An Efficient Algorithm for Fingerprint Reference-Point Detection

Thien Hoang Van Department of Computer Sciencies

Ho Chi Minh City University of Technology Ho Chi Minh City, Viet Nam vthoang@hcmhutech.edu.vn

Hoang Thai Le Department of Computer Sciencies

Ho Chi Minh City University of Natural Science Ho Chi Minh City, Viet Nam

lhthai@fit.hcmuns.edu.vn

Abstract — The reference-point played important roles in most algorithms of fingerprint recognition. It is widely used in fingerprint classification, and fingerprint matching. There are many methods proposed for reference point detection as Poincare index technique, Geometry of region technique, Direction curvature technique and Orientation-consistency-based technique. However, the experimental results show that the present methods are less accurate on the fingerprint database which contains many poor-quality fingerprint images (the most accuracy of the present methods is 93% on the fingerprint database FVC2004, DB2, set A). This paper proposes a novel algorithm to locate fingerprint reference-point consistently and accurately for all types of fingerprints. The method computes the convex orientation consistency which describes both direction of curvature and how well the orientations over a neighborhood are consistent with the dominant orientation. Experimental results show the effectiveness and superiority of our proposed method (96.9 % on the FVC2004, DB2 set A).

Keywords-fingerprint recognition, reference point, orientation consitency, orientation field, convex orientation consistency.

I. INTRODUCTION Fingerprint is widely used for personal recognition in the

commercial and forensic areas because of its uniqueness, immutability and low cost. Generally, there are two kinds of features for fingerprint recognition: global features like the special ridge flow pattern and local features like minutiae. At global level, there are unique landmarks of fingerprint, where the ridge curvature is higher than other areas and the orientation changes rapidly. They are commonly known as singular points (core and delta points, see Figure 1a). They have played important roles in most fingerprint recognition systems such as fingerprint classification [1], [2], [3], [4], [5], [6], fingerprint matching [7], [8], [9]. However, some fingerprints, especially the fingerprints captured with solid state sensor, contain only partial images with a part of singular points (usually the delta points) left outside the print. In addition, the number of core and delta points differs in different types of fingerprints. For example, the plain arch fingerprint has no singular points while the whorl fingerprint has two core points. To locate a unique reference point consistently for all types of fingerprints and partial fingerprints, the reference point is defined as the point with maximum curvature on the convex ridge, which is usually located in the central area of fingerprint

(see Figure 1b). Therefore, if there are core points existing in a fingerprint, the core point on the convex ridge is the reference point [10].

Figure 1. (a) Core point and Delta point. (b) Reference point with maximum curvature on the convex ridge

There are many approaches proposed for singular point detection in the literatures and most of them operate on the fingerprint orientation field. Liu et al. pointed out advantages and disadvantages of these methods in [10]. The Poincare index (PI) method [11], [12] is one of the commonly used methods. In this method, the PI of each block is computed by summing up the direction changes around a closed digital curve of the block. This method is efficient, but it is sensitive to noise as the orientation deviation caused by noise will affect the computation of PI, especially when the direction change is near π/2 or −π/2. In addition, this method cannot locate the corresponding reference point in plain arch fingerprint because the point with maximum curvature is not a core point in a strict sense. Koo and Kot [13] proposed a method of singular point detection based on searching the point with maximum curvature. This method does not work well in poor-quality fingerprint because the computed curvature is sensitive to noise. Jain et al. [7] proposed a sine-map-based method which is to locate a reference point based on multi-resolution analysis of the differences of sine component integration between two defined regions of the orientation field. This method is robust to noise, but the two defined regions are sensitive to the fingerprint rotation. In addition, this method is not effective for

(a) ( b )

Core point

Delta point

Reference point

978-1-4244-4568-4/09/$25.00 ©2009 IEEE1

reference-point localization in plain arch fingerprint. Park et al. [14] proposed an efficient algorithm for reference point detection based on orientation pattern labeling. This method is also not consistent to fingerprint rotation and its performance for plain arch fingerprint is inferior to that of the method proposed by Jain et al. [7]. Then, Liu et al. [10] proposed an orientation consistency-based method, in which the reference point localization is based on multiscale analysis of the orientation consistency to search the local minimum. This method is very efficient for delta point and core point detection by applying orientation consistency analysis. However, its limitation is the way to filter delta point based on incomplete analysis of curvature direction. Julasayvake et al. [15] proposed an optimal core point technique. This method based on the refinement of two existing techniques. Direction of curvature technique (DC) has been used in coarse core point detection whilst geometry of region (GR) technique is used in the fine finding of the core point. This technique can still not overcome the limitation of the sine-map-based method.

This paper proposes an effective approach to locate a unique reference point consistently and accurately for all types of fingerprints. This method improves the technique of Liu et al. in filtering the delta points by proposing a new formula which computes the convex orientation consistency of reference point candidates. The convex orientation consistency indicates both curvature direction and how well the orientations in a neighborhood are consistent with the computed dominant direction.

In the following sections, we present in detail our proposed algorithm of reference orientation computation. In section 2, fingerprint pre-processing steps are elaborated. Section 3 presents our proposed approach of reference point detection. The experimental results on the FVC2004 DB2, set A are presented in section 4. Finally, the paper conclusions are drawn in Section 5.

II. PRE-PROCESSING

A. Normalization Let ( , )I i j denotes the gray-level value at pixel ( , )i j , M

and V denote the estimated mean and variant of image I , respectively, and ( , )N i j denotes the normalized grey-level value at pixel ( , )i j . The normalized image is defined as follows:

2( ( , ) )0 ( , )0( , )

2( ( , ) )0 ,0

V I i j MM if I i j M

VN i jV I i j M

M otherwiseV

−+ >

=−

−

⎧⎪⎪⎨⎪⎪⎩

(1)

where 0M and 0V are the desized mean and variant values respectively. The mean and variant of a gray-level fingerprint images with dimension of M N× pixels, which are defined respectively as

1 11

( ) ( , ),0 0

M NM I I i j

MN i j

− −∑ ∑== =

(2)

and

1 11

( ) ( ( , ) ( ))0 0

M NV I I i j M I

MN i j

− −∑ ∑= −= =

(3)

The objective of this stage is to decrease the dynamic range of the gray scale between ridges and valleys of the fingerprint image in order to facilitate the process of the following stages. It does not change the clarity of the ridges and valleys.

The sub-block of the size k k× may be (linear consecutively) defined. Mean of the sub-block is compared to the mean of the whole image. The cropped area (interested region) is then defined.

B. Orientation field computation Since the reliable orientation field plays a very important

role in reference point detection, it is necessary to address the problem of noise attenuation in the fingerprint orientation estimation. Many methods are proposed for fingerprint orientation estimation in the literatures. The least mean square method of orientation estimation based on the gradients is most widely used to compute the dominant orientation of an image block because of its high efficiency and resolution [16]. Therefore, the least mean square method [16] is used to estimate the orientation of each block. Let θ be defined as the orientation field of a fingerprint image. ( , )i jθ is the least square estimate of the local ridge orientation at the block centered at pixel ( , )i j . The processing steps are summarized as follows.

1) Divide the fingerprint image into nonoverlapping blocks of size w w× pixels ( 8w = in our experiment).

2) Compute the gradients ( , )i jx∂ and ( , )y i j∂ of each pixel ( , )i j corresponding to the horizontal and vertical directions. The gradient operator varies from the simple Sobel operator to the complex Marr-Hildreth operator. The Sobel operator is employed in this work for simplicity.

3) Estimate the orientation of each block ( , )i j by averaging the squared gradients as follows:

/ 2 / 2

( , ) 2 ( , ) ( , ),/ 2 / 2

i w j wV i j u v u vx yy u i w v j w

+ +∑= ∂ ∂∑

= − = − (4)

/ 2 / 2 2 2( , ) ( ( , ) ( , ) ),

/ 2 / 2

i w j wV i j u v u vx yx u i w v j w

+ +∑= ∂ −∂∑

= − = − (5)

2

subsequently,

( , )1

( , ) arctan2 ( , )

V i jyi jV i jx

θ⎛ ⎞

= ⎜ ⎟⎜ ⎟⎝ ⎠

(6)

C. Orientation smoothing After orientation estimation, the orientation field may still contain some unreliable elements resulting from heavy noise such as scars, ridge breaks, and low gray value contrast. Orientation smooth is expected to further attenuate noise of the orientation field and to compute a reliable orientation field. The orientation smoothing method based on averaging the unit vectors of doubled orientation over a neighborhood is widely used in orientation smoothing because of its high efficiency and resolution [16]. The adaptive neighborhood method of fingerprint orientation smoothing is used in this work, because it not only maintains the orientation localization of high-curvature area but also has a good performance on attenuating noise [10]. In this method, orientation consistency that describes how well the orientations over a neighborhood are consistent with the dominant orientation is introduced. In a smoothing neighborhood ( )sΩ of each block, consistency is defined as

( ) ( )2 2( , ) ( ) ( , ) ( )cos(2 ( , )) sin(2 ( , ))

( )i j s i j si j i j

Cons sM

θ θ∈Ω ∈Ω+∑ ∑=

(7)

where M is the number of orientations ( , )i jθ in ( )sΩ .

The processing steps of the orientation smoothing method for each block ( , )i j are described as follows.

1) Convert the doubled orientation of each block to a unit vector [ ]cos(2 ( , )), sin(2 ( , ))i j i jθ θ and compute

(1)Cons ( 1s = ) in (7) with (1)Ω being the outside 8 blocks of its 3 × 3 neighborhood.

2) 1s s= + . Compute ( )Cons s with ( )sΩ being the outside 8s surrounding blocks of its (2 1) (2 1)s s+ × + neighborhood.

3) If ( )Cons s is smaller than a threshold (0.5 in our experiment) or smaller than ( 1)Cons s − , go to step (2) until s reaches its maximum (4 in our experiment).

4) If s equals its maximum, Ω(s) is reset to the neighborhood of size 3 × 3 blocks.

5) Compute the smoothed orientation by

sin(2 ( , ))1 ( , ) ( )( , ) arctan

2 cos(2 ( , ))( , ) ( )

u vu v si ju vu v s

θθ

θ

⎛ ⎞∑ ∈Ω⎜ ⎟=⎜ ⎟∑ ∈Ω⎝ ⎠

(8)

III. REFERENCE-POINT DETECTION As mention in section 1, the reference point is defined as

the point with maximum curvature on the convex ridge, which is usually located in the central area of the fingerprint. If core points exist in the fingerprint, the core point on the convex ridge is the reference point. Although there are no core points in a strict sense in plain arch fingerprint, the point with maximum curvature is always unique and on the convex ridge. We propose a novel algorithm which improves Liu's Method [10] in order to locate reference point more efficiently. These sections details two techniques: the orientation consistency-based method (Liu's method) and the convex orientation consistency-based method (our method).

A. Orientation Consistency-based Technique [10] A multiscale analysis (see Figure 2) of orientation

consistency is used to search the local minimum orientation consistency from large scale to fine scale. The orientation consistency-based technique can be summarized as follows.

1) Compute the orientation consistency ( )Cons s of each block based on the outside 8s surrounding blocks of its (2 1) (2 1)s s+ × + neighborhood.

2) Find the minimum orientation consistency denoted as ( )minCons s . Compute candidate threshold as,

( ) 0.15 ( ) 0.5min min( ) 0.05 ,min

Cons s if Cons sT

Cons s Otherwise⎧ + >⎪

= ⎨+⎪⎩

(9)

3) Select the blocks if their ( )Cons s T< .

4) Compute ( )dx s and ( )dy s , and select the blocks with both ( )dx s and ( )dy s larger than 0 as the candidate blocks in the next finer scale.

( ) cos(2 ( , )) cos(2 ( , )),s s

dx s i s j k i s j kk s k s

θ θ∑ ∑= − + − + +=− =−

(10)

( ) sin(2 ( , )) sin(2 ( , )).s s

dy s i k j s i k j sk s k s

θ θ∑ ∑= + − − + +=− =−

(11)

5) If no candidate blocks for the reference point are located, let 0.01T T= + , go to step (3).

6) Repeat steps (1), (2), (3), (4), and (5) in the selected candidate blocks with 1s s= − until 1s = .

7) Locate the block with minimum orientation consistency (1)Cons from the selected finest scale blocks as the unique reference point.

3

Figure 2. The mutiscale analysis of orientation consistency

Liu's formula for orientation consistency computation is very efficient. We could detect core points, delta points and eliminate noise by mutiscale analysis of the orientation consistency value which is computed by the equation 7. Specifically, the orientation consistency values of high-curvature area on varying neighborhood sizes are always small while the orientation consistency of noisy area on the large neighborhood gets larger than that on the small neighborhood.

So, there are more than one core point and delta point in the fingerprint by Liu's formula. The next step to determine the unique core point (reference point), a method of the representative core point selection, is essential. Liu's method determines the unique reference point according to the direction of curvature. The reference point have to be satisfied the condition which ( )dx s and ( )dy s are larger than 0 (red block in Figure 3b, ( )dx s and ( )dy s are computed by equation 10, 11). According to the method, the core points with minimum orientation consistency could be eliminated wrongly (Figure 3a, 3b) because of the same characteristics of these points with delta points. Therefore, search in the remaining blocks fall into local minimum problem.

To overcome the limitation, we propose a formula which determines convex curvature of each block in whole image to eliminate the core point on the concave ridge and the delta point. Then, we combine orientation consistency value (Liu proposed in [10]) with our convex curvature value in order to have a value of general evaluation (namely, the value of convex orientation consistency, see Figure 6c) on the whole fingerprint image. Then, the unique reference point is determined (the reference point locate center of the block with global minimum).

The next section details the technique.

Figure 3. (a) The orientation consistency field. (b) The threshold field dx and dy . (c) The wrong core point detection using Liu's algorithm.

B. Convex Orientation Consistency-based Technique The convex curvature of each block ( , )i j is defined as

( , ) ( , )( , )

12DX i j DY i j

CCEnergy i j+

= (12)

where, ( , )DX i j and ( , )DY i j are computed in the 3 3× neighborhood of block ( , )i j as follows:

1 1

( , ) cos(2 ( 1, )) cos(2 ( 1, )),1 1

DX i j i j s i j ss s

θ θ∑ ∑= − + − + +=− =−

(13)

1 1

( , ) sin(2 ( , 1)) sin(2 ( , 1)).1 1

DY i j i s j i s js s

θ θ∑ ∑= + − − + +=− =−

(14)

(Figure 6b illustrates the convex curvature energy CCEnergy )

The energy value expresses the convex curvature of each block. It plays a role as threshold value. The value combines with orientation consistency value in order to have the convex orientation consistency value of each block. Then, the unique reference point with global minimum is determined consistently and accurately. The formula of convex orientation consistency computation is defined as (see Figure 6)

( , ) ( , ) ( , )COCons i j ConsAV i j CCEnergy i j= − (15)

( ) ( )2 1 2 1s s− × −

3 3×

( ) ( )2 1 2 1s s+ × + The largest scale

The finest scale

(a) (b)

Core point

Wrong core point

(c)

4

1( , ) '( ),

1

SConsAV i j Cons s

S s∑==

(16)

where the scale S is initialized as 3 in our experiments. '( )Cons s is smoothed orientation consistency of block ( , )i j

with a neighborhood mask size s. The smoothed orientation consistency field (see Figure 4b) is computed by applying the two dimension low-pass filter G with unit integral. The specified size of the filter is w w×Φ Φ . Let '( , )Cons i j is the smoothed orientation consistency in the (2 1) (2 1)s s+ × + neighborhood of block ( , )i j . As a result,

/ 2 / 2

'( , ) ( , ). ( , )/ 2 / 2

w wCons i j G u v Cons i u j v

u w v w

Φ Φ∑= − −∑

=− =−Φ Φ,(17)

where the orientation consistency ( , )Cons i j in the (2 1) (2 1)s s+ × + neighborhood of each block ( , )i j is computed in (7).

Average smoothed orientation consistency ( , )ConsAV i j of block ( , )i j is the average value of the smoothed orientation consistency. The objective of computation '( )Cons s and

( , )ConsAV i j is to stand out the reference point and to eliminate noisy areas (see Figure 5).

Figure 4. (a) The orientation consistency field. (b) The smoothed orientation consistency field.

The processing steps of the proposed algorithm are summarized as follows:

1) Compute ( , )DX i j , ( , )DY i j of each block ( , )i j by applying equations (13), (14).

2) Compute the convex curvature energy ( , )CCEnergy i j of each block ( , )i j in (12).

3) Compute the convex orientation consistency ( , )COCons i j of each block ( , )i j by applying

equations (15), (16), (17), (7).

4) Locate the block ( , )ip jp with minimum convex orientation consistency ( , )COCons ip jp as the unique reference point.

Figure 5. The averaging smoothed orientation consistency is computed in (16). The orientation consistency field is computed with 3x3 neighborhood (a), 5x5 neighborhood (b), 7x7 neighborhood (c). (d) The averaging smoothed orientation consistency field.

.

Figure 6. The convex orientation consistency is computed in (15). (a) The averaging smoothed orientation consistency field. (b) The convex curvature field. (c) The convex orientation consistency field. (d) The correct detection of reference point.

(a) (b) (d)

- =

(c)

(a) (b)

Attenuate noise

+ ( +

(a) (b) (c)

) / 3=

(d)

5

IV. EXPERIMENTAL RESULTS The proposed algorithm has been tested on the FVC2004

DB2, set A, in which 800 fingerprint images from 100 fingerprint images (with 8 images from each finger) are captured (using a low-cost Capacitive Sensor). The image size is 328 × 256 pixels and the resolution is 500 dots per inch. This fingerprint database contains many poor-quality fingerprints such as the partial images with the reference point left outside and the images with heavy noise like scars, ridge breaks, too wet or dry fingerprints, and so forth.

Figure 7. The accepted cases: (a) very oily, (b) partial and oily, (c) dry and oily,(d) very dry.

Figure 8. The failed cases: (a) wrinkle, (b) very dry and wrinkle, (c) oily, (d) very oily.

The judgment of accepted location (Accepted Reference Point, ARP) and false location (False Reference Point - FRP) were eye-observed by fingerprint experts. Notice low-quality fingerprint images such as dry, wet or oily fingerprints, the proposed method still locate more accurately than others (see Figure 7 a, b, c, d).

The results are summarized in table 1 and table 2. The algorithm fails 25 images in locating the reference point. Major fails are very poor-quality of fingerprint images such as very oily, very dry and wrinkle fingerprints (see Figure 8 a, b, c, d).

TABLE I. EVALUATE OF PROPOSAL TECHNIQUE COMPARED TO OTHERS

FVC2004 (DB2_A) 800 images

Accepted RP False RP No. % No. %

Poin' care index 488 61 312 39 Geometry of Region 616 76.5 184 23.5 Direction of Curvature 704 88 176 22 Optimal Core Point 743 92.9 57 7.1 M. Liu et al. [10] 659 82.4 144 17.6 Our approach 775 96.9 25 3.1

TABLE II. FAILS CASES (OUR APPROACH)

Fails cases

Dry Very dry Oily Very Oily Wrinkle and Arch Arch

1 4 2 6 9 3

CONCLUSIONS In this paper, a novel algorithm is proposed to consistently

locate a unique reference point with high accuracy which is based on the convex orientation consistency to find global minimum. The convex orientation consistency describes both direction of curvature and how well the orientations over a neighborhood are consistent with the dominant orientation. To eliminate noise, two solutions are used: smoothed orientation consitency and averaging smoothed orientation consistency which are expected to further attenuate noise. Experimental results show that the proposed approach is better than other approaches in which it can achieve a good performance even when fingerprint images have poor quality.

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