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FingerprintImage Enhancement? Algorithmand

P erformanceEv aluation

Lin Hong?YifeiW an?and AnilJain

P atternRecognition andImagePro cessingLab oratory

Department of ComputerScience

Mic higanState Univ ersity

EastLansing?MI?????

fhonglin?wan yifei?jaing?cps?msu?edu

Abstract

A critical step inautomatic ?ngerprint matching istoautomatic ally andr eliably extract

minutiae fr omtheinput ?ngerprintimages? However?thep erformance ofa minutiaeex?

traction algorithmr eliesheavily on thequalityofthe input ?ngerprintimages?In order to

ensure that thep erformance of anautomatic ?ngerprintidenti?c ation?veri?c ationsystem

willber obust withr espe ct tothe quality ofinput ?ngerprintimages?itis essentialto inc or?

p or atea ?ngerprint enhancement algorithm inthe minutiae extr action mo dule?Wepresent

a fast?ngerprintenhancement algorithm?whichc an adaptively improve the clarityof ridge

andfurr owstructur es ofinput?ngerprint imagesb ased on theestimated loc alridge orienta?

tionandfre quency? Wehave evaluated theperformance ofthe image enhanc ementalgorithm

usingthe goo dnessindex oftheextr acted minutiaeand the ac cur acyof anonline ?ngerprint

veri?cation system? Experimentalr esultsshow thatincorp oratingthe enhancement algorithm

improvesb oth thegoo dnessindex andtheveri?cation ac cur acy?

? Introduction

Fingerprint iden ti?cation isoneof themost important biometric technologieswhich has

drawna substantial amount of attentionrecen tly ???? ????A ?ngerprint is thepattern of

ridges andfurro ws onthe surface ofa ?ngertip?Each individual hasunique?ngerprin ts?

Theuniqueness ofa ?ngerprint isexclusiv elydeterminedby thelo cal ridgecharacteristics

?

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(x,y)

(x,y)

θ

θ

Y

X

Ridge BifurcationRidge Ending

?a?

Ridge Bifurcations

Ridge Endings

?b?

Figure ??Examples ofmin utiae? ?a?a minutiae canbec haracterizedby itsp osition andits

orien tation??b? minutiaeov erlaid ona ?ngerprint image?

andtheir relationships???? ????A totalof oneh undredand ?fty di?erent localridgec har?

acteristics?called min utedetails?haveb eeniden ti?ed????? These local ridgec haracteristics

are not ev enlydistributed? Mostofthemdep end hea vilyonthe impression conditionsand

quality of ?ngerprints andare rarelyobserv ed in ?ngerprin ts?Thetwo most prominent ridge

c haracteristics?calledmin utiae?are?i? ridge endingand?ii? ridgebifurc ation?A ridgeend?

ing isde?ned as thep oint wherea ridgeends abruptly?Aridge bifurcationis de?nedas the

p oint wherea ridge forksor div erges in to branch ridges?A good quality ?ngerprintt ypically

con tains about ??????minutiae? Examples ofmin utiae areshown inFigure ??

Automatic?ngerprint matc hingdep ends onthe comparison ofthese lo cal ridgec har?

acteristics and theirrelationships to makeap ersonalidenti?cation ??? ??A critical stepin

?ngerprint matching is toautomaticallyand reliablyextract minutiaefrom theinput ?nger?

print images? which isa di?cult task?Thep erformance ofa minutiae extractionalgorithm

relies heavily onthe quality of theinput ?ngerprint images?In anideal ?ngerprint image?

ridgesandfurro wsalternateand ?ow ina lo callyconstantdirection andminutiae areanoma?

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Figure??Fingerprint imagesofv erypo orquality?

liesofridges? i?e?ridge endings and ridgebifurcations? Insuch situations? theridgescanbe

easilydetected and min utiaecanbeprecisely locatedfromthe binaryridges? Figure??b?

shows anexampleofgood quality live?scan?ngerprint image? How ev er? inpractice? due

tov ariationsin impression conditions?ridge con?guration? skinconditions ?aberrant forma?

tionsof epidermal ridgesof ?ngerprin ts?p ostnatalmarks?o ccupationalmarks?? acquisition

devices? and non?co operative attitudeof sub jects?etc?a signi?cantp ercen tageofacquired

?ngerprint images?appro ximately??? according toour experience? isofpo orquality? The

ridgestructures inpo or?quality ?ngerprint images arenot alwa ysw ell?de?ned and hencethey

can notbecorrectly detected?This leads tofollowingproblems??i?a signi?cantn umb er of

spurious minutiaemaybe created??ii?a largep ercent of genuine minutiae maybe ignored?

and?iii? large errorsin theirlocalization?p osition and orientation?maybe intro duced?Ex?

amples of ?ngerprint imagesofv erypo orquality? inwhich ridge structuresarecompletely

corrupted?are sho wn inFigure ?? Inorder toensurethat thep erformance of themin utiae

?

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?a?

?b?

?c?

Figure??Fingerprint regions??a?w ell?de?nedregion? ?b?recov erablecorrupted region? ?c?

unrecov erablecorrupted region?

extraction algorithmwillbe robust with respect tothe quality of inputdigital ?ngerprint

images?anenhancement algorithm which can improve theclarity oftheridge structures is

necessary?

A ?ngerprint expertisoften able tocorrectly iden tifythe minutiaeby usingv arious

visual cluessuch aslo calridge orien tation? ridge con tin uity? ridge tendency? etc?? aslong

as theridge and furrow structures are notcorrupted completely? Itisp ossible to develop

anenhancement algorithm thatexploits these visual cluesto improve the clarity of ridge

structures incorrupted ?ngerprint images? Generally? fora giv endigital?ngerprint image?

theregion of interest canbe divided into thefollo wing threecategories?Figure???

? Wel l?de?nedre gion? whereridges and furrows are clearlydi?erentiated fromone an?

othersuch thata minutiae extractionalgorithm is abletoop erate reasonably?

?Rec over ablec orruptedre gion? where ridgesandfurro wsare corruptedbya small amount

ofcreases? smudges?etc?But? theyarestill visible and the neighb oring regions pro vide

su?cient informationabout thetrueridge andfurrow structures?

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? Unrec over ablec orruptedre gion? where ridgesandfurro wsare corruptedby sucha

severe amount ofnoise anddistortion thatnoridges andfurro wsare visibleand the

neighb oringregions donotprovide su?cient informationab outthe trueridge and

furrow structureseither?

We refertothe?rsttwo categories of regionsasrec over ableand thelast category asunrec ov?

er able? The goal ofan enhancement algorithm isto impr ovetheclarityof ridge structuresof

?ngerprint images in recov erableregions andto remove the unrecov erableregions? Sincethe

objective ofa ?ngerprint enhancement algorithmis toimprove the clarity ofridge structures

ofinput?ngerprint imagestofacilitate the extractionof ridges andmin utiae?a ?ngerprint

enhancement algorithm should notresult inany spurious ridgestructures?This isv eryim?

p ortantb ecausespurious ridgestructure mayc hangetheindividuality of input?ngerprints?

Fingerprint enhancement canbeconducted oneither?i? binaryridge images or?ii? gray?

level images?A binaryridge image is animagewhereall theridge pixels are assignedav alue

? and non?ridgepixels areassignedav alue ?? Thebinary imagecanbe obtainedby applying

a ridgeextractionalgorithm ona gray?lev el?ngerprint image????Since ridgesandfurro ws

ina ?ngerprint imagealternateand run parallelto each other ina local neighb orhoo d?a

n umb er ofsimple heuristics canbe usedto di?erentiate the spuriousridge con?gurations

fromthe trueridge con?gurationsina binary ridge image???? How ever?afterapplying

aridge extraction algorithmon the originalgra y?level images?informationab outthetrue

ridge structuresisoftenlostdep ending onthep erformanceof theridge extraction algorithm?

Therefore?enhancement ofbinaryridgeimageshas itsinherent limitations?

Ina gray?level?ngerprint image?ridges and furro wsina lo calneighb orhood forma

?

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sin usoidal?shapedplanewave which hasaw ell?de?ned frequencyand orientation?An umb er

of techniques thattake adv an tageofthisinformationhaveb een proposedto enhance gray?

lev el?ngerprint images ?????? ?? ??????? How ever? they usually assumethat thelo calridge

orientations canbe reliablyestimated?In practice? thisassumption isnotv alidfor ?ngerprint

images ofpo or quality? which greatlyrestricts theapplicability ofthese techniques? Hong

etal? ???prop oseda decomp ositionmethod toestimatethe orientation?eld froma set of

?lteredimagesobtainedby applyinga bank of Gabor?lters onthe input?ngerprint images?

Although this algorithmcanobtaina reliable orientationestimate even forcorrupted images?

it iscomputationally exp ensive which mak esit unsuitable foranon?linev eri?cation system?

We will presenta fastenhancementalgorithm which is able toadaptively enhancetheridge

andfurrow structures usingb oth thelo cal ridgeorien tationandlo calfrequency information?

Insteadofusingacomputational expensive method to precisely estimate thelo cal ridge

orien tation?a simplebut e?cient method isused?In addition?sincethis algorithmis designed

tobe integrated in anonline system?a computationally e?cient ?ltering technique is used?

In thefollowingsectionswe will describe indetailour fast?ngerprint enhancement al?

gorithm?Section?addresses themain stepsof ouralgorithm?A goal?directedp erformance

ev aluationofthe implemented?ngerprint enhancementalgorithm on?ngerprint databases

is describ ed in section ?? Section? con tainsthe summary anddiscussion?

? Fingerprint Enhancement

A ?ngerprintimage enhancementalgorithm receiv esan input ?ngerprint image?appliesa set

of intermediatesteps on the inputimage?and?nally outputstheenhancedimage? Inorder

?

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toin troduceour ?ngerprint imageenhancement algorithm?a listof notationsand somebasic

de?nitions aregivenb elow?

???Notation

A gray?level ?ngerprintimage?I? is de?nedasaN?N matrix? whereI?i?j? represen ts the

in tensity ofthe pixel attheith row andj th column?We assume thatallthe images are

scanned ata resolution of???dotsp erinch?dpi?? which is the resolutionrecommendedby

FBI? The me an andvariance ofa gray?level ?ngerprint image?I? are de?ned as

M?I??

?

N

?

N??

X

i??

N??

X

j ??

I?i?j? and ???

V AR?I??

?

N

?

N??

X

i??

N??

X

j ??

?I?i?j??M?I ??

?

? ???

respectively?

An orientation image?O? is de?neasaN?N image?whereO?i?j? represen tsthe loc al

ridgeorientation at pixel?i?j ?? Local ridgeorien tation is usuallyspeci?ed fora block rather

than at every pixel? animage is dividedintoa setofw?w non?ov erlapping bloc ksanda

single lo calridge orientation is de?nedfor each bloc k?Notethat ina?ngerprint image?there

is nodi?erenceb etw eena local ridgeorien tation of??

o

w

and ???

o

? since theridges oriented

at??

o

andthe ridges oriented at???

o

ina local neighb orhood can notbe di?eren tiatedfrom

each other?

A fre quencyimage?F? isaN?N image?whereF?i?j? represents theloc alridge fre quency?

which is de?ned as thefrequency ofthe ridgeandfurrostructures ina local neighborhood

?

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Normalization

Orientation Image

Estimation

Frequency Image

Estimation

Region Mask

Generation

Filtering

Enhanced Image Input Image

Figure??A ?owc hartof theprop osed?ngerprint enhancement algorithm?

alonga directionnormal tothe local ridgeorientation?The ridge and furrow structures ina

lo cal neighb orhood where minutiaeorsingularp oints ???appear donot formaw ell?de?ned

sin usoidal?shap edwav e?In such situations? the frequencyis de?nedas theav eragefrequency

of its neighb ors?Like orien tationimage? frequencyimage is speci?ed bloc k?wise?

There gionmask?R? isde?ned asaN?N image withR?i?j? indicatingthe category

ofthepixel?A pixel couldbe either?i?a non?ridge?and?furr ow?unrecov erable?pixel ?with

v alue ?? or?ii?a ridge?and?furrow ?recov erable? pixel?withv alue??? Region mask is also

sp eci?edbloc k?wise?

???Algorithm

The?owc hartof the ?ngerprint enhancement algorithm issho wnin Figure ?? Themain

stepsof thealgorithminclude?

?? Normalization? aninput ?ngerprint imageis normalized so thatit hasa pre?sp eci?ed

meanandv ariance?

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??Loc alorientationestimation? the orien tationimageisestimated fromthe normalized

input ?ngerprint image?

??Loc alfre quencyestimation? the frequency imageiscomputed fromthe normalized

input ?ngerprint imageandtheestimated orientation image?

??Re gion mask estimation? theregion maskisobtainedby classifyingeach block in the

normalizedinput ?ngerprint image intoa recov erableora unrecov erable bloc k?

?? Filtering?A bank of Gab or?lters which istuned tolo cal ridge orientationand ridge

frequency isapplied totheridge?and?furrow pixels in thenormalized input?ngerprint

image toobtain anenhanced ?ngerprint image?

???Normalization

LetI?i?j? denote the gra y?levelv alue atpixel?i?j ??M andV ARdenote theestimated mean

andv ariance ofI? resp ectively? andG?i?j? denote thenormalizedgra y?levelv alue at pixel

?i?j ?? Thenormalized image isde?ned asfollows?

G?i?j??

?

?

?

?

?

?

?

?

?

M

?

?

q

V AR

?

?I?i?j??M?

?

V AR

? ifI?i?j??M

M

?

?

q

V AR

?

?I?i?j??M?

?

V AR

? otherwise?

???

???

whereM

?

andV AR

?

are the desired mean andv ariancev alues?respectiv ely? Normalization

isa pixel?wiseoperation? It do esnotchange the clarity ofthe ridgeandfurrow structures?

The main purp oseofnormalization isto reducethev ariations ingray lev elv alues along

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?a? ?b?

Figure ??Theresult of normalization??a?input image??b? normalizedimage?M

?

?

????V AR

?

? ?????

ridges andfurro ws?which facilitates thesubsequent pro cessingsteps?Figure? showsan

exampleof image normalization?

??? Orien tationImage

Theorien tationimage representsan intrinsic property of the ?ngerprint images andde?nes

inv ariant coordinatesfor ridgesand furrowsina localneighb orhoo d?By viewinga ?ngerprint

image as an orien tedtexture?an umb er ofmetho dshaveb een prop osedto estimate the

orientation?eld of?ngerprint images ???? ??? ??? ???We have dev elopeda least mean

square orientation estimation algorithm?Giv ena normalizedimage?G? the mainsteps of

thealgorithmareas follo ws?

?? DivideG into bloc ksof sizew?w ???? ????

?? Compute thegradien ts?

x

?i?j? and?

y

?i?j? at each pixel??i?j ??Dep endingon the

??

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computational requiremen t?the gradient operator mayv aryfromthe simpleSobel

op eratorto the morecomplex Marr?Hildreth operator?

?? Estimatethe lo cal orientationofeach block centeredatpixel?i?j? using the following

equations?

V

x

?i?j??

i?

w

?

X

u?i?

w

?

j?

w

?

X

v?j?

w

?

??

x

?u?v??

y

?u?v?? ???

V

y

?i?j??

i?

w

?

X

u?i?

w

?

j?

w

?

X

v?j?

w

?

??

?

x

?u?v???

?

y

?u?v ??? ???

??i?j??

?

?

tan

??

?

V

y

?i?j?

V

x

?i?j?

?? ???

where??i?j? is theleast squareestimate of thelo calridgeorien tationat theblock

centered atpixel?i?j ?? Mathematically? it represen tsthedirection that isorthogonal

to thedominantdirection oftheF ourierspe ctrumofthew?w window?

?? Duetothepresence ofnoise? corruptedridge andfurrow structures? minutiae? etc? in

the input image?theestimatedlo calridgeorien tation???i?j ??may not alwa ysbea

correct estimate?Since local ridgeorien tationv aries slowly ina local neighb orhood

where nosingularp oin ts appear?a lo w?pass?lter canbe used to modify the incorrect

local ridgeorien tation? Inorder top erform the lo w?pass?ltering? theorien tationimage

needs tobe converted in toacontinuous ve ctor ?eld? which isde?ned as follo ws?

?

x

?i?j?? cos????i?j ??? and ???

?

y

?i?j?? sin????i?j ??????

??

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where?

x

and?

y

? are thex andy comp onents ofthev ector?eld?resp ectiv ely? With

theresultingv ector?eld?the low?pass?ltering canthenbep erformedas follo ws?

?

?

x

?i?j??

w

?

??

X

u??w

?

??

w

?

??

X

v??w

?

??

W?u?v ??

x

?i? uw?j?vw? and????

?

?

y

?i?j??

w

?

??

X

u??w

?

??

w

?

??

X

v??w

?

??

W?u?v ??

y

?i? uw?j?vw?? ????

whereW isa ??dimensional low?pass?lter withunit in tegralandw

?

?w

?

speci?esthe

sizeof the?lter? Notethat thesmo othing op eration isp erformedat the block level?

Thedefault size ofthe ?lter is?? ??

?? Computethe local ridgeorien tation at?i?j? using

O?i?j??

?

?

tan?

?

?

y

?i?j?

?

?

x

?i?j?

?? ????

Withthisalgorithm?a fairly smo othorientation ?eld estimate canbeobtained? Figure?

shows anexample ofthe orientation imageestimated withouralgorithm?

??? RidgeFrequency Image

Ina lo calneighb orhood where nominutiae and singularp oin ts appear? thegray levels along

ridgesandfurro wscanbe mo deled asa sinusoidal?shap edwave alonga direction normalto

the localridge orien tation?seeFigure ???Therefore?lo calridgefrequency is anotherin trinsic

property ofa?ngerprint image? LetGbe thenormalized image andObe the orientation

image? thenthesteps inv olved in localridgefrequency estimationare asfollo ws?

??

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?a? ?b?

Figure??Comparison of orientation ?eldsby themethod proposedin ????and our method?

w? ?? andw

?

? ??

X

α

x-signature

Oriented Window

Local Ridge Oirentation

Block

β

Figure ??Orien tedwindow andx?signature?

??

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?? DivideG into bloc ksofsizew?w ???? ????

??F or each block centeredatpixel?i?j ?? compute anoriented windowof sizel?w ???? ???

that is de?ned intheridge coordinates system ?Figure???

??F oreach block cen teredat pixel?i?j ?? computethe x?signature?X ????X ???? ???X?l? ???

of the ridgesandfurro wswithin theoriented window?where

X?k??

?

w

w??

X

d??

G?u?v??k????? ????l???????

u?i??d?

w

?

? cosO?i?j???k?

l

?

? sinO?i?j?? ????

v?j??d?

w

?

? sinO?i?j???

l

?

?k? cosO?i?j?? ????

Ifno min utiae andsingularp ointsappear intheorien tedwindow? the x?signature

formsadiscrete sin usoidal?shapewav e? which has the samefrequencyas that ofthe

ridgesand furrows in theorien tedwindow?Therefore? thefrequencyofridges and

furrows canbe estimated from the x?signature?LetT?i?j?be theav eragen umb erof

pixelsb etw eentwo consecutivep eaks inthex?signature? thenthe frequency? ??i?j ??

is computedas? ??i?j????T?i?j ??Ifno consecutivep eaks canbe detectedfrom the

x?signature? thenthefrequencyis assignedav alue of?? todi?eren tiateitfrom the

valid frequencyv alues?

??F ora ?ngerprint imagescanned ata ?xedresolution?thevalue of thefrequency of

the ridges andfurro ws ina localneighb orhoodlies inacertainrange?F ora ???dpi

image? thisrangeis ???????????Therefore?iftheestimatedv alueofthefrequency is

outofthis range?then thefrequency isassignedavalue of??to indicatethat anv alid

??

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frequency can notbe obtained?

?? Thebloc ks in which minutiae and?orsingularp oin tsapp ear and?orridges and furrows

arecorrupted do notformaw ell?de?nedsinusoidal?shap edwav e? Thefrequencyv alues

for these bloc ksneedtobe in terp olated fromthefrequencyof the neighb oring bloc ks

which haveaw ell?de?ned frequency

?

? The

?

in terpolation isp erformed asfollo ws?

?i?F or each block centered at?i?j ??

?

?

?i?j??

?

?

?

?

?

?

?

?

?

?

?

??i?j?? if??i?j?????

P

w

?

??

u??w

?

??

P

w

?

??

v??w

?

??

W

g

?u?v?????i?uw ?j?vw ??

P

w??

u??w

?

??

P

w??

v??w

?

?

??

W

g

?u?v?? ???i?uw?j?vw ????

otherwise?

????

where

??x?

kernel

?

where

?

?

?

?

?

?

?

?

?

?? ifx??

x?otherwise?

??x??

?

?

?

?

?

?

?

?

?? ifx??

?? otherwise?

W

g

isa discreteGaussianmean andv arianceis? and ?? respectiv ely?

andw

?

?? is thesize of thek ernel?

?ii? Ifthere exists atleast oneblock with thefrequencyv alue of???then sw ap? and

?

?

andgoto step?i??

??Inter?ridgesdistancesc hange slowly ina lo cal neighb orhoo d?A low?pass ?lter canbe

??