2004 A O Not Such a Small Whorl After All

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1、NotSuchaSmallWhorl245NotSuchaSmallWhorlAfterAllBrianCamleyPascalGetreuerBradleyKlingenbergUniversityofColoradoatBoulderBoulder,COAdvisor:AnneM.DoughertySummaryFingerprintidentificationdependsontheassumptionthataperson'sfin-gerprintsareunique.Weassessthetruthofthisassumptionbycalculatingtheto

2、talnumberofdistinctfingerprints.Weassumeaccuratefingerprints(ignoringproceduralerror)thatarede-finedby12pointsofdetailorminutiae.Thenumberofdistinctfingerprintsdependsalsoonthenumberofpotentialpositionsoftheseminutiae.Twohis-toricalmethodsandageometricanalysisestimatetheretobe1,400positions,

3、afigureconfirmedbyouralgorithmforcountingridgesinafingerprint.Wecreatetwomodelstoestimatethenumberofuniquefingerprints:*Onemodelcomputesfingerprintsasarrangementsinminutiae;*theotherextrapolatesthenumberoffingerprintsfromtheShannonentropyoftheinformationthatdefinesafingerprint.Thesetwomodels

4、agreetowithinanorderofmagnitudethatthereare5x1033uniquefingerprints,acompellingvalidationofourgeneralapproach.Tohandlethelargenumberoffingerprints,weimplementanapproximationforthecalculationofprobabilities.Givenacumulativeworldpopulationof120billion[Catton2000],theprobabilityoftwopeopleeverh

5、avingthesamefingerprintis1.4x10-6.Theprobabilityoftwohumanslivingtodaysharingafingerprintis3.5x10-15,whichsuggeststhatfingerprintsareatheoreticallymorereliablemethodofidentificationthanDNAanalysis,whichhasafalsepositiveprobabilityof10-9.Noneofthesecalculationstakeintoaccountproceduralerrors.

6、TheUMAPJournal25(3)(2004)245-258.®Copyright2004byCOMAP,Inc.Allrightsreserved.Permissiontomakedigitalorhardcopiesofpartorallofthisworkforpersonalorclassroomuseisgrantedwithoutfeeprovidedthatcopiesarenotmadeordistributedforprofitorcommercialadvantageandthatcopiesbearthisnotice.Abstractingwithc

7、reditispermitted,butcopyrightsforcomponentsofthisworkownedbyothersthanCOMAPmustbehonored.Tocopyotherwise,torepublish,topostonservers,ortoredistributetolistsrequirespriorpermissionfromCOMAP.246TheUMAPjournal25.3(2004)IntroductionThepossibilityofdupl