Fingerprint Matching Using Features Mapping

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1 Proceedings of the World Congress on Engineering nd Computer Science 204 Vol I WCECS 204, Octoer, 204, Sn Frncisco, USA Fingerprint Mtching Using Fetures Mpping Griel B. Iwsokun, Oluwole C. Akinyokun, nd Olumuyiw J. Dehino Astrct Fingerprint systems hve een feturing prominently mong Biometric identifiction systems for individuls. The dominnce of fingerprint is een promoted through continuous emergence of different forms of Automted Fingerprint Identifiction Systems (AFIS). In the course of performing its ssigned roles, n AFIS conducts severl ctivities including fingerprint enrolment, cretion of its profile dtse nd minutie enhncement which involves imge segmenttion, normliztion, Gor filter, inriztion nd thinning. The ctivities lso involve extrction of minutie, pttern recognition nd mtching, error detection nd correction nd decision mking. In this pper, fetures mpping pproch to fingerprint pttern recognition nd mtching is presented with the distnce etween the minutie nd core points used for determining the pttern mtching scores of fingerprint imges. Experiments were conducted using FVC2004 fingerprint dtse comprising four dtsets of imges of different sources nd qulities. Flse Acceptnce Rte (), Flse Rejection Rte () nd the Averge Mtching Time (AMT) were the sttistics generted for testing nd mesuring the performnce of the proposed lgorithm. Findings from the experimentl study showed the effectiveness of the lgorithm in distinguishing fingerprints otined from different sources. It is lso reveled tht the ility of the lgorithm to mtch imges otined from sme source is hevenly dependent on the qulities of such imges. Index Terms Fetures mpping, Pttern Mtching,,, FVC2002, Fingerprint F I. INTRODUCTION INGERPRINT is known to e n impression of the friction ridges of ll or ny prt of the finger. It is deposit of minute ridges nd vlleys formed when finger touches surfce. The extrcted ridges nd vlleys from fingerprint imge re shown in Figure with the ridges represented y rised nd drk portions while the vlleys re the white nd lowered regions. A fingerprint is clssified s n enrolled or ltent print []. An enrolled fingerprint my e otined when person is rrested for criminl ct. As prt of the investigtion process, the security gent such s police officer will roll the rrestee s fingertip in ink efore it is pressed on crd to otin the impression. The fingerprint crd is then stored in lirry of such crds. Mnuscript received July 2, 204; revised August 6, 204. This work ws supported in prt y the Tshwne University of Technology, under postdoctorl fellowship progrmme nd Ntionl Reserch Foundtion. Griel Iwsokun is with the Deprtment of We nd Multi-Medi, Tshwne University of Technology, Pretori, South Afric (Phone: ; e-mil: IwsokunGB@tut.c.z). Chrles Akinyokun is with Deprtment of Computer Science, Federl University of Technology, Akure, Nigeri (Phone: , e- mil: kinwole200@yhoo.co.uk). Johnson Dehino is with the Deprtment of We nd Multi-Medi, Tshwne University of Technology, Pretori, South Afric (Phone: ; e-mil: jdehino@yhoo.com). Enrolled fingerprints my lso e otined with modern dy fingerprint scnner [2]-[]. The most pproprite method for rendering ltent fingerprints visile, so tht they cn e photogrphed, is complex nd depends, for exmple, on the type of surfce involved. A developer, usully powder or chemicl regent, is often used to produce high degree of visul contrst etween the ridge ptterns nd the surfce on which the fingerprint ws left [], [4]. Whether enrolled or ltent fingerprint, there is n exclusive owner. This implies tht no two individuls including identicl twins possess sme fingerprints [5]-[6]. Fcts lso exist tht the ridges of individul finger never chnge throughout his or her lifetime regrdless of wht hppens. Even in cse of injury or mutiltion, they repper within short period. The five commonest fingerprint ridge ptterns re rch, tented rch, left loop, right loop nd whorl with exmples shown in Figure 2 [5]-0]. In the rch ptterns, the ridges enter from one side, mke rise in the center nd exit generlly on the opposite side. The ridges enter from either side, re-curve nd pss out or tend to pss out the sme side they entered in the loop pttern. In the right loop pttern, the ridges enter from the right side while the ridges enter from the left side in the left loop. In whorl pttern, the ridges re usully circulr round the core point. The core point of n imge is the point of mximum or minimum ridge turning where the ridge grdient is zero. Fingerprint hs proved to e very relile humn identifiction nd verifiction index which hs enjoyed superiority over ll other iometrics including er, nose, iris, voice, fce, git nd signture []. The mjor resons for these include vilility for ll individuls irrespective of rce, gender or ge nd vilility of esy, smooth opertionl nd chep fingerprint cpturing devices. Other resons include permnent form of pttern or structure over time is retined. Also, the distinct nd highly unique form of individuls fetures is permnently mintined. The components of fingerprints tht re mostly responsile for their high performnce in identifiction nd verifiction systems re ctegorized into three levels [], [2]. Level One component consists of the mcro detils, which include friction ridge flow, pttern type, nd singulr points. They re minly used for ctegorizing fingerprint imges into mjor pttern types. Level Two component includes minutie such s ridge ifurctions nd endings which show significnt vrition from one fingerprint to nother. Level Three components re the dimensionl ttriutes of the ridge such s ridge pth devition, width, shpe, pores, edge contour nd other detils including incipient ridges, creses, nd scrs. Level Two nd Level Three components re mostly used for estlishing fingerprints individulity or uniqueness. WCECS 204

2 Proceedings of the World Congress on Engineering nd Computer Science 204 Vol I WCECS 204, Octoer, 204, Sn Frncisco, USA Fingerprint pttern mtching is crried out when the need for scertining the exctness or vritions mong fingerprint imges rises. It involves the genertion of mtching scores y using the level one nd two components []. When fingerprints from the sme finger re involved, the mtching scores re expectedly high nd low for fingerprints from different fingers. In this study, n lgorithm for fingerprint pttern mtching sed on minuti nd core point direct distnce mesurement is developed. Section 2 presents the proposed lgorithm for fingerprint pttern mtching. The cse study of the enchmrk fingerprints is presented in Section. The findings from the cse study nd conclusion drwn re presented in Section 4. N(i, j) denotes the normlized gry level vlue t pixel (i, j), M i nd V i denote the estimted men nd vrince of the imge I respectively. The locl field orienttion is computed s follows: II. PROPOSED FINGERPRINT PATTERN MATCHING ALGORITHM A new method for generting fingerprints mtching scores using the sptil prmeters existing etween the minutie points is proposed. The motivtion ehind the lgorithm is the need to ddress the mtching prolems due to imge ridge orienttion nd size vritions. The lgorithm tke dvntge of the fct tht the reltive distnce to the core point from ech minuti point does not chnge irrespective of the imge directionl flow for given imge size. The core point is the point of mximum turning t which the grdient is zero. The core points re the points of mximum turning of the ridge structures in the two imges. They re lso the points where the directionl fields experience totl orienttion chnges [4] - [5]. Among the common feture points tht uniquely descrie fingerprint imge re ifurctions nd ridge endings [], [6]. Fig. illustrtes typicl interconnecting lines etween nine (9) minutie points leled A, B, C, D, E, F, G, H nd I nd the core point O in region of n imge. The connecting lines re in different directions with lengths proportionte to the distnces from point O to the connecting minutie points. nd re the grdients in the x nd y directions respectively nd nd re the locl ridge orienttion in the x nd y directions respectively for pixel (i, j). is the lest squre estimte of the locl ridge orienttion of the lock cntered t pixel (i, j). Soel verticl nd horizontl opertors of size w= re used to compute nd respectively. With imge size of w x w, the direction of grvity of the progressive locks (non-overlpping su-lock) is defined s follows with P = : I G H A F O B E C D (6) Fine tuning the orienttion field for corse core point detection y djusting orienttion using the following pseudo code: Procedure: Fig : Interconnecting lines etween feture nd core points The procedure for the proposed lgorithm is in the following phses:. Otin the core point using the following procedure [7]-[9]: The imge is normlized using eqution () where the lock size is of 6 6 pixels, M 0 = 50 ndv 0 = 50. WCECS 204

3 Proceedings of the World Congress on Engineering nd Computer Science 204 Vol I WCECS 204, Octoer, 204, Sn Frncisco, USA The core point is determined upon the detection of Direction of Curvture technique y pplying the following equtions: w= is the input lock size nd k=, l= re the pixel neighourhood sizes. nd re the difference of the directionl components in y nd x directions. The otined core point is then used s the centre of the cropping rectngulr size 00 x 00 pixels. The cropped re is defined s A II. The orienttion field is smoothened y converting to its corresponding vector field nd pplying low pss filter to A II. The optiml core point is derived from the ppliction of Geometry of Region technique with su-lock size of pixels nd rdius of 5 pixels.. Otin the x nd y coordintes for ll the true ifurctions nd ridge endings in the thinned imge. The Crossing Numer (CN) vlue for cndidte ridge ending nd ifurction is otined from [2], []: (7) (8) The numer of trnsitions from 0 to (T 0 ) long the order of M is counted in clockwise direction. The cndidte minuti point is vlidted s true ifurction if T 0 = s shown in Figure 9. For cndidte ridge ending point: All the pixels in the x neighourhood of the cndidte point re leled with. The numer of 0 to trnsitions (T 0 ) long the order of M is counted in clockwise direction. The cndidte minuti point is vlidted s true ridge ending if T 0 = s shown in Fig () () Fig. : 0 to trnsitions. () Bifurction (T 0 = () Ridge ending (T 0 =) c. The distnce, i etween the i th minuti point P i (r i,s i ) nd the imge core point M( ) is otined from: d. The degree of closeness for imge K with imge L is derived from: N, N 2,, N 8 represent the 8 neighours of the cndidte minuti point N, in its x neigourhood which re scnned in clockwise direction: Fig. 2 shows cndidte ridge pixel with CN vlue of 2 corresponding to ridge ending nd CN vlue of 6 corresponding to ifurction. f is the smller of the respective numer of feture points in the two imges, G(i) nd H(i) represent the distnce etween the i th minuti point nd the core points in K nd L respectively. e. The correltion coefficient vlue, S etween K nd L, is then computed s the pttern mtching score y using the formul: () CN=2 () CN=6 Fig 2: CN vlues for ridge ending nd ifurction points For the purpose of extrcting only vlid minutie from the imge, minutie vlidtion lgorithm proposed in [] is implemented. The lgorithm tests the vlidity of ech cndidte minuti point y scnning the skeleton imge nd exmines its locl neighourhood. An imge M of size W x W centered on the cndidte minuti point is firstly creted efore its centrl pixel is leled with 2. The remining pixels re initilised to zero. Then for cndidte ifurction point: The x neighourhood of the ifurction point is exmined in clockwise direction. The three pixels tht re connected with the ifurction point re lelled with the vlue of. The three ridge pixels tht re linked to the three connected pixels re lso leled with. From this formul, the closeness vlue will e = 0 for exct or sme imges nd, consequently, the mtching score will e S =. III. EXPERIMENTAL RESULTS The implementtion of the proposed fingerprint mtching lgorithm ws crried out using Mtl version 7.6 on Ms- Window 7 Operting System. The experiments were performed on Pentium GHz processor with.00gb of RAM. The experiments were conducted for the nlysis of the performnce of the proposed lgorithm when sujected to imges of vrious qulities. The experiments lso serve the sis for the genertion of metric vlues relevnt for the comprison of the otined results with results from relted works. The cse study of fingerprint imges otined from Fingerprint Verifiction Competition ws crried out. The fingerprints re in four dtsets DB, DB2, DB nd DB4 of FVC2004 fingerprint dtse [20] whose summry is presented in Tle I. WCECS 204

4 Proceedings of the World Congress on Engineering nd Computer Science 204 Vol I WCECS 204, Octoer, 204, Sn Frncisco, USA The dtse contins enchmrk fingerprints jointly produced y The Biometric Systems Lortory, Bologn, Pttern Recognition nd Imge Processing Lortory, Michign nd the Biometric Test Center, Sn Jose, United Sttes of Americ. Ech of the four dtsets contins 800 imges tht differ in qulities. The 800 fingerprints re mde up of 8 imges from 00 different fingers. The first two dtsets were cquired using n opticl fingerprint reder. The third nd fourth dtsets were cquired using Therml Sweeping nd computer softwre ssistnce respectively. TABLE I: DETAILS OF FVC2004 FINGERPRINT DATABASE Dtse Sensor Type Imge size Numer Resolution DB Opticl Sensor 640 x dpi DB2 Opticl Sensor 28 x dpi DB Therml- 00 x dpi Sweeping DB4 SFinGe v x Aout 500 dpi Flse Rejection Rte (), Flse Acceptnce Rte () nd Averge Mtching Time (AMT) were the indictors tht were mesured. is the rte of occurrence of scenrio of two fingerprints from sme finger filing to mtch (the mtching score flling elow the threshold) while is the rte of occurrence of scenrio of two fingerprints from different fingers found to mtch (mtching score exceeding the threshold). They were chosen eing the commonest indictors for mesuring the performnce of ny fingerprint pttern mtching systems []. The ws mesured y mtching ll the fingerprints from the sme finger while mesuring ws done through mtching every fingerprint of ech finger with ll fingerprints from the other fingers. The nd results otined for threshold vlue for the first two dtsets re shown in Tle II nd Tle III respectively. TABLE II: AND VALUES FOR DATASET DB Sttistics Vlue (%) 6.92 TABLE III: AND VALUES FOR DATASET DB2 Sttistics Vlue (%) 8.45 These results reveled tht for imges otined using opticl fingerprint reder, the proposed lgorithm produced of 0%. The impliction is tht the lgorithm successfully identified ll the fingerprints in the two dtsets tht were otined from different fingers. However, the otined vlues of 6.92% nd 8.45% present the extent to which the lgorithm filed to mtch fingerprints of the sme finger. The vlue of 9.07% is n indiction tht if the lgorithm were to e used in rel-life humn verifiction nd uthentiction scenrios with imges in Dtset DB, 6.92 out of 00 genuine ttempts will fil for the selected threshold. Similrly, 8.45 out of 00 genuine ttempts will fil sed on imges in dtset DB2. Some fctors which include vrition in pressure, rottion, trnsltion nd contct re during enrolment of the imges in the dtsets re responsile for these filure rtes nd their disprity []. These fctors constrined imges from the sme finger to differ in qulity, contrst nd noise level. Consequently, different mtching scores for different pirs of fingerprints of the sme finger. The otined nd vlues otined for the dtset DB re presented in Tle IV. The proposed lgorithm produced n of 0% nd n of 7.6%. The lgorithm lso recognized fingerprint imges cptured from different fingers using cpcitive fingerprint reder. However, vlue of 7.6% reveled the extent to which the lgorithm could not mtch sme finger imges in the dtset. TABLE IV: AND VALUES FOR DATASET DB Sttistics Vlue (%) 7.6 TABLE V: AND VALUES FOR DATASET DB4 Sttistics Vlue (%) 9.07 Dtset DB4 s nd vlues re shown in Tle V with vlues reveling tht the proposed lgorithm produced n of 0% for imges in dtset DB4 which mens unique identifiction of fingerprints cptured from different fingers using computer ids. The otined vlue of 9.07% indictes the degree to which the lgorithm could not mtch imges in dtset DB4 tht re from the sme finger. This lowest vlue of 6.92% recorded for dtset DB is ttriuted to superior qulity its imges. Visul inspection of fingerprint imges in the four dtsets (Fig. 4) revels tht imges in DB is est in term of clrity leding to etter enhncement nd extrction of predominntly true minutie points. Imge in DB Imge in DB2 Imge in DB Imge in DB4 Fig. 4: Selected imges from the four dtsets The highest vlue recorded for dtset DB4 lso implies tht the enhncement process is more dversely ffected y rtifcts rising from foreign ridges nd vlleys introduced inform of cross over, hole or spike structures into the imges during enhncement [2]-[]. The impct of these rtifcts is more pronounced s they misled the minutie extrction lgorithms into extrcting highest numers of flse minutie (ridge ending nd ifurction) points cross imges from sme finger therey cusing inequlity in minutie sets. The trend of the vlues of the four dtsets is represented y the stright-line grph of Fig. 5 WCECS 204

5 Proceedings of the World Congress on Engineering nd Computer Science 204 Vol I WCECS 204, Octoer, 204, Sn Frncisco, USA Fig. 5: The Trend of vlues for the four Dtsets Fig. 5 shows the pttern of vlues for the four dtsets in decresing order of 9.07, 8.45, 7.6 nd 6.92 for dtsets DB4, DB2, DB nd DB respectively. This order is in line with the fct tht dtset DB imges re the est in terms of qulity while those in dtset DB4 re the lest. In the overll, the proposed pttern mtching lgorithm recorded verge of 0% nd n verge vlue of 8.02% for the four dtsets. The verge mtching times in seconds nd their trend for nd for the four dtsets re presented in Tle VI nd the column chrt of Fig. 6 respectively. TABLE VI AVERAGE MATCHING TIME FOR THE FOUR DATASETS Dtset Averge Mtching time (sec) DB DB DB DB DB DB2 DB DB4 Dtset Fig. 6: Column chrt of the mtching completion for the four dtsets Dtset DB hs the lowest verge mtching time of 0.6 seconds nd verge mtching time of 0.69 seconds followed y DB, DB2 nd DB4 with verge : mtching time of 0.7:0.82, 0.79:0.88 nd 0.8:0.9 seconds respectively. The lowest verge mtching rte for dtset DB is ttriuted to fewest minutie points nd consequently, smllest numer of computtions. Similrly, the highest verge mtching times recorded for dtset DB4 indicte highest minutie points resulting in gretest numer of computtions. Tle VII presents otined nd vlues for four different lgorithms. The lgorithms presented in [2] [2] were selected for comprison ecuse they re mong the most recent. In Tle VII, the originl vlues otined y the uthors in [2] [22] re presented. However, we implemented the lgorithm proposed in [2] under the conditions of experiments in this reserch to otin the stted vlues DB 60 c d c d c d c d DB c DB 0 d DB4 Ref [2] Ref [22] Ref [2] Current Study Algorithm Fig 7: Colum Chrt of vlues for different fingerprint mtching lgorithms TABLE VII AND FOR DIFFERENT ALGORITHMS Perez-Diz, et l., 200, (Ref. [2]) (Peer, 200) Ref. [22] (Li et., 2009) Ref. [2] Current Study Dt DB DB DB DB c d Ref [2] Ref [22] Ref [2] Current Study The superior performnce of the proposed lgorithm over the other lgorithms is clerly exhiited with its lowest vlues for ll the dtsets. In ddition, it is the only lgorithm with n vlue of zero for ll the dtsets. The column chrts of Figures 7 nd 8 re sed on vlues presented in Tle VII. Tle VIII fetures the recorded computtion times (in seconds) for nd experiments in [22] [2] nd the current study. We lso implemented the originl lgorithm proposed in [2] under equl condition of experiments of the reserch to otin the stted vlues. For ll the dtsets, the proposed lgorithm hs the lowest computtion time, which confirms its gretest speed. Grphicl representtions of these vlues re presented in the column chrts of Figures 9 nd 0. c cd d Fig.. 8: Colum Chrt of vlues for different fingerprint mtching lgorithms Time (s) c c c c Time (s) Ref [22 Ref [2] Current Study DB DB DB2 DB2 DB c ddb DB4 DB4 DB DB2 DB DB4 Dtset Fig. 9: Colum Chrt of Computtion time for vlues for different fingerprint mtching lgorithms 5 4 Ref. [22] 2 Ref [2] Ref. [2] c c c c c c Current Study DB DB2 DB DB4 Dtset Fig. 0: Colum Chrt of Computtion time for vlues for different fingerprint mtching lgorithms c WCECS 204

6 Proceedings of the World Congress on Engineering nd Computer Science 204 Vol I WCECS 204, Octoer, 204, Sn Frncisco, USA AV. Ref.[2] Ref.[22] Ref.[2] Ref [28] Algorithm Ref [29] Ref 0] Fig. : Colum Chrt of Averge vlues for different fingerprint mtching lgorithms over the four dtsets AV. Comp Time (s) Ref. [22] Ref. [2] Algorithm Current Study Fig. 2: Colum Chrt of Averge Computtion time for nd vlues for different fingerprint mtching lgorithms over the four dtsets TABLE VIII MATCHING TIME IN SECONDS FOR DIFFERENT ALGORITHMS (Peer, 200) (Ref. [29]) (Li et., 2009) (Ref. [0]) Current Study Dt DB DB DB DB Fig. shows the column chrt of the verge sed on the dt presented in Tles VII over the four dtsets while Fig. 2 represents the column chrt of the verge nd computtion times sed on dt presented in Tle VIII. Visul inspection of the two Figures revels superior performnce of the proposed lgorithm hving recorded the lest heights in oth cses. IV. CONCLUSION AND FUTURE WORKS Current Study The implementtion of new fingerprint pttern mtching lgorithm hs een presented. The lgorithm used the reltive distnces etween the minutie nd the core points. The lgorithm hinged on the premise tht irrespective of imge orienttion, ech minuti point mintins constnt distnce with the core point for given imge size. The results otined showed the effectiveness of the lgorithm in distinguishing fingerprints from different sources with verge of 0%. However, the ility to mtch imges from sme source depends on the qulities of such imges. Since the corruption levels vry cross the used dtsets, the lgorithm yielded different vlues. The first dtset is mostly ffected with vlues of 22.2% while the third dtset is lest ffected with vlue of 4.5%. The sme order of performnce ws recorded for the nd the verge mtching time over the dtsets. A comprtive review of the otined, nd the computtion time vlues with wht otined for some recently formulted lgorithms over the sme dtsets reveled est performnce for the proposed lgorithm. Future reserch direction ims t the optimiztion of the proposed lgorithm for further reduction in the vlues nd the computtion times. REFERENCES [] S. Nnvti, M. Thieme nd R. Nnvti (2002): Biometrics, Identifying Verifiction in Networked World, John Wiley & Sons, Inc., pp [2] K. J. Anil, F. Jinjing nd N. Krthik (200): Fingerprint Mtching, IEEE Computer Society, pp [] H. N. McMurry nd G. Willims (2007): Ltent Thum Mrk Visuliztion Using Scnning Kelvin Proe ; Forensic Science Interntionl. [4] W. G. Eckert (996): Introduction to Forensic Science ; New York: Elsevier [5] FIDIS (2006): Future of Identity in the Informtion Society, Elsvier Inc. [6] D. Slter (2006): Thumprint An Emerging Technology, Engineering Technology, New Mexico Stte University. [7] J. Wymn, D. Mltoni, A. Jin nd D. Mio (2005): Biometric Systems ; Springer-Verlg London Limited [8] O. C. Akinyokun nd E. O. Adegeyeni (2009): Scientific Evlution of the Process of Scnning nd Forensic Anlysis of Thumprints on Bllot Ppers, Proceedings of Acdemy of Legl, Ethicl nd Regultory Issues, Vol., Numers, New Orlens [9] L. Yount (2007): Forensic Science: From Fires to Thumprints Chelse House Pulisher. [0] C. Roerts (2005). Biometrics ( newsroom/informtion-notes/2005/iometrics.pdf) [] G. B. Iwsokun, O. C. Akinyokun, B. K. Alese nd O. Olode. (20): Adptive nd Fster Approch to Fingerprint Minutie Extrction nd Vlidtion. Interntionl Journl of Computer Science nd Security, Mlysi, Volume 5 Issue 4, pp [] G. B. Iwsokun, O. C. Akinyokun, B. K. Alese nd O. Olode (20): A Modified Approch to Crossing Numer nd Post- Processing Algorithms for Fingerprint Minutie Extrction nd Vlidtion. IMS Mnthn Interntionl Journl of Computer Science nd Technology, Indin, Vol. 6 Issue, pp. -9 [4] L. Hong, Y. Wu nd J. Anil (2006): Fingerprint imge enhncement: Algorithm nd performnce evlution ; Pttern Recognition nd Imge Processing Lortory, Deprtment of Computer Science, Michign Stte University, pp. -0 [5] G. B. Iwsokun, O. C. Akinyokun, B. K. Alese nd O. Olode (202): Fingerprint Imge Enhncement: Segmenttion to Thinning, Interntionl Journl of Advnced Computer Science nd Applictions (IJACSA), Indin, Vol., No., 202 [6] G. B. Iwsokun (202): Development of Hyrid Pltform for the Pttern Recognition nd Mtching of Thumprints, PhD Thesis, Deprtment of Computer Science, Federl University of Technology, Akure, Nigeri. [7] J. Atipt nd S. Choomchuy (2007): An lgorithm for fingerprint core point detection, , Vol 7, Issue 2007, IEEE [8] J. N. Kur nd A. Kmr (20): A Novel Method for Fingerprint Core Point Detection, Interntionl Journl of Scientific & Engineering Reserch, Vol. 2, Issue 4, April-20. [9] A. M. Usmn, A. Triq nd S. A.. Khn (2008), Fingerprint imge: pre- nd post- processing, Interntionl Journl on Biometrics, Volume. [20] D. Mio, D. Mltoni, C. R.Wymn. nd A. K. Jin, "FVC2002: Second Fingerprint Verifiction Competition," in 6th Interntionl Conference on Pttern Recognition, 2002, 2002, pp [2] A. J. Perez-Diz. nd I. C. Arronte-Lopez (200): Fingerprint Mtching nd Non-Mtching Anlysis for Different Tolernce Rottion Degrees in Commercil Mtching Algorithms, Journl of Applied Reserch nd Technology, Vol. 8, No. 2, pp [22] P. Peer (200): Fingerprint-Bsed Verifiction System A Reserch Prototype, IWSSIP 200-7th Interntionl Conference on Systems, Signls nd Imge Processing, pp [2] T. Li, C. Ling nd K. Sei-ichiro (2009): Fingerprint Mtching Using Dul Hilert Scns, SITIS, pp WCECS 204

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