimation in the Frequency Domain

1

Fingerprint Orientation Image Estimation in the Frequency Domain Victor-Valeriu PATRICIU, Stelian SPÎNU, and Cezar PLEŞCA

Abstract—The orientation image estimation is a critical step in fingerprint image processing and feature extraction. The computation of local ridge orientation in low quality fingerprints is still a difficult task. A simple and reliable method for estimating the fingerprint orientation image in the frequency domain is proposed. The results of the experiments conducted on a collection of fingerprints, in order to evaluate the performance of the proposed method, are also presented. Index Terms—biometrics, feature extraction, fingerprint recognition, spectral analysis.

I. INTRODUCTION

T

HE need for reliable person identification is ever growing in today’s globally interconnected information society [1]. The use of fingerprints as a biometric identifier is both the oldest mode of automated person identification and the most widely used today [2]. The deployment of fingerprint recognition technology in a wide range of government and commercial applications has been favored by a series of factors. These factors include: the well-known individuality and permanence properties of fingerprints, the enormous success of fingerprint identification in law enforcement applications, the existence of a large market of small and inexpensive fingerprint sensing devices, and the increasing availability of affordable computing power [3]. A fingerprint consists of a pattern of interleaved ridges and valleys. The local ridge orientation at pixel ( i, j ) in a

fingerprint image is the angle θ ij ∈ [ 0, 180° )

that the

fingerprint ridges, crossing through an arbitrary small neighborhood centered at ( i, j ) , form with the horizontal axis [3]. By estimating the local ridge orientation at discrete positions, a fingerprint orientation image is obtained. Manuscript received November 11, 2013. V.-V. Patriciu is with the Faculty of Military Electronic and Information Systems, Military Technical Academy, 39-49 George Cosbuc Ave., Sector 5, 050141, Bucharest, Romania (e-mail: [email protected]). S. Spînu is with the Faculty of Military Electronic and Information Systems, Military Technical Academy, 39-49 George Cosbuc Ave., Sector 5, 050141, Bucharest, Romania (corresponding author to provide phone: +40740970758; e-mail: [email protected]). C. Pleşca is with the Faculty of Military Electronic and Information Systems, Military Technical Academy, 39-49 George Cosbuc Ave., Sector 5, 050141, Bucharest, Romania (e-mail: [email protected]).

The ridge orientation estimation in fingerprint image processing represents a very important step. The computation of local ridge orientation is required in: fingerprint image enhancement [4]–[9], fingerprint classification [10], [11], feature extraction from a dermatoglyphic point of view [12], and fingerprint image segmentation [13]–[15]. The rest of the paper is organized as follows. In section 2, a review of previous approaches for estimating the fingerprint orientation image is presented. Section 3 describes the method proposed for extracting the local ridge orientation in fingerprint images in the frequency domain. The results of the experiments conducted on a set of fingerprints, in order to evaluate the proposed method, are presented in section 4. Section 5 concludes the paper. II. PREVIOUS WORK The approaches proposed in the literature for the computation of fingerprint orientation use image processing in both the spatial and frequency domains. A. Ridge Orientation Estimation in the Spatial Domain Sherlock et al. [4] determine local ridge orientation at a square grid spaced 16 pixels apart. A window of size 32×32 pixels is centered at the pixel of interest and rotated to 16 different orientations. At each orientation, a projection along the y-axis of the window is formed and the noise from the projections is removed with a second-order Butterworth band-pass filter. When the window is aligned with its x-axis orthogonal to the ridges, we expect maximum variation of the projection. Conversely, alignment of the x-axis along the ridges should give minimum variation. The computation of gradients in the fingerprint image is the most widely used approach for extracting local ridge orientation. Ratha et al. [13] divide the input fingerprint image into blocks of size 17×17 pixels and compute the gradients at each pixel in the block. Let Gx ( i , j ) and G y ( i, j ) be the gradient magnitudes in the x and y directions, respectively, at pixel ( i, j ) , obtained using the classical Sobel masks. The dominant ridge orientation in a block, centered at pixel ( i, j ) , can be computed using the following equation:

2

θ ij =

π 2

2p 2p

f (θ ) = ∑∑ Dθ ( i, j ) × F ( i, j ) , θ max = arg maxθ f (θ ) . (3)

+

i =0 j =0

8

1 tan −1 2

8

∑ ∑ 2G ( i + h, j + k ) G ( i + h, j + k ) x

(1)

y

h =−8 k =−8 8 8

2 2 ∑ ∑ Gx ( i + h, j + k ) − Gy ( i + h, j + k )  h =−8 k =−8

.

Bazen and Gerez [16] demonstrate that the gradient-based method is mathematically equivalent to the principal component analysis of the autocovariance matrix of the gradient vectors. The orientation image of a good quality fingerprint image can be reasonably obtained with the gradient-based method. Nevertheless, the presence of high-curvature ridges and noise leads to a poor estimate of the local ridge orientation. To overcome this limitation, Jain et al. [17] employ a multiresolution approach resulting in a fairly smooth orientation image. Karu and Jain [10] compute the gray-value sum of pixels along a number of eight reference orientations. The local ridge orientation corresponds to the minimum-sum slit for pixels lying on ridges and to the maximum-sum slit for pixels lying on valleys. Based on the observation that the total variation of the gray levels is minimum along the ridge orientation and maximum in the orthogonal direction, analogous approaches are proposed by He et al. [18] and Oliveira and Leite [19]. B. Ridge Orientation Estimation in the Frequency Domain Based on the intrinsic characteristics of the ridge pattern in fingerprint images, Kamei [5], [8] proposes a filter designed in the Fourier domain, having two distinct components, a frequency filter corresponding to ridge frequency and a directional filter corresponding to ridge orientation. The local ridge orientation is selected not only according to the maximum filter response, but also taking local smoothness in the fingerprint into consideration. Park and Park [11] compute the fingerprint orientation image at a square grid spaced 16 pixels apart. The Fast Fourier Transform (FFT) is applied on the blocks of size 32×32 pixels centered at each inner grid point. In order to detect the dominant ridge orientation in each block, a directional filter Dθ is used in the FFT image:

  u 2 v2  u 2 v2 exp  − 2 − 2  , if 2 + 2 ≤ 1, Dθ ( i + p, j + p ) =  (2) a b  a b   0, otherwise,  − p ≤ i, j ≤ p ,

for

where

v = i cos θ + j sin θ ,

a = 1.5 , b = 32 3 , and u = i + j −v , p = 16 , θ = 0, 10, … , 170° . The local ridge orientation in each block is perpendicular to orientation θ that maximizes the sum of FFT coefficients weighted by directional filter Dθ : 2

2

2

The algorithm proposed by Chikkerur et al. [9] is based on short time Fourier transform analysis. The fingerprint image is divided into partially overlapping, raised cosine windows. The Fourier spectrum of each window is analyzed and a probabilistic estimate of the local ridge orientation is obtained. III. PROPOSED APPROACH The pattern of the ridge-valley structure in fingerprint images can be locally modeled as a sinusoidal-shaped surface. The Fourier spectrum of this surface consists of two peaks, symmetrical about the origin. The direction perpendicular to the line connecting these peaks indicates the local ridge orientation [8]. In our approach, fingerprint orientation image is estimated at a square grid spaced 16 pixels apart. For each window of size 32×32 pixels, centered at each grid point, the largest spectral component in the range of valid ridge frequencies is determined. The location of this maximum frequency component is used to estimate local ridge orientation and its magnitude to segment the fingerprint area from the image background. The fast Fourier transform is applied on each block of size 32×32 pixels centered at each grid point. The maximum value of the centered Fourier spectrum is searched in the upper half of the frequency rectangle, in the region of valid ridge frequencies, i.e., the points (u, v) satisfying the double

f min ≤

(u − N 2 )

2

+ (v − N 2)

2

for ≤ f max , N 0 ≤ u ≤ N 2 and 0 ≤ v ≤ N − 1 , where N = 32 , f min = 1 15 ,

inequality:

and f max = 1 5 , for 500 dpi images. Let um and vm be the coordinates of the maximum value of the Fourier spectrum,

F ( um , vm ) . These are separately

adjusted for each coordinate axis by taking into account the neighbor in the Fourier spectrum with the largest value. Therefore: um′ =  F ( um , vm − 1) , if F ( um , vm − 1) > F ( um , vm + 1) , um − F u , v (  m m − 1) + F ( u m , vm ) (4)  F ( um , vm + 1)  um + F u , v + 1 + F u , v , otherwise, ( m m ) ( m m) 

and vm′ =  F ( um − 1, vm ) , if F ( um − 1, vm ) > F ( um + 1, vm ) , vm − F u − ( m 1, vm ) + F ( um , vm )  (5)  F u + 1, v ( )  m m vm + F u + 1, v + F u , v , otherwise. ( m ( m m) m) 

3 The local ridge orientation at point ( i, j ) is computed as:

um′ − N 2 . (6) 2 vm′ − N 2 The values of the local ridge orientation obtained with (6) are considered only for the fingerprint ridge area. In order to segment the fingerprint area from the image background, we applied the Otsu’s method [20] to threshold the magnitudes of the previously determined spectral components. Morphological closing and opening are further performed on the resulted binary image, in order to eliminate holes and smooth the region of interest for the local ridge orientation estimation.

θ ij =

π

+ tan −1

IV. EXPERIMENTAL RESULTS Two previous approaches for estimating local ridge orientation (the ones presented in [13] and [11]) and the proposed method were implemented in MATLAB®. Experiments were conducted on set B of FVC2004 databases [21] (a total of 320 fingerprint images) in order to compare the three methods. The set of fingerprints includes four different databases (DB1, DB2, DB3, and DB4), collected by using different sensors/technologies (see Table I).

DB1

DB2

DB3

DB4

TABLE I FVC2004 DATABASES [21] Sensor type Image size 640×480 optical sensor “V300” (307 by CrossMatch Kpixels) optical sensor “U.are.U 328×364 4000” (119 by Digital Persona Kpixels) thermal sweeping 300×480 sensor “FingerChip (144 FCD4B14CB” by Kpixels) Atmel synthetic fingerprint 288×384 generation (108 SFinGe v3.0 Kpixels)

Resolution 500 dpi

500 dpi

512 dpi

about 500 dpi

Fig. 1 shows sample images from each of the four databases DB1, DB2, DB3, and DB4.

Fig. 1. Sample images from each of the four databases DB1, DB2, DB3, and DB4 [21].

As indicated in [16], there exists no ground truth for the orientation image of fingerprints. Consequently, it is difficult to quantitatively evaluate the quality of an orientation image estimate. We solved this problem using the same approach as described in [22]. A reliable orientation image can be computed for each fingerprint by using a Gabor filter-bank [23], providing that the number of filters is large enough. We employed a bank of 100 Gabor filters (25 discrete orientations and 4 discrete frequencies). The orientation images obtained by each of the three methods, the previous approaches presented in [13] and [11] and the proposed method, were compared with the orientation image extracted by using the Gabor filter-bank. Nevertheless, there should be noted that the computation of fingerprint orientation image by using a Gabor filter-bank is too computationally expensive and, therefore, not suitable for realtime applications [22]. For each fingerprint, the mean absolute error between the orientation estimate of each of the three approaches and the orientation estimate obtained by using the Gabor filter-bank was computed. The averages of the mean absolute errors of the orientation estimates obtained by using the three methods, for each of the four databases, are presented in Table II. The results show a decrease of the average error of the fingerprint orientation estimates obtained by using the proposed approach, for all of the four databases. TABLE II THE AVERAGE ORIENTATION ESTIMATION ERRORS DB1 DB2 DB3 Method 5.24 5.85 5.59 in [13] Method 5.27 6.41 5.12 in [11] Proposed 4.91 5.54 4.90 method

DB4 4.78 4.98 4.34

Fig. 2 shows samples of orientation images obtained with the proposed method for each of the four fingerprint databases DB1, DB2, DB3, and DB4. The region of interest is also displayed. The average processing times for estimating the local ridge orientation are presented in Table III. These values were obtained using an Intel® Core™2 Quad Processor at 2.4 GHz.

4

TABLE III THE AVERAGE PROCESSING TIMES Method Method Proposed in [13] in [11] method 54 ms 330 ms 162 ms

Fig. 2. Samples of orientation images obtained with the proposed method for each of the four fingerprint databases DB1, DB2, DB3, and DB4. The region of interest is also displayed.

5 V. CONCLUSION The computation of local ridge orientation is an important step in fingerprint image processing and feature extraction. A reliable orientation estimate is required in fingerprint enhancement, feature extraction, classification, and segmentation. The orientation image extraction in fingerprint areas of low quality is still a difficult task and most approaches to the computation of local ridge orientation result in poor estimates. A simple and accurate method for fingerprint orientation image estimation in the frequency domain was proposed. The results of the experiments conducted on a collection of fingerprints show a better performance of the proposed method compared to previous approaches. The proposed method is robust with respect to the noise specific to low quality images and reliable fingerprint orientation images are obtained. Our future work will apply the proposed method for fingerprint image enhancement. REFERENCES [1]

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