fingerprint matching

Fingerprint Matching Method Using Minutiae Clustering and Warping

Dongjin Kwon, Il Dong Yun†, Duck Hoon Kim‡, and Sang Uk LeeSchool of EECS, Seoul Nat’l Univ., Seoul, 151-742, Korea

†School of EIE, Hankuk Univ. of F. S., Yongin, 449-791, Korea‡Institute for RIS, Univ. of Southern California, Los Angeles, CA 90089, USA

[email protected], [email protected], [email protected], [email protected]

Abstract

Solving non-linear distortion problems in fingerprintmatching is important and still remains as a challeng-ing topic. We have developed a new fingerprint match-ing method to deal with non-linear distortion problems ef-ficiently by clustering locally matched minutiae and warp-ing the fingerprint surface using minutiae clusters. Specif-ically, local invariant structures encoding the neighbor-hood information of each minutia are utilized in cluster-ing the matched minutiae and then the fingerprint surfaceis warped to describe the deformation pattern properly. Fi-nally, to make an additional increase in performance, theoverlapped region of two fingerprints is considered in thescore computation stage. Experimental results show thatthe proposed algorithm is performed best compared withother ones.

1. Introduction

Fingerprint recognition is coming into the spotlightamong the biometric technologies while having a very goodbalance of all the desirable properties: distinctiveness, per-manence and performance etc [7]. In the last ten years thereare great advances in the field of automatic fingerprint iden-tification system (AFIS), and it is a matter of course that themost important stage of AFIS is the fingerprint matching.Although there are several fingerprint matching paradigms,we focus on minutia (ridge ending and ridge bifurcation)based approach which is known to the most popular and ac-curate method for the verification. For supporting compati-bility to an ANSI/NIST standard [8] and also using alreadyextracted minutiae templates of existing systems, it is re-quired for a fingerprint matching system to use only locationand orientation information of the minutiae. In this context,the fingerprint matching can be considered as a simple pointpattern matching problem finding number of correspondingpoint pairs.

In general, there are several difficulties have to be con-sidered in this simple problem. One is a possibility of spuri-ous or dropped minutia from the minutiae extraction stage,usually this problem is caused by differences of user’s skincondition as well as pressure and position changes to the fin-gerprint reader. Next problem is non-linear distortions dueto non-uniform finger pressure and elastic characteristics ofthe skin. Any of fingerprint matching algorithms must dealwith above problems for achieving a good performance.

Especially for the distortion problem, various methodshave been developed in the literature. Jain et al. [4] usesampled ridge information and adjustable bounding box forfinding corresponding pair. However it is not an efficientmethod for large deformation errors since they basicallyconsider only the rigid transformation. Cappelli et al. [3]propose a mathematical deformation model for describingnon-linear distortion. However, since this model relatesnon-distorted with distorted fingerprints, it is not appro-priate to the purpose of fingerprint matching that usuallyneeds a relation between two distorted fingerprints. Actu-ally, the relation of two deformed surface is not simple todescribe as a mathematical model. Bazen and Gerez [1]applied a thin-plate spline (TPS) model to deform finger-prints in an iterative manner. However, there are no appro-priate constraints to control iterative warping procedures.Though their method significantly raises the scores of gen-uine matching, it raises the scores of imposter matching sothe false matched rate.

In this paper, we present a new fingerprint matchingmethod solving non-linear distortions. First of all, lo-cal neighborhood structures reliable to spurious as well asdropped minutiae are created for each of template and inputfingerprints. The input fingerprint is aligned to the templatefingerprint using this local structures. With transforminginput fingerprint from aligned location iteratively, matchedminutiae clusters are found. Then undistorted input finger-print is obtained by warping input fingerprint using match-ing clusters as control points. Finally, matching pairs areachieved using global matching strategy. For the score com-

The 18th International Conference on Pattern Recognition (ICPR'06)0-7695-2521-0/06 $20.00 © 2006

putation, an overlapped area between two bounding boxesof template and input fingerprint minutiae is considered inaddition to a summation of similarities from matched minu-tiae pair. The proposed method is intuitively natural sinceclustering local matches and combining the information ofthese clusters resembles human expert’s behavior.

2. The matching algorithm

In this section, we firstly explain the local neighborhoodstructure which is used in most algorithm stages. Next, wepresent detailed explanations of each functional part of theproposed method.

2.1. Local neighborhood structure

We contrive a local neighborhood structure for eachminutia, i.e. k-directional nearest neighbor (k-DNN). Thisstructure is invariant under translation and rotation, and re-liable on global deformation effects. The procedure of con-structing the k-DNN as follows: Arrange local coordinatewhich makes the ridge orientation as x axis, divide the planeto be k slots, and find the nearest neighbor (NN) for eachslot. One can avoid selecting spurious minutiae using min-imum distance threshold for selecting NN, and also distor-tion invariant properties can be given by maximum distancethreshold. For the kth NN, we encode the angle and dis-tance from the reference minutia and the orientation of NNas θk, dk and ϕk, respectively. In Figure 1, a square (blue),round (red) and cross (green) headed line represent a refer-ence minutia, a minutia selected NN for each slot and a re-maining minutia around k-DNN structure, respectively. Inthe left of the figure one can see a k-DNN example, and rightshows encoding parameters for the kth NN. We empiricallyset k = 8 for k-DNN in the experiment.

2.2. Alignment

After constructing k-DNN structures for all minutiae oftemplate and input fingerprints, alignment parameters is ob-tained by comparing these structures. For each k-DNNstructure of template fingerprint, a similarity is comparedwith each of the k-DNN structures of input fingerprint. Thesimilarity is computed by counting the number of the sup-port NN which is determined by checking differences ofeach component of kth NN. If the similarity is above thepre-defined threshold, transformation parameters and sim-ilarity for the current minutia correspondence are stored.The transformation is assumed to be the rigid transforma-tion and one set of the translation and rotation parameterscan be computed from one minutia correspondence pair bycomparing location and orientation. After comparing allpossible minutia pairs, we compute a total similarity for

2 / kπ2 / kπ

kθ

kϕ

kd

kθ

kϕ

kd

Figure 1. A k-DNN (left) and encoding para-meters for the kth NN (right).

each stored parameter. The total similarity is calculated assumming up the similarities of stored elements which fall onthe pre-defined bin sizes of reference transformation para-meters. Final alignment parameters are determined by find-ing the element having the maximum total similarity. Thislocal structure based alignment is significantly faster thanHough transformation based approach which searches thefull parameter space [9].

An alignment example is shown in Figure 2 (a). Inthis figure, template and input minutiae represented asround (red) and square (blue) headed lines, respectively, andbounding boxes of template and input minutiae are drawn inrectangles.

2.3. Minutiae clustering

In this stage, we find one minutiae cluster at one itera-tion step. After aligning the input fingerprint to the tem-plate, we firstly find minutiae correspondences by applyingpre-defined distance and angle bounds on the each templateminutia location. By means of discarding a number of iso-lated matching which is detected by checking connectiv-ity of k-DNN structure, we can obtain the largest numberof matched minutiae clustered in some region. This firstmatched minutiae group is called as cluster 1. We observethat it is hard to find minutiae pairs in the distance fromthe cluster region because the deformation effect is accu-mulated in the outside direction. From the observation thatthe local structure similarities between template and inputminutiae are also preserved at the unmatched region, the re-maining unmatched minutiae is aligned to the appropriateposition using the same method of previous section whileneglecting the minutiae of previously matched region. Thenan additional cluster is found by the same matching methodas above and named as cluster k in sequential order. Thisalignment-matching process is iterated until there’s no pos-sible clustered region. During finding clusters, a minutiamatching cost w ∈ [0, 1] is saved.


In Figure 2 (a) the result of minutiae clustering is super-imposed on the alignment configuration, where four clus-ters are obtained and represented in different colors. Onecan see all clusters are properly localized due to the rigor-ous connectivity check.

2.4. Warping

In the previous stage, we find clusters localized severalregions of fingerprint surface. Because there are still re-maining unmatched minutiae among cluster regions, morepossible correspondences can be found by warping inputfingerprint surface to the template using all matched pairson clusters. We use thin-plate spline (TPS) to model thefingerprint surface warping. The TPS model is a populartool which interpolates surfaces over given point correspon-dences and represents an analytic solution for minimizingbending energy of thin plates [2].

The fingerprint surface is interpolated exactly by follow-ing basic TPS equation [10],

Kw + Pa = v (1)

where K is basis function matrix, w defines an non-lineardeformation, a gives affine part of transformation, P andv are input and template minutiae location matrices respec-tively. However exact interpolation can distort fingerprintsurface erroneously by low reliable correspondences whichhave low minutia matching cost. To approximate the in-terpolation in vicinity of low reliable correspondences, wepropose to use the weighted regularization method as fol-lows,

(K + Λ)w + Pa = v (2)

where Λ = diag(λ1, λ2..., λn) is a regularization parame-ter matrix. Each λk defines a degree of surface smooth-ness at the kth correspondence, which is calculated fromthe minutia matching cost.

A warping example is showed in Figure 2 (b), the gridpattern represents undistorted surface of the input finger-print. One can observe the locations of template and inputminutiae are properly fitted.

2.5. Global matching and scoring

As the previous process warps the surface of input fin-gerprint to make similar shape of template one, smallerdistance bounds than that of clustered matching is appliedfor finding matched minutiae in the global matching stage.However more angle difference is allowed as the minutiaeorientation is not changed during warping. Though minu-tiae orientations can also be used for TPS warping [10], wedo not use them from the fact that the edge is more er-roneous than the corner. In addition, the isolated minutiachecking is not applied for global matching.

Cluster 2

Cluster 4

Cluster 1

Cluster 3

Cluster 2

Cluster 4

Cluster 1

Cluster 3

(a) (b)

Figure 2. An example of genuine matchingbetween 78 1 (template) and 78 6 (input) fromFVC2002 DB1 A.

For score computation, the following equation [1] iscommonly used,

s(T, I) =N2

P

N1N2(3)

where N1 and N2 are the numbers of template (T) and in-put (I) minutiae, respectively, and NP means the number ofmatched minutiae. However, the similarity also depends onan overlapped region of aligned fingerprints, so (3) is nota reliable model. A new score computation method is pro-posed which considers an overlapped area of two boundingboxes of template and input fingerprint as following,

s(T, I) =AO

min(A1, A2)

(SP

NO

)2

(4)

where AO, A1 and A2 are area of overlapped, template andinput minutia, respectively, SP =

∑NP

i=1 wi means the totalminutia matching cost, and NO is the number of minutiaein the overlapped region. In (4) the overall confidence levelis limited by AO/min(A1, A2), and for more robust mea-surements in the overlapped region NP , (N1N2) in (3) arechanged to SP , N2

O, respectively.

3. Experimental results

The proposed algorithm has been evaluated usingFVC2002 DB1 A database. The database consists of 800fingerprint images with 100 distinct fingers and 8 impres-sions per finger. We performed a total of 2,800 and 4,950comparisons for genuine and imposter matching, respec-tively, in accordance with the protocols of FVC2002 [6].The evaluation parameters used in this results are referred


to [5]. The comparative results of the proposed approach,two rigid matching methods and BOZORTH3 algorithmfrom NIST Fingerprint Image Software 2 [11] are presentedin Table 1 and Figure 3. The same minutiae extractionresults are applied to all tested algorithms for comparingthe performances of matchers only. The rigid matching 2uses the same functional parts as proposed approach with-out minutiae clustering and warping procedure. The rigidmatching 1 uses the identical procedure with rigid matching2 except using (3) for score computation. The BOZORTH3algorithm implicitly allowing non-linear distortion effectsduring traversing the inter-fingerprint compatibility table,detailed description to be referred in [11].

The result shows the proposed approach is performedbest among the all comparing algorithms, and BOZORTH3algorithm performed worse than rigid matching 1 which isour most simple approach. By comparing rigid matching1 and 2, we see that the better result is achieved using theproposed scoring method. An average matching time is 7.9ms for genuine matching tests and 2.5 ms for imposer caseson an Intel Pentium 4, 3.4 GHz machine. The imposter testis usually faster than the genuine test since the number ismatched minutiae is small and the count of cluster is belowone in most cases, so the warping stage is passed.

4. Conclusions

We have presented a new minutia-based fingerprintmatching method that incorporates three new ideas. Firstlythe new representation named k-DNN is defined to encodethe local neighborhood of each minutia. Next, the clusteredmatching method is presented which finds local invariantstructures the warping is used to describe entire surface de-formation. Lastly the new score computation method is pro-posed which uses the overlapped region of two boundingboxes. We showed that the proposed algorithm performedbetter than rigid transformation based fingerprint matchingmethods as well as NIST BOZORTH3 algorithm in exper-imental results. The proposed score computation methodprovides substantial performance improvement.

References

[1] A. M. Bazen and S. Gerez. Fingerprint matching by thin-plate spline modelling of elastic deformations. PatternRecognition, 36(8):1859–1867, 2003.

[2] F. Bookstein. Principal warps: Thin-plate splines and thedecomposition of deformations. IEEE Trans. Pattern Anal.Machine Intell., 11(6):567–585, 1989.

[3] R. Cappelli, D. Maio, and D. Maltoni. Modelling plastic dis-tortion in fingerprint images. In Proc. Int’l Conf. Advancesin Pattern Recognition, 2001.

Table 1. Results on FVC2002 DB1 AMethod EER FMR100 FMR1000

BOZORTH3 3.35% 5.25% 7.14%Rigid matching 1 2.03% 2.43% 4.18%Rigid matching 2 1.18% 1.21% 2.11%

Proposed 0.92% 0.93% 1.43%

0.001

0.01

0.1

1

0.00001 0.0001 0.001 0.01 0.1 1

FMR (False Match Rate)F

NM

R (

Fal

se N

on M

atch

Rat

e)

BOZORTH3Rigid matching 1Rigid matching 2Proposed

Figure 3. Comparative ROC curve.

[4] A. K. Jain, L. Hong, and R. Bolle. On-line fingerprintverification. IEEE Trans. Pattern Anal. Machine Intell.,19(4):302–314, 1997.

[5] D. Maio, D. Maltoni, R. Cappelli, J. L. Wayman, and A. K.Jain. FVC2000: Fingerprint Verification Competition. IEEETrans. Pattern Anal. Machine Intell., 24(3):402–412, 2002.

[6] D. Maio, D. Maltoni, R. Cappelli, J. L. Wayman, and A. K.Jain. FVC2002: Second Fingerprint Verification Competi-tion. In Proc. Int’l Conf. Pattern Recognition, volume 3,2002.

[7] D. Maltoni, D. Maio, A. K. Jain, and S. Prabhakar. Hand-book of Fingerprint Recognition. Springer-Verlag, 2003.

[8] R. M. McCabe. Data format for the interchange of finger-print information: ANSI/NIST-CSL-1-1993. American Na-tional Standard Institute, 1993.

[9] N. K. Ratha, K. Karu, S. Chen, and A. K. Jain. A real-time matching system for large fingerprint databases. IEEETrans. Pattern Anal. Machine Intell., 18(8):799–813, 1996.

[10] K. Rohr, M. Fornefett, and H. S. Stiehl. Approximating thin-plate splines for elastic registration: Integration of landmarkerrors and orientation attributes. In Proc. Int’l Conf. In-formation Processing in Medical Imaging, pages 252–265,1999.

[11] C. I. Watson, M. D. Garris, E. Tabassi, C. L. Wilson, R. M.McCabe, and S. Janet. User’s Guide to NIST FingerprintImage Software 2 (NFIS2). National Institute of Standardsand Technology, 2004.


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