Fingerprint Minutiae Matching Using Adjacent Feature Vector

Transcription

1 Fingerprint Minutiae Matching Using Adjacent Feature Vector X. Tong, J. Huang, X. Tang and D. Shi 2* School of Computer Science and Technology, Harbin Institute of Technology, Harbin, P. R. China 2 School of Computer Engineering, Nanyang Technological University, Singapore ABSTRACT Minutia matching is the most popular approach to fingerprint verification. In this paper, we propose a novel fingerprint feature named Adjacent Feature Vector (AFV) for fingerprint matching, which consist of four adjacent relative Features of a minutiae and the ridge counts between the minutiae and the four adjacent point. In the first stage, AFV is used to find possible minutiae pairs. Then one minutiae set is rotated and translated according to two minutiae. This is followed by a preliminary matching to ensure reliable matching. At last, a fine matching is performed to overcome possible distortion. Experiments have shown the promising results of the proposed algorithm. Keywords: fingerprint verification, adjacent Feature vector INTRODUCTION Fingerprints are texture on the top of human fingertip. Because of the uniqueness of fingerprint [], fingerprint verification has been applied to many fields including criminal verification, financial security, access control, etc. In the past three decades, automatic fingerprint verification is used more widely than other branchs of biometrics such as face identification and signature identification.

2 Fingerprint matching usually consist of two procedures: feature extraction and feature matching. Feature matching is usually evaluated by the following factors: False matching rate, usually including false accept rate and false reject rate. Computational time cost, usually including time cost of corresponding fingerprint matching and time cost of non-corresponding fingerprint matching. Robustness of matching, the ability to overcome low quality of fingerprint image and the ability to overcome deformation. In order to improve fingerprint verification performance, many techniques have been designed to improve the previous three factors. The most popular matching strategy for fingerprint verification is minutia matching [2, 3, 4]. The simplest pattern of the minutiae-based representations consists of a set of minutiae, including ridge endings and bifurcations defined by their spatial coordinates. Each minutia is described by its spatial location associated with the direction and minutia type. Although a set of minutiae has been widely used for matching, the noise problem in a fingerprint image has not been fully solved. The disadvantage of minutia-based method is the lack of robustness, there are some alternative methods proposed, for instance, Jain et al. s filterbank method[5] and Isenor and Zaky s graph matching method [6]. Many researchers have tried to make the minutiae-based method robust. Ross [7] described an algorithm using both minutiae and texture features. Most fingerprint algorithms are minutiae based algorithms. Kovács-Vajna [8] used triangular matching to cope with the deformation and validate the matching by Dynamic Time Warping. Ratha and Karu [2] adopted Hough transform based matching method. By specifying scale, rotation and shift parameters, a Hough transform was conducted on a

3 minutiae set. A score can be obtained by specifying these three parameters. The maximal score was considered as the final score. He et al. [9] introduced ridge information into the minutia matching process, which reduced the computational cost when minutia pair was selected. Jain et al. proposed an alignment-based mathing method in [4], which adopted the associated ridge to align the input minutiae with the template minutiae. Good performance is reported to overcome defomation by the method. However, if only short part of a ridges is saved, the algorithm may results in inaccurate alignment. But if long part of ridges is saved, the template size will increase badly. Furthermore, sometimes it is difficult to find long ridges in a thinned fingerprint image. Jiang and Yau [3] proposed a minutia matching technique using both local and global structure of information. In this method, local structure was used to find the correspondence of two minutiae sets and the global structure was used to determine the uniqueness of fingerprint. However, if less neighborhood minutiae is used, false reject may occur in case of the presence of spurious minutiae and the absence of genuine minutiae ; if more neighborhood minutiae is used, the template size will increase greatly. Tico and Kuosmanen [0] adopted an Feature-based minutia descriptor for minutiae matching, and good performance are reported. However, ridge count are not included in the descriptor, which has been widely used and redported good performance[3][]. An other drawback lies in this descipor will lead to a huge template space.

4 Lee et al. [2] proposed a local alignment method, in his method, ridge frequency was adopted to minimize distance error by normalizing the distance between minutiae. But the minimizing distance by frequency makes the algorithm more complex, which will lead to the algorithm time-consuming. The rest of the paper is organized as follows. Section 2 describes a novel fingerprint feature named Adjacent Feature Vector in detail. Our robust minutia matching method is presented in Section 3. The experimental results are reported in Section 4. Section 5 concludes our work. 2 ADJACENT FEATURE VECTOR As we know, adjacent feature of a minutia is very important for matching because it is rotation invariant and translation invariant. In this section, we will present a fingerprint feature called Adjacent Feature Vector (AFV). The fingerprint verification system in this work consists of minutiae extraction and minutiae matching. Since this paper mainly discuss minutiae matching, we assume minutiae have been extracted and we ll give a brief description of minutiae extraction algorithm at experimental results section.

5 Figure Illustration of adjacent Feature vector. Figure illustrates an Adjacent Feature Vector. If a is a minutia of a fingerprint, b is the corresponding direction point, whereas,, and t are the four adjacent point satisfying t t2 t3 4 at = at2 = at3 = at4 = ADis, bat = π / 4, bat 2 = 3π / 4, 3 = 5π / 4 bat, and bat = 7 / 4, where ADis is a constant. Since,, and t are four adjacent points in the fingerprint image, there will be certain t t2 t3 4 Feature at the four adjacent points. We assume the Feature of,, and are,, θ and θ seperately, and the direction of a is ϕ, then o θ ϕ, o θ ϕ, o θ ϕ and o θ ϕ 4 = 4 π t t2 t3 t4 θ θ = 2 3 = 3 4 = 4 constitute the four adjacent Features of minutia a. Apparently,,, and o are rotation invarient o o o and translation invarient. As the ridge counts between at, at2, at3 and at4 are also rotation invarient and translation invarient, the four ridge counts are also included in AFV. As shown in Fig., assuming point sets T {[ X, Y ] i [,4], j [, ADis ]} ij ij T constitute the four line at i and Val([ X ij, Y ij ] ) denote the value at the point [ X, ] ij Y ij T in the binary fingerprint image. We use the following equation to calculate the four ridge counts between the minutia and the four adjacent points : ADis T T n = ( ( Val([ X, Y ] ) Val([ X, Y ] ))) / 2 () i j= ij ij ij+ ij+

6 Then the AFV for a can be defined by the following equation : Aov ( a) =< oa, oa2, oa3, oa4, na, na2, na3, na4 > (2) Let Aov ( p) and Aov( denote two AFVs of the two minutiae. A function is needed to evaluate the simliarity of the two AFVs. We use the following functions to get the distance between Aov( : Aov( p) and 4 i= 4 ( o pi oqi /( m + o pi oqi ) + ( n pi nqi /( k + n pi nqi ) AovDis ( p, = (3) i= From the illustration of AFV we observe that AFV is easy to be extracted, and the corresponding distance function is also simple. More importantly, it has fixed data structure, so it does little to increase computational cost. Furthermore, the template size is very small. Ridge counts are also used in Adjacent Feature Vector, which ensures a more reliable matching. 3 MINUTIA MATCHING Lee introduced eighteen kinds of local ridge descriptions in [3]. In this work only two most popular ridge descriptions are used, i.e. ridge ending and ridge bifurcation. Assume that there are two sets of minutiae P and notations : Q extracted from two fingerprint images. For convenience, we use the following { p p } = {[ p, p, p, p ],...,[ p, p, p, p ]} P =,..., m x y θ t mx my mθ mt (4) Q { q q } = {[ q, q, q, q ],..., [ q, q, q, q ]} = (5),..., n x y θ t nx ny nθ nt

7 th where p, p, p, p ] corresponds to four features of the i minutia in set P : denotes the x [ ix iy iθ it coordinate, p denotes the y coordinate, p denotes the minutia direction and p denotes the minutia iy iθ it p ix type (ridge ending or ridge bifurcation). The definition of Q is similar to P. 3. Alignment of Point Patterns Jain et al. [4] used the associated ridge in template fingerprint and input fingerprint to align fingerprint, which reduce the number of possible correspondences to be tested. In this research, an other method i.e. two-minutiae-based method is used to align point patterns. (a) (b) (c) Figure 2 Alignment with two minutiae. (a) minutia pair in set P. (b) minutia pair in set Q. (c) transformed minutia pair in set Q. As shown in Figure 2, assume p and p are two minutiae from fingerprint P ; q and q are two a c b d minutiae from fingerprint Q. We also assume little circles denote a minutia and the black points denote the corresponding direction point. Then θ a denotes minutiae a s direction, θ c denotes minutiae c s direction and θ ac denotes line p a p c s angle. The defination of other angles is similiar to

8 the two definations. Only if it contains the following five conditions a alignment is achieved and we can build a coordinate system according to q and q : b d p p q q < T _ pdis (6) a c b d ( θ θ ) ( θ θ ) T _ pdir (7) a ac b bd < ( θ θ ) ( θ θ ) T _ pdir2 (8) c ac d bd < p at = q bt (9) p ct = q dt (0) where T _ pdis is a threshold for distance; T _ pdir and T _ pdir 2 are thresholds for direction. Since there are many possible corresponding minutia pairs, it is necessary to reduce the corresponding number. In this paper, AFV matching is used to decrease the corresponding number. As has been approved in Experimental Section (Section 4), AFV has a good performance to distinguish corresponding and non-corresponding minutiae pairs. With equation (3), FAR = 0.4 and FRR = 0. 5 can be reached with a threshold of 3.4, which will decrease corresponding number greatly. Detail information is exhibited in experimental results section. Jain et al. [4] indicated that the nonlinear deformation in a fingerprint image usually starts from a certain center point (region) and nonlinearly radiates outward, so he consider it is beneficial to model in polar space. Both Jain et al. [4] and He et al. [9] used polar coordinate. But there are some drawbacks with their method: () Both Jain et al. [4] and He et al. [9] didn t give a method to find the certain center point (region);

9 (2) Both the template fingerprint and the input fingerprint need coordinate transform. In this research, a preliminary matching stage and a fine matching are introduced which are robust enough to overcome deformation. So cartesian coordinates is adopted in this work. A merit of cartesian coordinates lies in only one minutia set needing coordinate transform. 3.2 Minutia Matching The block diagram of minutia matching is shown in Fig. 3. There are four stages in minutiae matching : minutiae pair searching, coordinate transform, preliminary matching and fine matching. In minutiae pair searching stage, all corresponding minutiae pairs will be found based on AFV matching, and all matched pair will be add to sets S m. The following coordinate transform stage will make a coordinate transform using two pair of minutiae from S m which contend several conditions. A preliminary matching stage will give a matching score based on the similarity of angle, position and AFV. Finally, considering the relative position between matched and unmatched minutiae pair, a fine matching stage is adpoted to overcome possible deformation. Minutiae Pair Searching Coordinate Transform Preliminary Matching Fine Matching Figure 3 Block diagram of minutia matching

10 3.2. Minutiae Pair Searching Algorithm In this algorithm all corresponding minutiae pairs will be found with equation (3). The algorithm is as follows: S m = NULL MatchedPai r = 0 For all p m P and q n Q { if ( AovDis( p, q ) < T _ aov ) { add < p, q m n > to S m MatchedPai r = MatchedPair + } } If ( MatchedPai r > T _ p ) go to coordinate transform stage Else Return False Figure 4 Minutiae Pair Searching Algorithm m n In the above algorithm, S is corresponding pair sets, T _ aov is the threshold for AFV, and T _ p is the threshold for minutia pair searching. m Coordinate Transform Algorithm As shown in Fig. 2, we select two minutiae pairs p, q > and p, q > from. At first we < a b < c d determine if the two pairs have similar relative position. If conditions from (6) to (0) can be contented, it is considered to be aligned. The algorithm is as follows : S m

11 For all < p a, qb > S m and < p c, qd > S m if( pa pc qbqd < T _ pdis and ( θ a θ ac ) ( θ b θ bd ) < T _ pdir and ( θ θ ) ( θ θ ) T _ pdir2 and c ac d bd < p ct = q dt and p at = qbt ) For all q i Q p p q q { cy ay dy by θ = tan tan p p q q cx ax dx bx q q ix iy cosθ, sinθ q = sinθ,cosθ q q θ q i = + θ i θ q it = q it Preliminary Matching Stage ix iy q q bx by p + p ax ay Fine Matching Stage } Figure 5 Coordinate Transform Algorithm After the above stage, ( q, q, q, q ) θ is transformed to ( q, q, q ) ix iy i it q θ. We name the new set, ix iy i it Q Preliminary Matching Algorithm We use a fuzzy strategy to get matching score in this work. Considering that distance error, direction error and AFV error all have contribution to similarity between minutiae, we get machting score using the following equation: M _ Score( p, = ( AovErr( p, * 2 + DisErr( p, + DirErr( p, ) / 4 ()

12 Where AovErr( p, is the AFV error between p and q. DisErr ( p, and DirErr( p, are distance error and direction error between p and q seperately. They are defined as follows :.0 if ( AovD < 2.0) 0.8 if (2.0 AovD < 3.0) AovErr ( p, = 0.5 if (3.0 AovD < 3.4) (2) 0.3 if (3.4 AovD < 4.0) 0. if (4.0 AovD).2 if ( pq < 2). if (2 pq < 3) DisErr ( p, = 0.9 if (3 pq < 4) (3) 0.7 if (4 pq < 5) 0.4 if (5 pq ).2 if ( d _ e < 0.). if (0. d _ e < 0.5) DirErr ( p, = 0.9 if (0.5 d _ e < 0.2) (4) 0.7 if (0.2 d _ e < 0.3) 0.4 if (0.3 d _ e) Where AovD is the AFV distance between p and q calculated by equation (3). pq is the euclidean distance between p and q. d _ e is the relative direction between p and q. There may be distortion during fingerprint acquisition, but the local distortion usually is small. Therefore, if the two images come from the same finger, there will be several minutiae being matched. We use the following preliminary matching algorithm to get matching score.

13 S g = NULL MatchScore = 0 For all p m P and q Q if( pq < T _ dis and p q < T _ dir θ θ ) { add < p,q > to sets S g } MatchScore = MatchScore + M _ Score( p, q ) If ( MatchScore < T _ ms ) Return False Else if ( MatchScore > T _ ss ) Return True Else go to fine matching procedure Figure 6 Preliminary Matching Algorithm Fine Matching Algorithm In Figure 7, the black minutiae come from sets P, and the gray minutiae come from sets Q. In the preliminary matching stage, minutiae pair <a, a >, <b, b >, <c, c >, and <d, d > can be matched and then added to S g. <e, e > can t be added to S g as the distance between e and e is more than the threshold. Considering that the relative position <c, e> is very similar to <c, e > and <c, c > is an element of S g, we can add <e, e > to S g. Since <e, e > is an element of S g, and the relative position <e, g> is very similar to <e, g >, we can still add <g, g > to S g.

14 Fig. 7. A minutia matching example Hence we can observe that a fine matching is essential, which makes the algorithm more robust. Many deformed minutia can be matched by fine matching. The fine matching algorithm is as follows : Flag= While ( Flag== ) { Flag=0 If exist ( < i j >, < p q > S and < s, t > S ) { If( ( i s ) ( j t ) < T _ dis x x x, S g, g g and ( i s ) ( j t ) < T _ dis y y y y x and ( i s ) ( j t ) < T _ dir and θ θ θ θ ( p s ) ( q t ) < T _ dis x and x x ( p s ) ( q t ) < T _ dis y y y x and ( p s ) ( q t ) < T _ dir ) θ θ θ θ y { add < s,t > to S g } } MatchScore = MatchScore + M _ Score( s, t ) If ( MatchScore > T _ ss ) } Return False Flag= Return True Fig. 8. Fine Matching Algorithm

15 In the above algorithm, two correspondences in S g should be found in order to add < s,t > to S g, which make the matching more reliable. 4 EXPERIMENTAL RESULTS We have carried out experiment for two categories : experiment for AFV and experiment for minutiae matching. AFV experiment is use to find better distance function and better parameters. Minute matching experiment is used to test the performantce of the propoese system. 4. Experiment for AFV Let Aov ( p) =< o p, o p2, o p3, o p4, n p, n p2, n p3, n p4 > and Aov ( =< oq, oq2, oq3, oq4, nq, nq2, nq3, nq4 > denote two AFVs which associated with two minutiae. A AFV matching experiment has been conducted to evaluate AFV. There are two kinds of AFV pair in the matching experiment: AFV pairs from consponding minutiae pair and AFV pairs from non-corresponding minutiae pair. If Aov( p) and Aov( are from corresponding minutiae but the distance is more than certain threshold we call it false reject. Similarly, if Aov ( p) and Aov( are from non-corresponding minutiae but the distance is less than certain threshold we call it false accept corresponding AFV pairs and 0000 noncorreponding AFV pairs were collected in this experiment. The following three distance functions were tested besides function (3):

16 4 2 2 ( o pi oqi ) + k * ( n pi nqi ) ) AovDis ( p, = (5) i= 4 ( o pi oqi + k * n pi nqi ) AovDis 2( p, = (6) 4 i= i= AovDis 3( p, = o + * pi oqi k n pi n (7) qi Figure 9 shows the four Receiver Operating Characteristics (ROC) curves. From Fig. 9. we can observe that equation (6) has a better performance than equation (5), equation (7) has a better performance than equation (6), and equation (3) has the best performance among the four functions. From Fig. 9 we also observe that AFV has a good performance to distinguish corresponding and noncorresponding minutiae pairs. We got an error rate of FAR = 0. 4 and FRR = 0.5 with equation (3) when a threshold of 3.4 is specified. Fig. 0 and Fig. show the distance distribution of corresponding AFV pairs and non-corresponding AFV pairs with equation (3). In different fingerprint verification application there usually are different strategies for the determination of AFV matching threshold. In a safety preferential application such as coffer fingerprint lock, a lower threshold should be specifyed to make it more reliable. In other applications, such as criminal fingerprints database searching, a higher threshold should be specifyed to find more similar fingerprints.

17 False Accept Rate ROC with Equation (3) ROC with Equation (7) ROC with Equation (6) ROC with Equation (5) False Reject Rate Figure 9 Four ROC of four corresponding distance. 00 Number of AOV Pair Distance of AOV Pair Fig. 0. Distance distribution of corresponding AFV pair with equation (3).

18 Number of AOV Pair Distance of AOV Pair Figure Distance distribution of non-corresponding AFV pair with equation (3). 4.2 Experiment for minutiae matching The fingerprint verification system consists of two procedures : minutia extraction and minutia matching. Both of them will take an effect on the matching result. So it is necessary to introduce the minutia extraction procedure used in this work. The procedure consists of building Feature map, image enhancement, binarization, thinning and minutia detection. Bazen and Gerez s method [4] is used to build Feature map. In image enhancement we adopt Hong et al. s method [5]. He et al. [9] proposed a mehod for enhance and binarize image. We use this method to get binary image after enhancement. The binary image is thinned by Naccache and Shinghal s SPTA method [6]. Finally, Espinosa-Duró s method [7] is used to detect minutiae. To assess our methodology, we have test the proposed minutia matching system on a set of fingerprint image which is captured with ZY202B optical fingerprint sensor. The image set contain 96

19 fingerprint images from 28 different fingers with 7 images for each finger. The size of these images is 300*300 with 256 grayscales. All the images have been scanned at a resolution of 500 dpi. There was no restriction about the direction, but a little restriction about the position when fingerprint was captured, which ensured certain overlap area between each two images. Fig. 2 and Fig. 3 show some example of the fingerprint sets. Table shows the parameters used in the experiment and Fig. 4 shows the Receiver Operating Characteristics (ROC) curve on the given sets. We can observe that if AFV is adopted the false matching will be reduced greatly. When FAR is equal to , the FRR will be if AFV is adopted, but the FRR will be if AFV is not adopted. In order to test the computational time cost, we classified matching into two categories: matching between corresponding fingerprint and matching between non-corresponding fingerprint. Table 2 and Table 3 show that the both kinds of matching consume less time when AFV is adopted. Fig. 2. Fingerprint images examples of high quality Fig. 3. Fingerprint images examples of low quality

20 0. False Accept Rate 0.0 E-3 E-4 E-5 E-4 E False Reject Rate Fig. 4. ROC curve of minutia matching: the dash line is the result when AFV wasn t used and the solid line is the result when AFV was used Table. Parameters used in the experiment Parameters Value Exposition for parameters T_pdis 5.0 Threshold for distance in coordinate transform stage T_pdir 0.3 Threshold for direction in coordinate transform stage T_pdir2 0.3 Threshold 2 for direction in coordinate transform stage ADis 60 Distance between a minutiae and the four adjacent points m 0. Parameter in equation (3) k 3.0 Parameter in equation (3) T_AFV 4.0 Threshold for AFV matching T_p 6 Threshold for minutiae pair searching T_ms 5 Threshold for preliminary matching T_dis 5.0 Threshold for distance in minutia matching

21 T_dir 0.3 Threshold for direction in minutia matching Table 2. Computational time cost of fingerprint matching without AFV Matching count between corresponding fingerprint Time cost of corresponding fingerprint matching Matching count between noncorresponding fingerprint Time cost of non- corresponding fingerprint matching (s) (s) Table 3. Computational time cost of fingerprint matching with AFV Matching count between corresponding fingerprint Time cost of corresponding fingerprint matching Matching count between noncorresponding fingerprint Time cost of non- corresponding fingerprint matching (s) (s)

22 5 CONCLUSIONS In this paper, a minutia matching system is designed which uses a novel fingerprint feature called adjacent Feature vector. In minutiae pair searching procedure AFV matching is used to reduce computational cost but the matching error is reduced. Two minutiae are selected to build a coordinate system in coordinate transform procedure, which reduce alignment error. Considering possible distortion, a fine matching is used which make fingerprint matching more robust. Both false accept rate and false reject rate are tested. Experimental results show that with the same FAR, FRR can be reduced greatly if AFV is adopted. Experimental results also show that both time of corresponding matching of time of non-corresponding matching reduced greatly if AFV is adopted. All of the above experimental results show the excellent performance of the proposed algorithm. ACKNOWLEDGEMENTS This research is supported by the National Natural Science Foundation of China under Grant No REFERENCES [] W. F. Leung, S. H. Leung, W. H. Lau, and A. Luk. Fingerprint recognition using artificial network. Artificial networks for signal processing. Proceedings of the 99 IEEE Workshop. pp [2] N. K. Ratha and K. Karu. A real time matching system for large fingerprint databases. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(8) : , 996. [3] X. Jiang and W. Y. Yau. Fingerprint minutiae matching based on the local and global structures. Proc. ICPR2000, 2: , Sep, 2000.

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