Fngerprnt matchng based on weghtng method and SVM Ja Ja, Lanhong Ca, Pnyan Lu, Xuhu Lu Key Laboratory of Pervasve Computng (Tsnghua Unversty), Mnstry of Educaton Bejng 100084, P.R.Chna {jaja}@mals.tsnghua.edu.cn {clh-dcs}@tsnghua.edu.cn {lupnyan}@hotmal.com {lxh}@csnet1.cs.tsnghua.edu.cn Abstract. Fngerprnt verfcaton s an mportant bometrc technology. In ths paper, an mproved fngerprnt matchng approach that uses weghtng method and support vector machne (SVM) s presented. The tradtonal mnutae-based matchng task s transformed to a classfcaton task n the proposed approach usng SVM. Furthermore, a new weght feature s ntroduced based on the dstance between mnutae to supplement the mnutae nformaton, especally for fngerprnt mages of poor qualty. To gve an objectve assessment of the approach, both nternatonal and domestc fngerprnt verfcaton competton databases have been used for the evaluaton. Expermental results show substantal mprovements n the accuracy and performance of fngerprnt verfcaton. 1 Introducton Fngerprnt authentcaton s one of the most mportant bometrc technologes [1]. A fngerprnt s the pattern of rdges and valleys (furrows) on the surface of the fnger. In automatc fngerprnt verfcaton system (AFVS), the characterstc features obtaned from the test fngerprnt are to be matched aganst those from a template fngerprnt. As the fngerprnt of a person s unque and mmutable, the AFVS can be wdely used n both ant-crmnal and cvlan applcatons. Therefore, accuracy and performance mprovements are the key ponts n AFVS current research. The unqueness of a fngerprnt can be determned by the global pattern of rdges and valleys, and by the local pattern of bfurcatons and endngs whch are called mnutae (Fg 1). The mnutae are extracted from the thnned mage that s obtaned from fngerprnt preprocessng [2, 5, 6]. Usually, the smlarty between two fngerprnts s determned by computng the total number of matched mnutae, the process of whch s called mnutae-based [6]. However, general mnutae-based matchng algorthms (GMMA) n AFVS only make use of mnutae localzatons (postons and orentatons). 686
(a) Fg. 1. Examples of fngerprnt mnutae. (a) A rdge endng. (b) A rdge bfurcaton Our man work focuses on the mnutae-based matchng scheme. We present a fngerprnt matchng approach, whch uses not only the mnutae localzatons, but also a weght feature whch s the dstance between a mnuta and ts nearest neghbor mnuta. Consderng that the matchng process can be regarded as a two-class classfcaton problem (matched or not), usng the extracted mnutae postons, orentatons and weghts as features, we defne a vector standng for the smlarty of two fngerprnts, and choose SVM as the classfer. The proposed approach s motvated by the followng observatons: (1) The mnutae nformaton n fngerprnt mages may not be dscrmnatve because of the dfferent sensors and skn condtons. Most of the sensors especally capactve sensors capture only a small area of the fngertp, whch means some mnutae nformaton outsde the area s mssng. Further n practce, due to varatons n skn condtons lke postnatal marks or occupatonal marks, and mpresson condtons, a sgnfcant percentage of fngerprnt mages are n poor qualty. Ths leads to the problem that a large amount of errors n mnutae postons and orentatons may be ntroduced. In such cases, the weght based on two mnutae s dstance s not only an estmate of fngerprnt structure, but also a supplement for mnutae nformaton. (2) After gettng the total number t of matched mnutae, a judgment must be made: are these two mages matched? The normal method s to compare t wth a certan threshold λ, f t λ, then the two mages are matched, otherwse not. That means, the value of λ determnes the fnal concluson actually. In order to reduce the nfluence of evaluatng λ, the approprate way s usng a machne learnng technque to obtan the threshold for dfferent databases. In addton, SVM s a powerful classfcaton method whch can properly label the result wth matched or not. In summary, we present a fngerprnt matchng scheme that uses both mnutae localzatons and estmated weghts as features, transformng the matchng problem to a classfcaton problem and usng SVM to solve t. The experments wth both nternatonal and domestc fngerprnt verfcaton competton data show substantal mprovements n accuracy and performance of fngerprnt verfcaton. The rest of ths paper s organzed as follows: n secton 2 we gve the module analyss of GMMA. Secton 3 outlnes the problems of GMMA and the proposed soluton. In secton 4, our approach based on weghtng method and SVM s presented n detal. Before concluded wth dscussons, expermental results and analyss are gven n secton 5. (b) 687
2 Module analyss of general mnutae-based matchng algorthms All the GMMA [4, 5, 6] can be broadly classfed nto the followng stages: (1) extractng mnutae, (2) generatng the transformaton parameters that relate the test mage and the template mage, (3) algnng the two mages under these parameters to get the total number of matched mnutae, (4) determnng the fnal result accordng to the result of stage (3). Mnutae extracton: Most feature extracton methods are based on thnned mages. The mnutae are detected by tracng the rdge contours. Each mnuta s characterzed by ts locaton coordnate (x, y) and orentaton of the rdge on whch t s detected [3]. Generatng transformaton parameters: To ensure an overlap of common regons, the two mages need to be algned frst. Ths s done by determnng the transformaton parameters (t x,t y, ρ, θ), where t x,t y ndcate the adjustable dstances n x- axs and y-axs, ρ ndcates the flex coeffcent and θ ndcates the rotated angle. (t x,t y, ρ, θ) s computed by coordnates of two pars of mnutae (usually delta ponts and core ponts) from both mages [4]. These two pars of mnutae are called reference ponts. Algnng the test mage and the template mage: Once the transformaton parameters (t x,t y, ρ, θ) are obtaned, the test mage can be algned. Let (x, y) represent the orgnal coordnate, then the algned coordnate (u, v), s obtaned as Eq.1. u cosθ snθ x t x ρ v = + snθ cosθ y t y (1) After the mages are algned, the total number of matched mnutae can be computed. Result determnaton Due to the structures of fngerprnts themselves and the condtons of sensors, some fngerprnt mages do not have delta ponts or center ponts [5]. In such cases, every two pars of mnutae from test mage and template mage, as reference ponts, should be chosen to get the correspondng transformaton parameters (t x,t y, ρ, θ). For dfferent reference ponts, there wll be dfferent numbers of matched mnutae, and the maxmum number wll be compared wth a certan threshold λ to decde whether the two mages are matched. That means, f we adopt the method of exhauston, ths determnng process wll need an n 2 m 2 tmes of computng, where n and m ndcate the number of mnutae of the two mages. 3 Problem statement and soluton From the analyss of GMMA, we pont out three notceable problems: (1) fake mnutae do have a bad effect on the result. (2) the determnng process presented n Secton 2 wll hurt the algorthm performance. (3) an unsutable threshold λ wll lead to a wrong concluson. 688
3.1 Usng weghtng method to solve the problem of fake mnutae Fake mnutae are always from structures lke spacngs, brdges and pores (Fg 2(a)). Through observaton, we fnd an ntercommunty of these structures such that the fake mnutae on them are usually much closer to each other than real ones (Fg 2(b)). In other words, f the dstances between a mnuta and ts neghbors are very short, ths mnuta may be a fake one. (a) Fg. 2. Examples of fake mnutae. (a) the structures of spacng, brdge and pore. (b) agglomerate fake mnutae ponts marked by panes Therefore, to supplement mnutae nformaton, we defne a weght feature w besdes the mnutae localzaton. Defnton 1. A mnuta s weght w s the dstance between t and ts nearest neghbor mnuta. The value of w s normalzed n the [0 100] range. For a mnuta, the greater the value of ts weght w, the hgher the possblty of beng a real one. (b) 3.2 Usng rankng strategy to mprove performance As presented n Secton 2, for dfferent reference ponts, there wll be dfferent transformaton parameters and numbers of matched mnutae. Our experment shows that t wll take about 30 seconds to get the maxmum number of matched mnutae when usng exhauston algorthm. To reduce the number of operaton, we present a rankng strategy that sorts the mnutae by descendng order accordng to ther weghts w, and choose only the top 20 mnutae as the reference ponts. Ths strategy can reveal most of the real mnutae. And experment shows that the computng tme for matchng two mages can reduce to only about 0.5 second, whch means the performance s sgnfcantly mproved. 3.3 Usng SVM to solve the problem of result determnaton GMMA normally determne the fnal result by comparng threshold λ and the total number of matched mnutae t. That s a one-dmenson method usng two numbers, whch means the value of λ plays a key role n determnng the fnal result. To solve the problem of evaluatng the threshold λ, we present a method that uses a hyperplane and a set of matchng vectors whch stand for the smlarty of fngerprnts. That 689
means we transform the problem whch s hard to be solved n one-dmenson space to a multdmensonal space. Ths can be explaned clearly by Fg 3(a). A B l (a) (b) Fg. 3. Explanatons for SVM. (a)for crcles A and B, ther projecton to ether axs has superposton, but n two-dmensonal space, they are lnear- dvdable, whch means the lne l can dvde them. (b)an SVM s a hyperplane that separates the postve and negatve examples wth maxmum margn. The examples closest to the hyperplane are called support vectors Therefore, we choose SVM whch has shown outstandng classfcaton performance n practce as the classfer [7, 8]. SVM s based on a sold theoretcal foundaton structural rsk mnmzaton [9], and ts smplest lnear form s shown n Fg 3(b). Large margn between postve and negatve examples has been proven to lead to good generalzaton [9]. 4 A matchng scheme based on weghtng method and SVM Before matchng steps, fngerprnt preprocessng must be accomplshed frst. Here we use an enhancng algorthm based on estmated local rdge orentaton and frequency, and flter the mage by Gabor flter [2]. Our matchng approach ncludes the followng stages: 4.1 Extractng the mnutae features For each mnuta, we defne a 5-tuple (x, y, type, theta, w) to descrbe ts features. The x and y ndcate the mnuta s coordnate. The value of type, 1 or 2, ndcates that the mnuta s an endng or a bfurcaton. The theta ndcates the tangent angle of the rdge where the mnuta s located. And w ndcates the mnuta s weght. The 5-tuple (x, y, type, theta, w) s obtaned by the followng steps (Fg 4): Let I test represents the test mage, I temp represents the template mage. For I test and I temp : Step 1: Do mage normalzaton, estmate the local orentaton and frequency, flterng, and then get the threshold mage [2]. Step 2: Do rdge thnnng, and extract the coordnate (x, y) and orentaton theta of each mnuta. 690
Step 3: Compute the dstance between each mnuta and ts nearest neghbor mnuta as ts weght w. Step 4: Sort the mnutae by descendng order accordng to ther weghts w. That means, for each fngerprnt mage, we get a mnutae sequence p 1, p 2...p n wth degressve weghts. (a) (b) (c) Fg. 4. Fngerprnt mage preprocessng and mnutae extracton. (a)raw mage.(b)threshold mage.(c)thnned mage wth mnutae 4.2 Matchng the mnutae under the optmal transformaton parameters Let p 1, p 2...p n represent the mnutae sequence of I test and q 1, q 2...q n represent the sequence of I temp. We compute the total number of matched mnutae by the followng steps: Step 1: Choose the top 20 mnutae {p } (1 20) and {q j } (1 j 20) from the two sequences as the reference ponts. Step 2: For p, q j (1, j 20), f they have the same value of type, add (p, q j ) to set A. For every two members (p 1, q j1 ), (p 2, q j2 ) A, do Step3 to Step5. Step 3: Compute the transformaton parameters (t x,t y, ρ, θ) accordng to (p 1, q j1 ) and (p 2, q j2 ) by Eq. (1). Step 4: Select (t x,t y, ρ, θ) f ρ 1 > 0.1 or θ > π 3, skp Step5. Ths selecton ensures that the flex coeffcent ρ approxmates to 1 and the rotaton angle θ s less than π 3. Step 5: For p 1, p 2...p n, compute ther new coordnates and orentatons accordng to Eq. (1), then match them wth q 1, q 2...q m. Record the number of matched mnutae pars. When every two members (p 1, q j1 ), (p 2, q j2 ) A have been chosen to fnsh the Step3 to Step5, record the maxmum number of matched mnutae pars t and the correspondng translaton parameters (t x,t y, ρ, θ ). 4.3 Determnng the results usng matchng vector and SVM We defne a matchng vector V(n, m, t, ave, err) to descrbe the smlarty of I test and I temp. Ths vector V s obtaned by the next steps: 691
Step 1: Record the mnutae number n of I test and m of I temp, and maxmum matched mnutae number t. Step 2: For the matched mnutae pars, the weghts of the mnutae n I test are v, v,, v and n I 1 2 t temp are u 1, u 2,, u t. Let ave represent an average of the weght values of these matched mnutae, and ave s calculated by Eq.2. ave = 2 u v t = 1 u + v Step 3: Get a100pxel 100pxel sub-mage I sub from the center of the threshold mage of I test. Translate I sub by parameters (t x,t y, ρ, θ ) to I sub, and let err represent the number of pxels n I sub that have the same ntensty as ts correspondng pxel n I temp. The err descrbes an estmaton of the matchng error. For a matchng vector V(n, m, t, ave, err), we need to label t wth matchng success or matchng falure. The decson functon of an SVM s shown n Eq.3. f ( V ) = w V + b (3) w V s the dot product between w (the normal vector to the hyperplane) and V (the matchng vector). The margn for an nput vector V s yf( V ) where y { -1,1} s the correct class label forv. Seekng the maxmum margn can be expressed as mnmzng w w subject to y ( w V + b ) 1,. We allow but penalze the examples fallng to the wrong sde of the hyperplane. (2) 5 Experments and dscusson We conducted experments wth data of fngerprnt verfcaton compettons, to demonstrate the advantages of our proposed approach to fngerprnt verfcaton. 5.1 Datasets We have collected 5 datasets from FVC2002 1 (The Second Internatonal Fngerprnt Verfcaton Competton) and BVC2004 2 (Bometrcs Verfcaton Competton 2004). In order to prove the nfluence of dfferent mage qualtes to our matchng approach, 4 subsets of BVC2004 are chosen as db1 to db4. And db5, whch s a subset of FVC2002, s chosen to prove the nfluence of mage amount. The nformaton of each dataset, ncludng the number of dfferent fngers and total mages, sensor types, mage sze, etc. s shown n Table 1. 1 http://bas.csr.unbo.t/fvc2002/ 2 http://www.snobometrcs.com/chnese/conferences/snobometrcs%2704.htm 692
Table 1. The nformaton of datasets The source of the datasets dfferent fngers / total mages Sensors Image sze Resoluton 1 st db BVC2004 DB1 40/400 Optcal sensor 412 x 362 500 dp 2 nd db BVC2004 DB2 40/400 CMOS sensor 256 x 300 500 dp 3 rd db BVC2004 DB3 40/400 Thermal sweepng sensor 300 x 480 500 dp 4 th db BVC2004 DB4 40/400 Fngerpass 380 x 460 500 dp 5 th db FVC2002 DB1 230/1840 Optcal sensor 388 x 374 500 dp Each fngerprnt mage allows a rotaton angle that belongs to[ π 4,π 4] (compared wth the vertcal lne). Every two mages from one fnger have an overlap of common regon. But there may be no delta ponts or core ponts n some fngerprnt mages. 5.2 Experments setup We posed 2 experments. For db1 to db5, we compared our approach wth GMMA mentoned n Secton 2. Both of them use the same mage preprocessng algorthms [2]. Both the experments are done by the method of 5-folder cross valdaton, but have dfferences n the sze of test sets and tranng sets. Experment 1. For db1 to db4, 400 mages are dvded nto 5 parts, each of whch has 80 mages. Both the algorthms run fve tmes. For each tme, four of the fve parts are used as tranng sets (our approach only), and the other one part s used as test set. The averaged verfcaton result wll be reported over these 5 tmes. Experment 2. For db5, 1840 mages are dvded nto 5 parts, each of whch has 368 mages. Both the algorthms run fve tmes. For each tme, one of the fve parts s used as tranng set (our approach only), and the other four parts are used as test sets. The averaged verfcaton result wll be reported over these 5 tmes. We use SVMlght 3 for the mplementaton of SVM [8, 10], and take lnear kernel n experments. 5.3 Measures The accuracy and performance of a fngerprnt verfcaton algorthm can be measured by FNMR (False Non Match Rate: each sample n the subset A s matched aganst the remanng samples of the same fnger), FMR (False Match Rate: the frst sample of each fnger n the subset A s matched aganst the frst sample of the remanng fngers n A) and the average tme of matchng two mages. Especally for Experment 2, we also measure the maxmum memory sze of our approach. The confguraton of runnng computer s PIV1.0G, 256M DDR. 3 http://svmlght.joachms.org/ 693
5.4 Results and dscusson Table 2. Expermental results of db1 to db4 FNMR FMR Avg match tme Our approach GMMA (our approach) 1 st database 2.03% 6.67% 0 1.003 sec 2 nd database 12.78% 30.28% 0 0.603 sec 3 rd database 7.78% 24.17% 0 1.024 sec 4 th database 5.28% 13.05% 0 0.831 sec Table 3. Expermental results of db5 Our approach FNMR GMMA FMR Avg match tme (our approach) Max match Mem (our approach) 4.08% 13.84% 0.1% 0.583sec 6028 Kbytes Our approach GMMA 35.00% 30.00% 25.00% 20.00% 15.00% 10.00% 5.00% 0.00% db1 db2 db3 db4 db5 Fg. 5. Comparng the FNMR of our approach and GMMA n fve dfferent datasets The expermental results of db1 to db4 are shown n Table 2. We see that our approach really can acheve much better accuracy than GMMA for fngerprnt verfcaton, and the average tme for matchng a par of fngerprnts s also acceptable. As shown n Table 1, fngerprnts of these four datasets are captured by sensors of dfferent types. So the mages have dfferent qualtes. Ths strongly suggests that our feature extracton and SVM methods capture well the nformaton needed for fngerprnt verfcaton, and have a low nfluence by fngerprnt mage qualty. The expermental results of db5 are shown n Table 3. We see that although the proporton of tranng sets s reduced, and the number of test members s ncreased, our approach stll works better than GMMA for fngerprnt verfcaton. The average tme and the maxmum memory for matchng a par of fngerprnts are also acceptable. We thnk ths s because SVM makes effectve use of the matchng vectors to enhance classfcaton. 694
The expermental results of our approach and GMMA are compared n Fgure 5. It s clear that our matchng approach based on weghtng method and SVM outperforms GMMA consstently and sgnfcantly. 6 Concluson Our man contrbutons to fngerprnt verfcaton are: 1) transformng the tradtonal mnutae-based matchng task to a classfcaton task, and usng a powerful classfer SVM to solve t; 2) proposng a weght feature to supplement mnutae nformaton for fngerprnt mages of poor qualty. Future work may nclude: consderng use of TSVM (transductve SVM) [10] nstead of SVM to mprove the matchng accuracy and performance, because TSVM s especally benefcal when the number of tranng examples s small, and so forth. References 1. Newham, E.: The Bometrc Report. SJB Servces. New York (1995) 2. Ln, H., Yfe W., Jan, A.: Fngerprnt Image Enhancement: Algorthm and Performance Evaluaton. IEEE Transactons on Pattern Analyss and Machne Intellgence, Vol. 20, No.8 (1998) 3. Ratha, N.K., Chen, S., Jan, A.: Adaptve Flow Orentaton-Based Feature Extracton n Fngerprnt Images. Pattern Recognton, Vol.28, No.11 (1995) 4. Chongwen, W., Janwe, L.: Fngerprnt Identfcaton Usng Pont Pattern Matchng. Journal of Chongqng Unversty (Natural Scence Edton), Vol. 25, No.6 (2002) 5. Jan, A., Ln, H.: On-lne fngerprnt verfcaton. IEEE Transactons on Pattern Analyss and Machne Intellgence, Vol. 19, No.4 (1997) 302-314 6. Jan, A., Ross A., Prabhakar S.: Fngerprnt Matchng usng Mnutae and Texture Features. In: Internatonal Conference on Image Processng (ICIP). Thessalonk, Greece (2001) 282-285 7. Crstann, N., Shawe-Taylor J.: An Introducton to Support Vector Machnes. Cambrdge Unversty Press. Cambrdge, UK (2000) 8. Yuan, Y., Paolo, F., Massmlano P.: Fngerprnt Classfcaton wth Combnatons of Support Vector Machnes. Lecture Notes n Computer Scence, Vol. 2091. Sprnger-Verlag, Berln Hedelberg New York (2001) 253 258 9. Vapnk, V.N.: The Nature of Statstcal Learnng Theory. Sprnger-Verlag, Berln Hedelberg New York (2000) 10.Joachms, T.: Transductve Inference for Text Classfcaton usng Support Vector Machnes. In: Proceedngs of the 16th Internatonal Conference on Machne Learnng (ICML). Bled, Slovena (1999) 200-209 695