A Multi-stage Fingerprints Matching Algorithm*

Honglei Wei Danni Liu School of Mechanical Engineering Department of Computer Science & Technology

Dalian Fisheries University Dalian Neusoft Institute of Information Dalian, Liaoning Province, China Dalian, Liaoning Province, China

whl@ dlfu.edu.cn liudanni@ Neusoft.edu.cn

* This work is partially supported by the Start Fund for Doctor Research of Liaoning Province, China Grant #20071066 to Honglei Wei.

Abstract - This paper proposes a novel fingerprint matching algorithm. The matching process was divided into three stages. In first stage, local orientation structures matching was performed to evaluate the similarity of orientation information around the minutiae. In the second stage, local minutia structure matching was performed to evaluate the similarity of neighborhood minutiae distribution around the minutiae. In the third stage, the matching pair sets was built by matching the global minutia structures that extended from the local minutia structure, which evaluated the global similarity. The final similarity between two fingerprints was gotten according to the matching scores calculated from three stages. Experiments on four databases of FVC2002 show that this fingerprints matching technique is really effective.

Index Terms -fingerprint, minutia, matching.

I. INTRODUCTION

Fingerprints have long been used for person recognition due to their uniqueness and immutability. Main approaches proposed in the literature for the fingerprint automatic verification may be roughly classified as minutiae-based, correlation-based or image-based. Most of the approaches are minutiae-based: the matching between two fingerprints is based on the matching of their sets of minutiae extracted from the fingerprint images[1]. Minutiae are ridge ending and ridge bifurcation, which are shown in fig 1.

Fig. 1. Examples of minutiae.

Fingerprint minutiae matching is to find a similarity level between two global minutiae structures, one from the template fingerprint and another from the input fingerprint. Jain et al.[2] use the ridges associated with the minutiae to estimate the alignment parameters, which is capable of compensating for some of the nonlinear deformations and finding the correspondences. Tan and Bhanu [3] propose a fingerprint-matching approach based on genetic algorithms (GA), which tries to find the optimal transformation between two different

fingerprints. He et al. [4] build a minutia-simplex that contains a pair of minutiae as well as their associated textures as the matching features, and uses the ridge-based nearest neighborhood among minutiae to represent the ridge-based relative features among minutiae. Zhu et al.[5] propose a minutia matching method based on global alignment of multiple pairs of reference minutiae. The minutia points of a fingerprint capture only a very limited amount of information from the reach information content present in the fingerprint pattern. Consequently, a representation of the fingerprint pattern with respect to each minutia detail must employ non-minutia information like brightness, ridge orientation, transform features, etc[6]. In this paper, we use local orientation structure and local minutia structure to evaluate the local information similarity around two minutiae to be compared, and use global minutia structures to evaluate the similarity of global information. The final similarity between two fingerprints is calculated from the three stages matching.

II. LOCAL ORIENTATION STRUCTURE MATCHING

The orientation information provides a rough description of the fingerprint pattern that can be estimated with reasonable accuracy even from noisy input images. Since the ridge orientation typically exhibits small spatial variations between neighborhood pixels, a large area of the orientation field can be reconstructed from the orientation angles estimated in a relatively small number of sampling points. In this paper, excepting its position and its orientation, a minutia is characterized partly by local orientation structure, which is built by the orientation sampling points organized in a circular pattern around the minutia, which is illustrated in Fig.2 The circular pattern consists of n concentric circles of radii )1( niri ≤≤ , each one of them comprising m sampling points, equally distributed along its circumference. Using the minutia direction θ as a reference, the points on each circle can be ordered in a counterclockwise manner starting with the point located on the line which has the same angle θ as the minutia. Denoting the local ridge orientation estimated in

ijp by ijθ , we define the local orientation structure of a minutia as follows:

{ }1,1);,( ≥≥≥≥== inimDD ijij θθλ (1)

197

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International Conference on Automation and Logistics Shenyang, China August 2009

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where ),( θθλ ij denotes the acute relative angle from ijθ to θ . The local orientation structure defined as (1) is invariant to rotation and translation.

Fig.2. Illustration of local orientation structure

Let a and b denote the labels associated with two minutiae whose local orientation field are { }ijaD α=)( and

{ }ijbD β=)( , respectively. A similarity function between two local orientation structures is defined as:

∑∑= =

−×

=m

j

n

iijijO nm

baS1 1

)),()8(exp()1(),( βαλπ (2)

III. LOCAL MINUTIAE STRUCTURE MATCHING

In this section, we describe a minutia with rotation and translation invariant feature by using some other minutiae in its neighborhood. Fig.3 shows a minutia local structure consisted of its four neighborhoods.

km

1m

2m

3m

4m

1kr

2kr

3kr

4kr

1kθ

1ke

Fig.3. Example of minutia local structure

For each minutia km T

iii yx ),,( θ , the relative distance kir , radial angle kie and minutia direction kiθ between minutia

km and its neighborhood minutia im Tkikiki er ),,( θ calculated by

(3), which is referenced from [7].

( ) ⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−−

−+−

=⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−

ki

kki

ki

kiki

ki

ki

ki

d

xxyyd

yyxx

er

θθφ

θφθ

,

, tan

)()(

1

22

(3)

),( 21 ttdφ is the difference between two directions or angles, 1t

and 2t , ππ <<− 21, tt , which is calculated as:

⎪⎩

⎪⎨

⎧

>−+−−<−−+

<−<−−=

ππππ

ππφ

2121

2121

2121

21

if ,2 if ,2

if ,),(

tttttttt

ttttttd (4)

The features of two minutiae Pmk ∈ and Qml ∈ that describes their local structure characteristic with their neighborhoods in a range (circle with radius R=50 pixels in this paper) are given respectively by

)),,(),...,,,(( 111p

kmpkm

pkm

pk

pk

pk

k ererp θθ=

)),,(),...,,,(( lnlnln111qqqq

lql

ql

l ererq θθ=

The steps for matching between kp and lq are described as follows: 1) Let each minutia kp

kipki

pki per ∈),,( θ compare with each

minutia lqlj

qlj

qlj qer ∈),,( θ . If the conditions (5) are satisfied, the

pair is thought to be matched. The matching score is calculated by (6) in which the eD and θD are parameters for

specifying the maximal range of angle changing, and other parameters are shown in Fig.3

⎪⎪⎩

⎪⎪⎨

⎧

≤

≤

≤−

lim

lim

lim

),(

),(

θθθφ

φqlj

pki

qlj

pki

qlj

pki

d

eeed

rrr

(5)

θ

θθφφD

dD

eedL

rrS

qlj

pki

e

qlj

pki

qlj

pki

ij

),(),(3 −−

−−= (6)

2) The matching score of local structure kp and input

local structure lq are calculated as:

),min(

),(mn

smmS kl

lkLS∑= (7)

where n and m are the number of minutiae in input local structure and template local structure. ∑ kls is the sum of score of all matching minutiae in local structures. In cases when a minutia has more than one matched minutiae, the pair with the maximal score is believed to be the correct one.

IV. GLOBAL ORIENTATION STRUCTURE MATCHING

In this section, we extend a set top of best matched local structure pairs to global structures and use them to evaluate the similarity of two fingerprints in global degree. The five pairs with the highest matching score calculated by (8) are selected into the pair set, and they are called as reference pair in the following description.

),(),(),( 21 lkLSlkOlk mmSfmmSfmmS += (8)

In (8), 4.01 =f and 6.02 =f are parameters that specify the

weight associated with each component of the feature. For each reference pair ),( lk mm , where Pmk ∈ and Qml ∈ , the next

four steps will be performed. 1) Extend the minutiae local structures to global structures by including all the minutiae into the structures for two

198

fingerprints respectively. The global structures are denoted as following.

)),,(),...,,,(( 111p

kMpkM

pkM

pk

pk

pk

k ererP θθ=

)),,(),...,,,(( 111qlN

qlN

qlN

ql

ql

ql

l ererQ θθ=

2) If two minutia kpki

pki

pki

p PerB ∈),,( θ and lqlj

qlj

qlj

q QerB ∈),,( θ

satisfy the conditions (5), they will be added into a pair set which is denoted as )),(,),,(( 11

QK

PK

QP BBBBB …= , and the matching

score can be calculated as:

θ

θθφφD

dD

eedL

rrBBS

qlj

pki

e

qlj

pki

qlj

pkiqp

GS

),(),(3),( −−

−−= (9)

V. FINAL MATCHING SCORE

The final score that integrate three stages matching can be calculated by (10) in which M and N are the minutia number of two fingerprints in matching.

[ ]∑=

××+

=N

i

Qi

PiGS

Qi

PiLS

Qi

PiO BBSBBSBBS

NMS

1),(),(),(

)(2

(10)

There are five reference pairs in the set. For each reference minutia pair, a matching score can be calculated by (10). The maximal one will be chosen as the final similarity level of two fingerprints.

VI. EXPERIMENTAL RESULTS

Some experimental results are presented to demonstrate the performance of the proposed technique. The FVC2002 databases are used to test the performance of our approach. There are four sets in FVC2002 databases and in each set, there are 100× 8 images. The performance evaluation method in[8] is adopted in the experiments. EER (Equal error rate) is computed as the point where FNMR equal to FMR. FMR100 and FMR1000 are the values of FNMR for FMR=1/100 and 1/1000 respectively. The time is the average matching time of two ridge line sets and don’t include the preprocessing time. ROC is obtained by plotting FMR and FNMR in log-log scales. The total number of genuine and impostor matching attempts is ((8*7)/2)*100=2800 and ((100*99) /2) = 4950, respectively.

Literature [2] is a very important approach for fingerprint matching. We realized the method proposed in literature [2] to compare with our approach. Our approach and literature approach both use the same enhancement algorithm in [9]. All the experiments were conducted on Pentium IV1.6 Ghz PC. The experimental results show that the accuracy of our approach is better than the method proposed in literature [2] over the four databases.

TABLE I EXPERIMENTAL RESULTS OF DB1_A

Algorithm EER FMR100 FMR1000 Time Literature[10] 2.95% 4.35% 6.44% 0.01s Our approach 1.41% 1.64% 3.21% 0.01s

TABLE II EXPERIMENTAL RESULTS OF DB2_A

Algorithm EER FMR100 FMR1000 Time Literature[2] 2.45% 3.12% 4.54% 0.01s Our approach 1.44% 1.88% 4.46% 0.01s

TABLE III

EXPERIMENTAL RESULTS OF DB3_A Algorithm EER FMR100 FMR1000 Time Literature[2] 7.76% 13.55% 19.41% 0.01s Our approach 4.32% 6.67% 10.35% 0.01s

TABLE IV

EXPERIMENTAL RESULTS OF DB4_A Algorithm EER FMR100 FMR1000 Time Literature[2] 3.44% 5.13% 7.91% 0.01s Our approach 2.12% 3.31% 5.76% 0.01s

VII. CONCLUSIONS

This study describes a new fingerprint matching technique based on three stages matching, including local orientation structure matching, local minutia structure matching and global structure matching. The local orientation structure is rotation and translation invariant and can tolerate reasonable deformation, and used for evaluating the similarity of local orientation information. Local minutia structure matching was performed to evaluate the similarity of neighborhood minutiae distribution around a minutia. The global minutia structures are derived from the best matched local minutia structures and it is used for evaluating the global similarity. The final similarity between two fingerprints was gotten according to the matching scores calculated from three stages. The usefulness of the proposed approach was confirmed in the experiments conducted, which showed good performance in reliability and accuracy.

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matcher,” Pattern Recognition, vol. 41, 2008, pp. 3461 -- 3466. [2] A. Jain, L. Hong and R. Bolle, “On-Line Fingerprint Verification,” IEEE

Transactions on Pattern Analysis and Machine Intelligence, vol. 19, no. 4, 1997, pp. 302-314.

[3] X. Tan and B. Bhanu, “Fingerprint matching by genetic algorithms,” Pattern Recognition, vol. 39, 2006, pp. 465 – 477.

[4] Y.L. He and J. Tian, “Fingerprint Matching Based on Global Comprehensive Similarity,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 6, 2006, pp. 850-862.

[5] E. Zhu, J. P. Yin and G. M. Zhang, “Fingerprint matching based on global alignment of multiple reference minutiae,” Pattern Recognition, vol. 38, 2005, pp. 1685 – 1694.

[6] M. Tico and P. Kuosmanen, “Fingerprint Matching Using an Orientation-Based Minutia Descriptor,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 8, 2003, pp. 1009-1014.

[7] X. Jiang and W. Yau, “Fingerprint Minutiae Matching Based on the Local And Global Structures,” Proc. 15th International Conference on Pattern Recognition, IEEE Computer Society, 2000, pp. 1038~1041.

[8] D. Maio, et al., “FVC2000: Fingerprint Verification Competition,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 3, 2002, pp. 402-412.

[9] H. Lin, Y. Wang and A.K. Jain, “Fingerprint Image Enhancement: Algorithm and Performance Evaluation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 8, 1998, pp. 777-789.

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