IJCSS Inernonl Journl of Copuer Scence nd ewor Secur, VOL.6 o.3, Mrch 006 97 Fngerprn Regsron Usng Cenrod Srucure nd Lne Segens Deun Zho, Fe Su nd nn C ejng Unvers of Poss nd elecouncons, School of elecouncon ngneerng, ejng 00876, P.R.Chn Sur In hs pper novel dsoron-olern fngerprn regsron ehod sed on cenrod srucure vecor (CSV nd Vecor Lne Segen (VLS, s proposed. In hs ehod, nu feures of he uer fngerprn re clusered no vrous clusers nd se of VLS s erced. Severl lel rnsforons eween he uer nd he eple ges re esed usng VLS ses. hen, CSV under ech lel rnsforon s consruced usng he cenrods of nu clusers. he fne rnsforon s fnll deerned he nuer of VLS prs ogeher wh he slr level of CSV. peren resuls show h hs lgorh s n effecve nd effcen one for lgnng fngerprns wh sll nuer of nu nd hev dsorons. Such suons re ofen encounered n forensc pplcons. Ke words: Fngerprn, Regsron, Cluserng, Mnu. Inroducon Fngerprn regsron ens o recover he geoerc rnsforon eween wo fngerprn ges (he uer nd he eple ges o lgn he wo fngerprns nd her feures, nd s n porn sge n os of fngerprn chng lgorhs []. lhough here es soe orenon feld (OF-sed [] nd eure-sed [] fngerprn regsron ehods, os of fngerprn chng lgorhs h provde rel-e processng nd hgh codence re so fr sed on nue regsron. he jor reson for he wde usge nd populr of he nue-sed regsron s h he nue of fngerprn re he os dscrnng nd relle feures [3, 4]. he nu erced fro fngerprn ge cn e chrcerzed ls of rues h ncludes: ( he pe of nu (endng or furcon, ( he nu poson, (3 he nu drecon whch s defned s he ngle h he rdge ssoced wh he nu es wh he horzonl s [5], (4 he locl srucure coposed of he neghorng nue, (5 he glol srucure consruced ll nue. Mnu-sed regsron s dffcul prole for he followng resons: he posons nd orenons of he nue e chnged due o he effec of pressng conve elsc surfce (he fnger on fl surfce (he sensor. he overlpped res eween wo fngerprns (for eple Len nd enprn Iges e dsconnecve. Soe genune nue e ssed nd soe spurous nue e presen. nuer of pproches for nu-sed regsron hve een proposed n he lerure. hese nclude ehods sed on reference nu pr [5, 6, 7] nd on locl srucure pr [8, 9, 0]. In [6] nd [7], he nu pr h resuls n he u nuer of he chng prs s chosen s he reference pr. he uhors repored good perfornce. However, he nuer of chng prs oned cn no e consdered relle ecuse he genune nue no hve counerpr nd he spurous nue hve few counerpr due o deforon of he fngerprns nd defecs of he feure ercon lgorh. he ehod proposed co nd Kuosnen [5] uses he nu pr h ehs he lrges possl vlue o ese geoerc rnsforon. In [8] nd [9], he es-ched srucure pr serves s he correspondence of he wo fngerprns. However, we cn rgue h he locl srucure s no well dsnc feure ecuse s deerned onl sll suse of he nue. he locl srucure hve n slr srucures n he e ge nd spurous srucure pr ecoe he es-ched srucure pr. In [0], he rnsforon preer s esed cluserng nd lso onl sed on he locl srucure. hs pper presens novel nu-sed fngerprn regsron ehod whch e oh locl srucures (vecor lne segens nd he glol srucure (cenrod srucure no ccoun. s he nue of he uer ge hs wor s suppored he onl url Scence Foundon of Chn under grnd 6047069 Mnuscrp receved Mrch 5, 006. Mnuscrp revsed Mrch 30, 006.
98 IJCSS Inernonl Journl of Copuer Scence nd ewor Secur, VOL.6 o.3, Mrch 006 re clusered ccordng o he dsnce eween nue, se of vecor lne segens, ech of whch s coposed of wo nue fro one cluser, s frs consruced. Severl lel rnsforons eween he uer nd eple fngerprns re esed sed on he pred vecor lne segens (one-o-n ppng possl. he cenre of he cluser, n whch ech nu hs correspondng nu n he eple fngerprn, s hen clculed nd used o consruc he Cenrod Srucure Vecor CSV. he nuer of vecor-lne-segen prs wh he se rnsforon preer ogeher wh he slr level of CSV fnll deernes he glol geoerc rnsforon preer. lhough he sep of rnsforon preer cluserng n our ehod s slr o h of Gern e l [0], he conon of VLS nd CSV oll dfferen fro he locl srucure used Gern e l. es our lgnen lgorh unue nd rous. Due o nec ercon of nu posons nd nonlner deforons, he regsron lgorh should e cple of olerng, o soe een, he deforons. Usull, such n elsc regsron cn e cheved plcng oundng o round ech eple nu, whch specfes ll he possle posons of he correspondng eple nu wh respec o he uer nu []. hs ehod does no provde ssfcor perfornce n prcce, ecuse locl deforons e sll whle he ccuuled glol deforons cn e ue lrge. In [], n dpve oundng o s eploed o copense he nu loclzon errors nd nonlner deforons. In our regsron lgorh, under he glol rnsforon group of locl rnsforon preers s lso genered for correspondng feure cluser prs. Dfferen oundng oes wll e used he locl nd glol rnsforons. he pper s orgnzed s follows. In secon, 3 dels endn o he Cenrod Srucure Vecor nd Vecor Lne Segen re descred. he regsron lgorh s descred n secon 4. Secon 5 gves he eperenl resuls, nd dscussons re presened n secon 6.. Cenrod Srucure Le F e se of nue whch consss of F,,,M. nu F erced fro fngerprn ge cn e descred feure vecor FV wh poson p (, nd locl rdge dreconφ : FV ( p (,, φ ( o splf he descrpon of our lgorh, we defne funcon Su ( φ, φ for he dfference eween wo ngles, φ nd φ, π φ, φ < π,s follows: ( φ φ od( π ep ep, f π < ep π ( Su( φ, φ ep + π, f ep π π ep, f ep > π he se of uer nue, F, s frs clusered no severl feure clusers (Fgure FC,,,,. he cluserng ehod used here s Herrchcl Cluserng Mehod. he cenrod C of FC s defned s: C ( p (,, φ FV (3 FV FC where s he nuer of nue n FC nd FV s he feure vecor of nu fro FC. cenrod srucure s llusred n Fgure d, nd s descred edge d j, rdl ngle θ nd rdge drecon j ϕ eween wo j cenrods. d, j θ nd j ϕ re clculed usng X.D.Jng s j [9] euons (3, 4, 5 respecvel. Cenrod Srucure vecor CSV s defned s: CSV ( cv, cv3, Lcvj, Lcv, < j (4 cvj ( dj, θj, ϕj, j,, L Le CSV ( nd CSV ( denoe wo CSVs fro he uer fngerprn nd eple fngerprn respecvel. Le D denoe he u dsnce whch wo chng edges re llowed o dffer n her uclen dsnce. Le Φ denoe he u llowed dfference n roon ngle. We use he followng forul o evlue he slr eween wo correspondng CSVs : CsvDs(, Dcvj Dcvj (5 csv, j j d d θ θ ϕ ϕ Dcv (,, D Φ Φ where s he nuer of eleens of he CSV. csv If ech nu n one feure cluser FC fro he uer fngerprn hs correspondng nu n he feure cluser FC fro he eple fngerprn, FC nd FC re correspondng feure cluser pr nd he cenrod C of FC nd cenrod C of FC re he correspondng cenrod pr. wo cenrod srucures fro wo ges of he se fnger wll e slr. Copred wh he drecl consruced glol srucure usng ll nue, he cenrod srucure s spler. s resul, he slr level copuon eween wo CSV s speed.
IJCSS Inernonl Journl of Copuer Scence nd ewor Secur, VOL.6 o.3, Mrch 006 99 where, d nd ϕ θ re hresholds for dsnce, nu drecon nd rdl ngle respecvel. he dsnce eween VLS ndvls s hen defned s follows, whch s lso used o evlue he slr level eween he wo VLSs: d ϕ θ VlsDs(, ( + ( + ( (7 Φ Φ D Fg. he nu cluserng nd CSVs. ( he orgnl nu se. ( he nu feure clusers. (c he cluser ceners. (d he cenrod srucure If ech nu n one feure cluser FC fro he uer fngerprn hs correspondng nu n he feure cluser FC fro he eple fngerprn, FC nd FC re correspondng feure cluser pr nd he cenrod C of FC nd cenrod C of FC re he correspondng cenrod pr. wo cenrod srucures fro wo ges of he se fnger wll e slr. Copred wh he drecl consruced glol srucure usng ll nue, he cenrod srucure s spler. s resul, he slr level copuon eween wo CSV s speed. 3. Vecor Lne Segen Defnon : In he recngulr coordne sse f wo nue fro he se feure cluser, re pr dsnce D nd Dn D D, hs wo nue fors lne segen, or LS. Vecor Lne Segen VLS slr o he nu locl srucure wh -neres neghor n [9], cn e descred wh he relve dsnce d, nu drecon ϕ nd rdl ngle θ eween wo nue (see Fg. _ Suppose h here re VLS consruced wo nue F nd F fro he uer fngerprn nd VLS consruced wo nue F nd F fro he eple one. wo VLSs re correspondng pr f he followng relons re ll ssfed, d s( VLS. d VLS. d ϕ s( su( VLS. ϕ, VLS. ϕ < θ s( su( VLS. θ, VLS. θ < < d θ ϕ (6 Fg. he vecor lne segen. Suppose P s he rnsforon reled o wo correspondng VLSs fro he uer fngerprn nd he eple fngerprn respecvel. P s represened 3- uple P (, Δ, Δ nd clculed ( su ( F + su ( VLS Δ (( F ( F Δ (( F.. θ, VLS. ϕ, F.. ϕ + su ( F. θ cos( sn( cos( + ( F.. sn( / Defnon : Suppose h here re correspondng VLS pr wh rnsforon P (, Δ, Δ nd noher correspondng VLS pr wh rnsforon P (, Δ, Δ. We hn h s conssen wh f he followng foruls re ll ssfed, s( < Δ θ s( Δ Δ < (9 f (,, (( F f (,, (( F Δ s( Δ Δ < Δ. / 3 /.. ϕ, F. ϕ where Δ (,,, Δ (,,, Δ,, nd Δ,,. ( (, Δ nd Δ re hresholds. Lne Segens re he locl srucures used n our lgnen lgorh. Generll speng, he ore nue locl srucure conns, he ore dscrnve (8
00 IJCSS Inernonl Journl of Copuer Scence nd ewor Secur, VOL.6 o.3, Mrch 006 oron hs. However n cse h here re few (e.g. less hn 5 nue erced fro he fngerprn ge, or here re spurous nue genered fro poor-ul ges, whch re ofen encounered suons for len fngerprn ges, choosng locl srucure wh onl wo nue e good lernve. VLS s sple nd ndependen fro roon nd rnslon of he fngerprn. he deforon of he lne segen s no serous snce VLS consss of nue fro sll re. lhough wo fngerprns fro dfferen fngers hve n slr VLSs due o her sple srucure, n of he locl srucure correspondences wll genere he se rnsforon preers nd ccuule lrge nuer of voes for he hpoheszed ch onl when genune ch ess. In oher words, onl when wo fngerprns re fro he se fnger, n correspondng VLS prs wll hve conssen rnsforons. In our lgorh, he os lel rnsforon wll e cured rnsforon preer cluserng slr o Gern s [0]. 4. Regsron lgorh Frsl, we ese se of rnsforon preers eplong he conssenc of VLS prs. hen, we fnd he os possle rnsforon of wo fngerprns ng he slr level of wo CSVs no ccoun. he seps of our regsron lgorh re gven elow: Consrucng he uer VLS se: Le f nd f denoe he nuer of es nue nd j hve j een seleced respecvel. S s he se of VLS fro he uer fngerprn. s he nuer of eleens vls of S. M s he nuer of nue erced fro he uer fngerprn. Sep : vls 0 For M { f 0} f nd 80 Sep : For M { If ( f < f nd vls < { For j M { If ( f j < f nd ee defnon nd VLS S { dd VLS o ses S ; f + ; f j j + ; vls vls + }}}} Sep 3: f ( f > 6 or vls > { Goo Sep4} lse { f + ; Goo Sep } Sep 4: end Serchng for correspondng VLS prs: Le S e he se of VLS fro he eple fngerprn. S s he se of VLS h corresponds wh he VLS. s he pre-specfed u nuer of he eleens n S. 3 sng se S r of rnsforons: Suppose we hve correspondng VLS pr <, >, S, nd S. Le S denoe se of correspondng Con VLS prs conssen wh <, > ccordng o Defnon, e he nuer of VLS n S nd Con e he nuer of correspondng VLS prs. oe h e greer hn snce one VLS gh hve nuer of correspondng VLS s n S. hen he rnsforon (, Δ, Δ of S Con cn e clculed Δ θ Δ Δ θ Δ (0 Δ Δ where Δ (, nd Δ (,. nd score s ssgned o he ove rnsforon he followng euon: rn _ Score w + w ( where w nd w re he weghs of nd respecvel. We choose he op rnsforons r ccordng o rn_ Score on descen order o for se S. r For ll S { 0 For ll S { If <, > s correspondng pr { If < {dd o S + } lse Gven nd S VlsDs (, M{ VlsDs (, S } { f VlsDs(, > VlsDs(, {Replce wh } }}}
IJCSS Inernonl Journl of Copuer Scence nd ewor Secur, VOL.6 o.3, Mrch 006 0 4 sng he rnsforon of wo fngerprns usng CSV wo nds of oundng oes wh dfferen szes re used n hs sep o olere, o soe een, he deforons:. For ech rnsforon S, f nu r F fro he uer feure cluser FC hs ched nu F n he eple fngerprn whn corse oundng o, clled he glol oundng o, F s dded no he eple feure cluser FC, oherwse F s reoved fro FC. Repe unl no nu cn e dded nd e reoved.. he corse cenrods C of he uer feure cluser FC nd C of he eple feure cluser FC, re copued respecvel usng euon (3. Under he locl rnsforon defned cenrod pr < C, C > nd wh he fne locl oundng o repe he sep.. Respecvel consruc CSV nd CSV usng he uer feure clusers nd he eple feure clusers oned n sep. he rnsforon score Fgrn_ Score of he wo fngerprns wll e deerned rn_ Score of nd CsvDs (, ogeher. he fnl rnsforon fg of he wo fngerprns s he S h hs he u r Fgrn_ Score. hn wo genune nue n sll re. Fg.3 shows wo such eples. erl hlf of he fngerprn ges n IS SD7 hve less hn 5 nu nd os of he hve hev deforons. such crcusnces, vsul nspecon showed h for IS SD7, onl wo lgnens,.e. 0.7%, gven he proposed lgorh re wrong. hs ehs s dvnges. 6. Conclusons novel echnue of fngerprn regsron hs een presened usng cenrod srucure vecor nd vecor lne segen n hs pper. he use of oh he locl nd glol rnsforon preers es our lgorh e le o olere, o soe een, he nonlner deforon. he prr dvnge of hs pproch s s good perfornce under wde vre of crcusnces. In prculr, s rous o lgn fngerprns wh sll nuer of nue h re dsrued n lrge re of he fngerprn ge. 5. perenl Resuls he eperens repored n hs pper hve een conduced on D, D fro FVC00 copeon [3] nd IS Specl Dse 7(IS SD7. D nd D re cpured usng n opcl sensor nd conn 0 unue fngers, wh 8 pressons of ech fnger respecvel. he evluon ses conss of,800 genunel chng prs nd 4,950 non-chng prs respecvel. IS SD7 conns len fngerprns fro cre scenes nd her chng rolled fngerprn es. In ll here re 58 len cses. he resuls of our lgnen lgorh re copred o hose of lgnen lgorh sed on reference nue pr (RMP slr o H.Roser s [7]. le gves he lgnen sscs. he pleenon of our lgorh wh VC6.0 hs n verge copuonl e of 0.003 sec for he lgnen sep on.0 GHz PC. I s cler h he perfornce of our lgorh s eer hn h of RMP. oe h when here re few (e.g. less hn ffeen nue scered n lrge re, ercng VLSs s eser hn consrucng locl srucures connng ore Fg. 3. nd. nd. nd. re wo eples of ge pr fro he se fnger. he spurous nd ssng nue re red lue nd red respecvel.. le : Perfornce coprson Correc re of Dse lgnen (% verge es (s lgorh ours RMP ours RMP IS SD7 99.3 93.6.6 3. D 99.8 95.4.8 3.5 D 99.6 95.9.8 3.5
0 IJCSS Inernonl Journl of Copuer Scence nd ewor Secur, VOL.6 o.3, Mrch 006 References []. Yger,. n, vluon of Fngerprn Orenon Feld Regsron lgorhs, I Proc.7h Inernonl Coerence on Pern Recognon (ICPR 04 05-465,004. [] D. Zho, F. Su,. C, Herrchcl Fngerprn Mchng Mehod sed on Roon Invrn, Proc. 5h SIOIOMRICS 004, LCS 3338,498-505,004. [3] Federl ureu of Invesgon, he Scence of Fngerpns: Clssfcon nd Uses, Wshngon,D.C: GPO, 984. [4] H.C. Lee nd R.. Gensslen, ds., dvnces n Fngerprn echnolog, ew Yor:lsever,99. [5] M.co P.Kuosnen, Fngerprn chng usng n orenon-sed nu descrpor; Pern nlss nd Mchne Inellgence, I rnscons on, Volue: 5,Issue:8, ug. 003.5. H.C. Lee nd R.. Gensslen, ds., dvnces n Fngerprn echnolog, ew Yor:lsever,99. [6].Jn nd.ross, Fngerprn Moscng, I Proc. Inernonl Coerence on couscs, Speech, nd Sgnl Processng (ICSSP, Orlndo, Flord, M 00. [7] H.Roser,.Wchnn, H.schof, ffcen lgnen of fngerprn ges, Pern Recognon, Proc. 6h Inernonl Coerence, Vol.3, pp:748-75 ug. 00. [8].K.Rh, R.M.olle, V.D.Pnd, V.Vsh, Rous fngerprn uhencon usng locl srucurl slr, I Worshop Ffh pplcons of Copuer Vson, pp: 9 34,Dec. 000. [9] X.D.Jng nd W.Y.Yu. Fngerprn Mnue Mchng sed on he Locl nd Glol Srucures, I 5h Inernonl Coerence on Pern Recognon, :04-045.Sepeer 000. [0] Gern e l., Fngerprn Mchng Usng rnsforon Preer Cluserng, I CS, Ocoer- Deceer 997 (Vol. 4, o. 4 pp. 4-49. []. Rh, S. Chen, nd.k. Jn, dpve Flow Orenon sed Feure rcon n Fngerprn Iges, Pern Recognon,vol. 8, no., pp.,657-,67, 995. [] nl Jn, Ln Hong, nd Ruud olle, On-Lne Fngerprn Verfcon, I rnsons On Pern nlss nd Mchne Inellgence, VOL. 9, O. 4, PRIL 997. [3] FVC00, hp://s.csr.uno./fvc00/, oveer 003. Su Fe receved he Ph.D. n he School of elecouncons, ejng Unvers of Poss nd elecouncons (UP, Chn, n 000. She s currenl n ssoce Professor n UP. Her reserch neress nclude pern recognon, ge processng nd uled councon. She hs pulshed ore hn 0 ppers. nn C receved he.s. degree n rdo engneerng fro ejng Unvers of Poss nd elecouncons (UP, ejng, Chn, n 965. She receved he Ph.D. degree n elecrcl nd copuer engneerng fro Unvers of Clforn, Sn rr, C., US n 988 Snce 965, she hs een on he fcul of School of elecouncon ngneerng, UP, where she s presenl professor. She ws vsng scholr Clforn Se Unvers, Long ech, C., US fro 980 o 98. She hs co-uhored ore hn 50 journl ppers nd four oos. Her curren neress re n he felds of ge nd vdeo processng, pern recognon nd uled elecouncons Deun Zho receved he.s. nd M.S. degree n rdo engneerng nd elecouncon engneerng he school of oron scence nd engneerng fro Lnzhou Unvers, LnZhou, Chn, n 996 nd 003 respecvel. He hs een receved he Ph.D. course n pern recognon nd uled elecouncons he School of elecouncon ngneerng fro ejng Unvers of Poss nd elecouncons (UP, ejng, Chn. Hs n reserch neress re n he felds of ge processng, pern recognon nd uled elecouncons.