A Fingerprint Matching Algorithm Based on Radial ... - CiteSeerX

A Fingerprint Matching Algorithm Based on Radial Structure and a Structure-Rewarding Scoring Strategy Kyung Deok Yu, Sangsin Na, and Tae Young Choi Department of Electrical and Computer Engineering, Ajou University, Suwon, Korea {rokmc100,sangna,taeyoung}@ajou.ac.kr

Abstract. This paper proposes a new fingerprint matching algorithm for locally deformed fingerprints based on a geometric structure of minutiae, called the radial structure, which is a collection of lines from a minutia that connect its Voronoi neighbors. The proposed algorithm consists of local matching followed by global matching, in both of which a new robust scoring strategy is employed. The local matching compares individual radial structures of a query and a template, and the global matching, performed when the local matching fails, utilizes overall radial structures of a query. The algorithm has been tested using the FVC2002 DB1 fingerprint database on a Pentium-4 personal computer with 1.8 GHz clock and 256 Mbyte RAM. The test results show that the average matching time including preprocessing is 0.9 sec, and the equal error rate is 8.22%. It has been observed that the proposed algorithm has a smaller equal error rate by 7.18% than Mital and Teoh’s. This is a substantial improvement in the equal error rate on the angle-distance based algorithm of Mital and Teoh. This improvement is attributed to the following features of the proposed algorithm: the radial structure is obtained from Voronoi neighboring minutiae, which results in more robustness to false minutiae; and the scoring strategy rewards similarity in the geometric structure rather than feature types as in Mital and Teoh’s algorithm.

1

Introduction

Fingerprint recognition is the most reliable and popular among various biometric recognitions [1]. A typical automatic fingerprint identification system consists of fingerprint acquisition, image preprocessing such as image enhancement and feature extraction, and matching. Fingerprint matching algorithms can be roughly classified into the following three categories: minutia-based [2, 3]; ridge-based [4]; and hybrid methods [5]. Among these categories, the minutia-based algorithms are the most common because they usually perform better in recognition accuracy and the processing time than the others. Mital and Teoh proposed a minutiae-based matching algorithm in [6], which uses five minutiae of its closest neighbors to form geometric structure along with a scoring method. Their algorithm is simple, very effective, and rotationally T. Kanade, A. Jain, and N.K. Ratha (Eds.): AVBPA 2005, LNCS 3546, pp. 656–664, 2005. c Springer-Verlag Berlin Heidelberg 2005


A Fingerprint Matching Algorithm Based on Radial Structure

657

invariant. However, it has the following two weak points. First, their algorithm becomes sensitive to false minutiae because a false minutia is chosen, if it is closer to true ones, for the structure construction. Second, their scoring method penalizes too heavily discrepancy in the minutiae type between a query and a template even though the geometric structures are the same or similar. In this regard this paper proposes a matching algorithm that improves on Mital and Teoh’s. The proposed algorithm constructs a geometric structure of a minutia, called the radial structure, which consists of lines connecting its Voronoi neighbors. In addition, the algorithm employs a scoring strategy that rewards similarity in the geometric structure of a minutia, even when the feature types are different unlike Mital and Teoh’s. Consequently, the combination of the radial structure and the structure-rewarding scoring makes the proposed algorithm robust to false minutiae. To compare the proposed algorithm with the referenced algorithm of Mital and Teoh’s, we have performed the cross experiment of four types using FVC2002 DB1 fingerprint database. The proposed algorithm has a higher recognition rate by 7.18%: in the recognition rate, the proposed matching algorithm outperforms the reference by 2.61% while the proposed scoring method the reference by 5.54%. From the experimental results, it has been found that the proposed matching algorithm and scoring method are more robust to false minutiae than the counterparts of the referenced algorithm. This improvement is attributed to the following features of the proposed algorithm: the radial structure is obtained from Voronoi neighboring minutiae, which results in more robustness to false minutiae; and the scoring strategy rewards similarity in the geometric structure rather than feature types as in Mital and Teoh’s. The rest of the paper is organized as follows: Section 2 deals with Voronoi diagrams and the definition of the radial structure; Section 3 describes the proposed matching algorithm and the scoring method. Finally, Section 4 and 5 present experimental results and conclusions, respectively.

2 2.1

Background The Definitions of the Voronoi Diagram and the Radial Structure

The Voronoi Diagram. In the plane the Euclidean distance between two points p and q by dist(p, q) is defined:
dist(p, q) := (px − qx )2 + (py − qy )2 . P := {p1 , p2 , p3 , ..., pn } is a set of n distinct points in the plane, each of these points is called a site. We define the Voronoi diagram of P as the subdivision of the plane into n cells, one for each site in P , with the property that a point q lies in the cell corresponding to a site pi if and only if dist(q, pi ) < dist(q, pj ) for each pj ∈ P with i = j. We denote the Voronoi diagram of P by V or(P ). The cell that corresponds to a site pi is denoted V (pi ), which we call the Voronoi cell

658

Kyung Deok Yu, Sangsin Na, and Tae Young Choi

of pi . The follows represent the properties of Voronoi diagram. Let P be a set of n point sites in the plane. First, if all the sites are collinear, then V or(P ) consists of n − 1 parallel lines and n cells. Second, the number of vertices in V or(P ) is at most 2n − 5 and the number of edges is at most 3n − 6. Third, a point q is a vertex of V or(P ) if and only if its largest empty circle Cp (q) contains three or more sites on its boundary [7]. Figure 1 shows an example of the Voronoi diagram on a fingerprint image after preprocessing.

Fig. 1. An example of the Voronoi diagram of a fingerprint

In this paper we use a modified plane sweep algorithm to construct Voronoi diagram–Fortune’s algorithm. This algorithm is chosen because it has the O(n log n) complexity while the half plane intersection algorithm has the complexity of O(n2 log n) [7]. To introduce the sweep line algorithm, we consider the several definitions. Parabolas are useful in this sweep line algorithm because for any point pi , there is a parabola from the sweep line that every point on the parabola is equidistant from both p and the sweep line. Now, we explain the site event and circle event. As the sweep process, a new arc of some parabola is added to wave-front (beach line) only when sweep line touches the some site. This is called a site event. And, the only way that an arc can disappear from the wave-front is when two other adjacent arcs intersect it at a common point. This is called a circle event [8]. Figure 2 shows the breakpoint, wave-front (beach line) and sweep line, and Figure 3 shows the site event and circle event.

The Radial Structure. The radial structure is defined as follows. Figure 4 shows an example of the radial structure. A set P := {p1 , ..., pn } for n ∈ Z is a fingerprint image consisting of n minutia points. The radial structure of point pi ∈ P , denoted R(pi ), is defined to the set of all neighborhood minutiae sharing the edge with minutia pi . We call the center minutia of R(pi ) as ci , and the neighborhood minutiae of R(pi ) as ni out of order. So, an arbitrary R(pi ) is defined as follows R(pi ) := {ci , n1 , n2 , ..., nj } for 2 ≤ j ≤ n. Figure 5 shows that a radial structure consisting of center minutia and its neighbors in a fingerprint image after Voronoi diagram is constructed. The minutiae are extracted in the fingerprint image and the radial structures are formed for each R(pi ) is saved

A Fingerprint Matching Algorithm Based on Radial Structure

659

Fig. 2. The sweep line algorithm

Fig. 3. The site event and circle event

Fig. 4. The correlation factor of the radial structure

with a text file with a form of following set to perform the matching stage. R(pi ) = {(cix , ciy , ciO , ciT ), (n1x , n1y , n1θ , niO , n1T ), ..., (njx , njy , njθ , niO , njT )}

3

The Proposed Matching Algorithm

The proposed matching algorithm proceeds in the following two stages. Stage 1 : Search for the number CN of the radial structures which have scores higher than a preset threshold TS by comparing radial structures of a query and a template fingerprint image. If CN ≥ TN , we do not carry out second stage

660

Kyung Deok Yu, Sangsin Na, and Tae Young Choi

Fig. 5. A radial structure

Fig. 6. The comparison criteria of the radial structure

matching and display the same fingerprint image. These matching techniques are useful to locally deformed fingerprint image. If first stage matching is not employed, because total matching score is low, miss-match can occur in spite of same fingerprint image. The basis about similarity of radial structure is shown with Figure 6. Threshold (TS ) is predefined by experimental result to be repeated, and threshold number (TN ) is defined following threshold: TN = T otal number of radial structure ×

25 100

Stage 2 : If the number of similar radial structure is less than TN , the second stage is performed. At the second stage, estimate the transformation parameters by using three radial structures that scores highest at the first stage. The following pseudo code shows a method of extracting the translation and rotation parameters between a query and a template. After extracting parameters, similarity of two fingerprint images is decided on by translating and rotating the query along the extracting parameters. Figure 7 is the flow chart for the process.

A Fingerprint Matching Algorithm Based on Radial Structure

661

Algorithm for extracting_parameters(query radial structure Qhi, template radial structure Thi) while i less than 3 do coincide Qhi’s center point and Thi’s center point calculate the translation by subtracting Qhi from Thi while Qhi’s neighbor is not empty do rotate T as Qhi’s angle and score each stage each score is stacked the temporary memory do search the highest score from the temporary memory calculate the angle as sum of rotation angle of Qhi’s neighborhood end of while end of while end of Algorithm In Figure 7, CN is the number of the radial structures which has a higher score than threshold TS between a query and a template, and S denotes the total matching score.

Fig. 7. The proposed matching algorithm

4

Experimental Results

The proposed matching algorithm has been tested with the FVC2002 DB1 on a Pentium-4 personal computer with 1.8 GHz clock and 256 Mbyte RAM. The FVC2002 DB1 contains 800 impressions obtained from an optical sensor, with 8

662

Kyung Deok Yu, Sangsin Na, and Tae Young Choi Table 1. The experimental results of the matching rate (%) Matching
Scoring

Proposed

Mital and Teoh’s

Proposed

91.78

86.24

Mital and Teoh’s

89.17

84.60

impressions apiece from 100 fingers [9]. We carried out the experiment categorized in Table 1 in order to compare the proposed algorithm and scoring method with Mital and Teoh’s in [6]. Mital and Teoh’s algorithm uses a local feature group, in which each of the extracted features is correlated with its five nearest neighboring features to form a local feature group for a first stage matching. Their algorithm is more sensitive than the proposed algorithm to a false minutia, as an example in Figure 8 shows.

Fig. 8. The deformation of each structure when false minutiae is inserted

Each category in Table 1 was performed 2,800 times for genuineness, and 4,950 times for imposter. Figure 9 shows the distribution of the obtained matching score and Table 1 the matching rate. Table 1 clearly shows that the proposed algorithm outperforms Mital and Teoh’s.

A Fingerprint Matching Algorithm Based on Radial Structure

663

Fig. 9. The distribution of the matching score of the proposed (left) and Mital and Teoh’s (right) algorithm

The proposed and Mital and Teoh’s algorithms are similar in the sense that they both use a geometric structure of fingerprint minutiae, but they are different in the way of constructing the geometric structures and also in the scoring method. First, the proposed algorithm constructs the radial structure using Voronoi diagrams. Second, in the scoring method, the proposed algorithm gives priority to the geometric structure rather than minutia types such as ridge ending and bifurcation. Third, if a false minutia is inserted in the same geometric structure, the proposed algorithm usually undergoes less deformation than Mital and Teoh’s, although they suffer equally in the worst case.

5

Conclusions

This paper has proposed a fingerprint matching algorithm based on the radial structures of minutiae and a scoring method that rewards the geometric structure. Numerical results have shown that the proposed algorithm has a substantially improved equal error rate on an angle-distance based algorithm. The proposed matching algorithm and scoring method are found to be more robust to the false minutiae because of the radial structure and structure-rewarding scoring method. The proposed matching algorithm can be extended for higher recognition accuracy. One extension may involve a combined radial structure, which is a collection of radial structures of neighboring minutiae connected to a principal minutia.

Acknowledgement This work was supported in part by the Biometrics Engineering Research Center, KOSEF.

References 1. Biometric Market Report (International Biometric Group) 2. A. K. Jain, L. Hong and R. Bolle.: On-Line Fingerprint Verification. IEEE Trans. PAMI, Vol. 19, no. 4, pp. 302–313, 1997.

664

Kyung Deok Yu, Sangsin Na, and Tae Young Choi

3. N. K. Ratha, K. Karu, S. Chen, and A. K. Jain.: A Real-Time Matching System for Large Fingerprint Database. IEEE Trans. PAMI, Vol. 18, no. 8, pp. 799–813, 1996. 4. Y. T. Park.: Robust Fingerprint Verification by Selective Ridge Matching. The Institute of Electronics Engineers of Korea, no. 37, pp. 351–358, 2000. 5. A. K. Jain, A. Ross and S. Probhakar.: Fingerprint Matching Using Minutiae and Texture Features. ICIP, pp. 282–285, Thessaloniki, Greece, 2001. 6. D. P. Mital and E. K. Teoh.: An Automated Matching Technique for Fingerprint Identification. In Proceedings of the 1997 First International Conference on Knowledge-Based Intelligent Electronic Systems. KES ’97, Vol. 1, pp. 142–147, May 21-23, 1997. 7. M. de Berg, M. van Kreveld, M. Overmars and O. Schwarzkopf.: Computational Geometry: Algorithms and Applications. pp. 145–161, Springer, 1997. 8. M. Horn and J. Weber.: Computational Geometry Lecture Notes: Voronoi Diagrams. April 29, 2004. 9. D. Maio, D. Maltoni, R. Cappelli, J. L. Wayman and A. K. Jain.: FVC2002: Second Fingerprint Verification Competition.