Abstract—A SVM-based method is proposed in this paper, which is the first time that SVM is applied to the estimation of fingerprint and palmprint orientation, to the best of our knowledge. The orientation estimation problem can be regarded as a multi-classification problem by dividing the range [0 180] into 8 segments uniformly, which allows the introduction of classification methods and does not reduce the performance. In addition to the direct presentation of the estimated orientation, the rates of accuracy and recall of the minutiae are considered as statistical evaluation indexes of the performance to compare our method with the gradient-based method. Detailed analytical and experimental results are given to verify the feasibility and efficiency of our method.

I. INTRODUCTION

S two of the most important biometric technologies, fingerprint and palmprint recognition have received a substantial amount of attention during the last years. As

a result, fingerprint and palmprint have been widely used in authentication and identification for the uniqueness and convenience to extract. In general, there are 2 steps in a fingerprint/palmprint recognition process, one is feature extraction and the other is matching. In the former step, a fingerprint/palmprint image is processed by the following steps: orientation estimation, enhancement, thinning and minutiae extraction. Orientation plays an important role in the steps of enhancement and thinning. Good orientation guarantees good enhanced and thinned fingerprint/palmprint image, which is especially helpful for the recognition of poor quality images. Furthermore, orientation is also critical in fingerprint classification and fingerprint/palmprint matching. In short, the quality of orientation determines the accuracy of fingerprint/palmprint recognition system to some extent. Many methods have been proposed to solve the problem of orientation estimation, which can be roughly divided as the

Manuscript received January 27, 2013. This work was supported in part

by the National Natural Science Foundation of China under Grants 71271204, 11101420.

Yanping Wu is with the School of Computer and Control Engineering, University of Chinese Academy of Sciences, No.19A Yuquan Road, Beijing, China (e-mail: wuyanping0711@163.com).

Tong Zhao is with the School of Mathematical Sciences, University of Chinese Academy of Sciences, No.19A Yuquan Road, Beijing, China (phone: +86-136-4117-1653; e-mail: zhaotong@ucas.ac.cn).

Shuguang Wang is with Institute of Automation Chinese Academy of Sciences, 95 Zhongguancun East Road, Beijing, China (e-mail: lucas.wang.gm@gmail.com).

Yong A is with the School of Mathematical Sciences, University of Chinese Academy of Sciences, No.19A Yuquan Road, Beijing, China (e-mail: ayong08@mails.ucas.ac.cn).

Tiande Guo is with the School of Mathematical Sciences, University of Chinese Academy of Sciences, No.19A Yuquan Road, Beijing, China (e-mail: tdguo@gucas.ac.cn).

local orientation estimation methods and global model methods [1 2].

Local orientation estimation methods derive the orientation at a pixel by the neighboring pixels. The most popular local orientation estimation method is the gradient-based method [3-5], which calculates the gradient direction and the orientation is the perpendicular direction. The gradient-based method is based on the assumption that along the ridge orientation, the gray value varies the least, which results in noise sensitiveness, especially in the scars and creases regions where the assumption is not satisfied. Kalle Karu and Anil K. Jain proposed a slit method [6], in which 8 directional filters are utilized, and the strongest or the weakest response direction is chosen as the orientation depending on the pixel is in a valley or ridge. A similar method is proposed by Luping Ji and Zhang Yi [7], which projects the ridge lines along 4 discrete directions inside a local window, and the orientation is the direction that exhibits the smallest variation. The slit and project methods are computationally.

Realizing that the local orientation estimation methods do not solve the problem perfectly, effort is made to estimate the orientation through mathematical models. Sherlock and Monro introduced the zero-pole model [8], in which the orientation at a pixel is determined by number of singular points and the distance to them. The model gets good results in regions near singular points, but it’s not fit for other regions. A combination model is proposed by Zhou and Gu [9], in which a point-charge model is used to estimate the orientation in regions near singular points while another polynomial model is adapted in other regions. These methods rely on the accuracy of singular points, which in turn need the fingerprint orientation to extract. To solve this problem, Yi Wang proposed the FOMFE method [10], in which trigonometric polynomials are utilized to estimate the orientation. This method does not need singular points and performs well.

In this paper, the problem of orientation estimation is transformed into a multi-classification problem, and support vector machine (SVM) is introduced to tackle the problem. To the best of our knowledge, this is the first time that SVM is applied to the estimation of fingerprint/palmprint orientation. The remainder of this paper is organized as follows. Section 2 gives a brief review of the gradient-based method and SVM. Our SVM-based method is described in section 3. Section 4 presents experimental results and compares proposed SVM-based method with the gradient-based method. Finally, we conclude in section 5.

A SVM-based Method for the Estimation of Fingerprint and Palmprint Orientation

Yanping Wu, Tong Zhao, Shuguang Wang, Yong A, and Tiande Guo

A

2013 Fourth International Conference on Intelligent Control and Information Processing (ICICIP) June 9 – 11, 2013, Beijing, China

978-1-4673-6249-8/13/$31.00 ©2013 IEEE 343

II. A BRIEF REVIEW OF THE GRADIENT-BASED METHOD AND SVM

A. The gradient-based method As a simple and efficient method, the gradient-based

method is the most popular approach for fingerprint/palmprint orientation estimation. The fundamental idea of the gradient-based method is that along the ridge direction the gray value varies less, while the perpendicular direction much. So the orientation at [x, y] is orthogonal to the gradient direction there. To calculate the gradient direction, sobel operator is used to calculate ∇x and ∇y components, and the gradient direction is equal to the arctangent of ∇y/∇x.

As the existence of noise in the fingerprint/palmprint image, the orientation computed by the above method will be not robust, especially in the regions where the quality is bad. Since the local ridge orientation varies slowly in a local area, this problem can be solved by averaging the orientation of neighboring pixels locating in a w×h window centered at [x, y].

/2 /2

/2 /2

1'( , ) ( , )w h

i w j h

o x y o x i y jw h =− =−

= + +⋅ ∑ ∑ (1)

The orientation is defined in a cyclic space [0 180), if we compute the average orientation by dividing the sum by the total number simply, we will get 89 as the average orientation of 0 and 178, which is obviously not correct. Kass and Witkin [3] proposed a method to solve this problem. In their method, the orientation is represented as a vector:

[ cos(2 ), sin(2 )]o r rθ θ= ⋅ ⋅ (2)

r is the square of the gradient, and θ is the gradient direction. By this mean, the average orientation can be represented as below:

[ cos(2 ), sin(2 )]o r rθ θ= ⋅ ⋅ (3) The true orientation is:

11 sin(2 )' tan2 cos(2 )

ror

θθ

− ⋅=⋅

(4)

More specifically, the orientation at [i, j] can be calculated [5]:

/ 2 /2

/2 /21

/2 / 22 2

/ 2 / 2

2 ( , ) ( , )1

'( , ) tan2 ( ( , ) ( , ) )

0 0

w h

x yi w j h

w h

x yi w j h

x y

G x i y j G x i y jo x y

G x i y j G x i y j

G and G

=− =−−

=− =−

+ + + +=

+ + − + +

≠ ≠

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

∑ ∑

∑ ∑ (5)

B. Support vector machine Support vector machine [11] is introduced to solve the

classification problem, in which sets are not linearly separable. By mapping sets from original space into a higher or even infinite dimensional space, SVM derives a hyperplane in the latter space and makes separation possible. SVM consists of two phases, the training phase and the testing phase. In the former phase, a linear classifier is

derived with some samples the category of which is known, while in the latter phase, the classifier determines which category a new unknown sample belongs to.

Given p points ix with labels iy belonging to two classes A or B:

1 1 2 2 3 3( , ), ( , ), ( , ), , ( , )

11

p p

kk

k

x y x y x y x y

if x Awhere y

if x B

⋅⋅ ⋅

∈⎧= ⎨− ∈⎩

(6)

From these points, SVM tries to derive a decision function D(x) to separate points from A and B. The decision function D(x) will be used to classify unknown points in the testing phase according to the rule below:

( ) 0( ) 0

x A if D xx B if D x

∈ >∈ ≤

(7)

The decision function in the direct space is: ( ) ( )D x w x bϕ= ⋅ + (8)

where ( )xϕ is a predefined function of x , w and b are parameters. The decision function represents a hyperplane and the distance between point x and the hyperplane

is( )D xw

. Assuming that there exists a separation with

margin M, then all the p points satisfy the following condition:

( )k ky D x M

w⋅ ≥ (9)

From the above, a formal description can be derived:

, 1max

. . ( ) , 1, 2, ,w w

k k

M

s t y D x M k p=

⋅ ≥ = ⋅⋅⋅ (10)

which is equal to:

2min

. . ( ) 1, 1,2, ,w

k k

w

s t y D x k p⋅ ≥ = ⋅⋅⋅

(11)

By means of the Lagrangian, it can be transformed into the dual space and we can finally derive the best decision function. For more details about the above, please refer to [11].

SVM can also be used to process multi-classification problem by constructing a set of separations in the higher or infinite dimensional space, but here we don’t present in detail. For more details, please refer to [12].

III. SVM-BASED METHOD In this section, our method is presented. In section 3.1, the

problem of orientation estimation is transformed into a multi-classification problem, which will be tackled by SVM. The training phase is described in section 3.2. We illustrate the generation of training sets and use the orientation estimated by the gradient-based method of neighboring

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blocks as a kind of feature to represent a fingerprint block. Section 3.3 gives steps of the testing phase.

Fig. 1. The generation of a sample for training.

A. Motivation and transformation Fingerprint/palmprint orientation is continuous, ranging in

[0, 180). However, in this section, the problem of estimating orientation is transformed into a discrete classification problem. In our method, the range [0, 180] is divided into K segments, which represent K classes labeled by 0, 1, 2,…, 1K − . It’s defined that a fingerprint block belongs to class i if the orientation of the fingerprint block is in the i th segment. So the problem of orientation estimation is transformed into a multi-classification problem. In the following part of this paper, K is set as 8.

B. Training SVM consists of 2 phases, the training phase and the

testing phase. In the training phase, some labeled samples are provided and SVM finds the best decision function to classify samples from different classes. In short, SVM will learn from these labeled samples and when a new sample comes, SVM will decide which class it belongs to. The following presents how to generate samples for training as shown in Fig. 1. 1) Divide the fingerprint/palmprint into non-overlap blocks

of 13 by 13 pixels: 11b , 12b , …, mnb .

2) For each block ijb , compute the orientation ijo by the gradient-based method.

3) For each block ijb , use the orientation of the neighboring 5×5 blocks to represent the sample, while the label is decided by the true orientation ijc labeled manually.

2 2 2 1 2 2 1 2 2

1 2 1 1 1 1 1 1 2

2 1 1 2

1 2 1 1 1 1 1 1 2

2 2 2 1 2 2 1 2 2

, , , ,

, , , ,

, , , ,

, , , ,

, , , ,

i j i j i j i j i j

i j i j i j i j i j

ij ij ij ij ij ij

i j i j i j i j i j

i j i j i j i j i j

o o o o o

o o o o o

x o o o o o

o o o o o

o o o o o

− − − − − − + − +

− − − − − − + − +

− − + +

+ − + − + + + + +

+ − + − + + + + +

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟= ⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

(12)

[ * /180]modij ijy c K K= (13)

As mentioned before, to estimate the orientation of a pixel in the fingerprint image, the neighboring pixels are needed. So we divide the fingerprint into non-overlap blocks in the first step and estimate the orientation block by block. In fact, the size of the block is hard to set, and we choose 13×13 because it does not contain dramatic change of the curvature while be able to smooth the noise. In the third step, the orientation of the neighboring blocks is set to be the feature, because fingerprint orientation is always smooth and the estimated orientation is more accurate by the use of neighboring blocks.

With the labeled training samples, SVM derives the best decision function, which will be used to classify unknown samples in the testing phase.

C. Testing In the testing phase, SVM will use the decision function

trained from the training samples to classify new samples. The basic process is as follows, as shown in Fig. 2: 1) Divide the fingerprint/palmprint into non-overlap blocks

of 13 by 13 pixels: 11b , 12b , …, mnb .

2) For each block ijb , compute the orientation ijo by the gradient-based method.

3) For each block ijb , use the orientation of the neighboring 5×5 blocks to represent the sample.

4) Use the decision function derived by SVM to classify each sample, the orientation of a block belongs to class i is 180 /i K⋅ .

IV. EXPERIMENTAL RESULTS In this section, we present some experiments in which

proposed method is applied to estimate the orientation. It shows that the orientation estimated by proposed method is more accurate and the quality of minutiae by proposed method is better than the gradient-based method.

The experiment is running on NIST special database 4, which is a fingerprint image database containing 2000 8-bit gray scale fingerprint image pairs. Each image is 512-by-512

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Fig. 2. The process of the testing phase.

pixels, 19.7 pixels per millimeter resolution. NIST fingerprint database consists of F part and S part, either containing half of each pair. We use the S part as training set. By labeling the orientation of the first 75 fingerprints of the F part manually, we get 23000 samples as the training set. Testing set contains fingerprints from the S part and some palmprints. Our experiment is running on a pc of 3.1G HZ and it takes an average time of 3.688 seconds to process a fingerprint from NIST special database 4.

In addition to the direct presentation of orientation in section 4.1, the quality of minutiae is also provided by means of recall rate and accuracy rate in section 4.2.

A. The orientation estimation The first experiment is carried out to compare the

performance of proposed method and the gradient-based method. In the experiment, the orientation of the gradient-based method is estimated pixel by pixel, and only the orientation of the central pixel of each block is shown. The size of window in the gradient-based method is 13 by 13. The experiment result is illustrated in Fig. 3, in which (a) is original fingerprint image, (b) the orientation of (a) estimated

(a) (b) (c)

Fig. 3. Fingerprint orientation estimated by proposed method and the gradient-based method. a) original fingerprint b)the orientation estimated by the gradient-based method c)the orientation estimated by proposed method.

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using the gradient-based method and (c) the orientation of (a) estimated using proposed method. From the figure, it can be seen that the gradient-based method is prone to be affected by noise, resulting in bad orientation, especially in the regions where the quality of fingerprint is bad, for example, scars and creases regions. Compared with the gradient-based method, proposed method has the ability to handle these regions because it considers neighboring blocks information. In Fig. 4, it is also shown that proposed method performs better than the gradient-based method in palmprints.

B. Minutiae quality estimation Followed by the estimation of orientation, the fingerprint

and palmprint image is processed by enhancement, binarization, thinning and minutiae extraction. Orientation plays an important role in fingerprint enhancement and fingerprint thinning. If the orientation is bad, the quality of enhanced fingerprint and thinned fingerprint will be bad, which finally results in extracting bad minutiae. So the quality of fingerprint orientation determines the quality of minutiae, which is measured by two indicators: recall rate and accuracy rate. We divide minutiae into 3 parts:

A: extracted true minutiae B: extracted false minutiae C: missing true minutiae

Arecall rate

A C=

+ (14)

Aaccuracy rate

A B=

+ (15)

The higher the recall rate and accuracy rate are, the better the minutiae is. In the second experiment, we consider the quality of minutiae extracted using proposed method and the gradient-based method. The experiment is running on 40 palmprints, which have standard minutiae labeled by fingerprint experts manually. We get an average result of 45.42%+47.06% (recall rate + accuracy rate) by proposed method, and 44.81%+31.22% by the gradient-based method. Results of some representative cases are illustrated in Table I, in which we can see the comparison results by recall rate and accuracy rate. The recall rate of proposed method is almost the same with the gradient-based method, but proposed method is superior to the gradient-based method in terms of the accuracy rate.

V. CONCLUSIONS In this paper, we have proposed a SVM-based method for

the estimation of orientation. The problem of orientation

estimation is transformed into a multi-classification problem, which is tackled by SVM. The experiment shows that proposed method is robust and can resist noise of local regions well. In future work, we will continue this research and combine proposed SVM-based method with global model. By calculating the quality of blocks in the fingerprint, the orientation of bad quality blocks can be estimated according to the global model created by blocks with good quality.

REFERENCES [1] D. Maltoni, D. Maio, A. K. Jain, and S. Prabhakar, Handbook of

Fingerprint Recognition. 2003 :Springer-Verlag. [2] Z. Hou, W.Y. Yau, Y. Wang, “A review on fingerprint orientation

estimation,” Security and Communication Networks, 4 (5) (2011), pp. 591–599.

[3] M. Kass and A. Witkin, “Analyzing oriented patterns,” Computer Vision, Graphics, and Image Processing, vol. 37, no. 4, pp. 362-385, 1987.

[4] A.M. Bazen and S.H. Gerez, “Systematic methods for the computation of the directional fields and singular points of fingerprints,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 7, pp. 905-919, July 2002.

[5] N. Ratha, S. Chen and A.K. Jain, “Adaptive flow orientation based feature extraction in fingerprint images,” Pattern Recognition, vol. 28, no. 11, pp. 1,657-1,672, 1995.

[6] K. Karu and A.K. Jain, “Fingerprint classification,” Pattern Recognition, vol. 29 no. 3, pp. 389-404, 1996.

[7] Luping Ji, Zhang Yi, “Fingerprint orientation field estimation using ridge projection,” Pattern Recognition 41 (2008)1491-1503.

[8] B.G. Sherlock and D.M. Monro, “A model for interpreting fingerprint topology,” Pattern Recognition, vol. 26, no. 7, pp. 1,047-1,055, 1993.

[9] J. Zhou and J. Gu, “A model-based method for the computation of fingerprints orientation field,” IEEE Trans. Image Processing, vol. 13, no. 6, pp. 821-835, 2004.

[10] Y. Wang, J. Hu and D. Phillips, “A fingerprint orientation model based on 2D fourier expansion (FOMFE) and its application to singular-point detection and fingerprint indexing,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 4, pp.573-585, Apr. 2007.

[11] B. E. Boser, I.M. Guyon, and V. Vapnik, “A training algorithm for optimal margin classifiers,” In Fifth Annual Workshop on Computational Learning Theory, pp. 144-152, Pittsburgh, 1992. ACM.

[12] S. Abe, Support Vector Machines for Pattern Classification. Springer-Verlag, London, 2004.

TABLE I THE QUALITY OF MINUTIAE

The gradient-based method recall rate accuracy rate

Proposed method recall rate accuracy rate

50.80% 47.68% 54.27% 76.65% 39.70% 36.49% 41.51% 61.57% 57.75% 25.76% 60.93% 36.65% 33.99% 17.53% 36.15% 25.07% 40.04% 32.37% 40.44% 48.68% 28.50% 17.96% 30.92% 29.22% 55.79% 31.21% 58.80% 55.47% 41.17% 40.31% 44.30% 57.81% 51.72% 27.40% 54.48% 47.81% 52.69% 26.92% 52.69% 50.60%

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(a) (b) (c)

Fig. 4. Palmprint orientation estimated by proposed method and the gradient-based method. a) original palmprint b)the orientation estimated by the gradient-based method c)the orientation estimated by proposed method.

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