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Fingerprint Image Enhancemen t?Algorithmand

P erformanceEv aluation

LinHong?YifeiW an? andAnilJain

P atternRecognitionand ImagePro cessing Laboratory

Department ofComputer Science

MichiganState University

EastLansing? MI?????

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

Abstract

A critic al step inautomatic ?ngerprintmatching is toautomatically andr eliablyextr act

minutiaefr omthe input?ngerprint images?However?thep erformance ofa minutiaeex?

tractionalgorithmr elieshe avily on thequality of the input?ngerprint images? Inorder to

ensure that thep erformance ofan automatic ?ngerprintidenti?c ation?veri?cationsystem

willber obustwithr espe cttothe quality ofinput?ngerprintimages? itis essentialto inc or?

p or atea ?ngerprint enhancement algorithmin the minutiaeextr actionmo dule?We present

a fast?ngerprintenhancementalgorithm? whichc an adaptivelyimprove theclarity of ridge

and furr ow structures of input?ngerprint imagesb ased on theestimated loc al ridge orienta?

tionandfre quency? Wehave evaluated thep erformance of theimage enhancement algorithm

usingthe goo dnessindex ofthe extracted minutiae and the ac curacyof anonline ?ngerprint

veri?c ationsystem?Exp erimentalr esultsshowthat inc orp orating theenhancementalgorithm

impr ovesb oth thegoo dnessindex andthe veri?c ationac cur acy?

?Intro duction

Fingerprintiden ti?cationis one ofthemostimp ortant biometrictechnologieswhich has

drawn asubstantial amount of atten tionrecen tly ???? ????A ?ngerprint isthepatternof

ridgesand furro wson thesurface ofa?ngertip?Eachindividualhasunique ?ngerprints?

Theuniquenessofa ?ngerprint isexclusivelydeterminedby the localridgecharacteristics

?

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(x,y)

(x,y)

θ

θ

Y

X

Ridge Bifurcation Ridge Ending

?a?

Ridge Bifurcations

Ridge Endings

?b?

Figure??Examples of minutiae? ?a?a min utiaecanbec haracterizedby itsp osition and its

orientation? ?b? minutiaeov erlaidona ?ngerprint image?

andtheir relationships???? ????A total ofoneh undred and?fty di?erent lo calridgec har?

acteristics?calledmin utedetails? haveb een identi?ed????? Theselo calridgec haracteristics

arenot ev enly distributed? Most of themdepend hea vilyonthe impression conditionsand

quality of ?ngerprints andarerarely observedin ?ngerprints? Thetwo mostprominent ridge

c haracteristics?called minutiae? are?i? ridge ending and?ii? ridgebifurc ation?A ridgeend?

ingis de?ned asthep oint wherea ridgeends abruptly?A ridge bifurcation isde?nedasthe

p oint wherea ridge forks ordivergesin tobranch ridges?A good quality ?ngerprintt ypically

containsab out?????? min utiae?Examplesof min utiaearesho wn inFigure ??

Automatic?ngerprint matc hing dep ends onthecomparison oftheselo cal ridgec har?

acteristicsand their relationshipsto makeap ersonal identi?cation??? ??A criticalstep in

?ngerprint matc hingis toautomatically and reliablyextract minutiaefrom theinput ?nger?

printimages? which isa di?culttask? Thep erformance ofa minutiae extractionalgorithm

relies heavily onthequality of theinput?ngerprint images?In anideal?ngerprint image?

ridges andfurrows alternateand?ow inalo callyconstant direction andmin utiaeareanoma?

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Figure ?? Fingerprint imagesofv erypo orquality?

liesofridges? i?e?ridge endingsand ridge bifurcations? Insuch situations? the ridges canbe

easilydetected andmin utiaecanbe precisely locatedfrom thebinaryridges? Figure??b?

sho wsanexample of good quality liv e?scan ?ngerprint image?How ev er? in practice?due

tov ariations inimpressionconditions? ridge con?guration? skinconditions ?aberrant forma?

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

devices? andnon?coop erative attitude of sub jects?etc?a signi?cantp ercen tage ofacquired

?ngerprint images?appro ximately???according to ourexperience? is ofpo orquality? The

ridge structures inpo or?quality ?ngerprint imagesare notalwa ysw ell?de?nedand hencethey

cannotbe correctlydetected? Thisleads tofollo wing problems??i?asigni?can tn umb er of

spurious minutiaemaybe created??ii?a largep ercent ofgen uineminutiae maybe ignored?

and?iii? largeerrors intheir localization ?positionand orien tation? maybe in tro duced?Ex?

amples of?ngerprintimages ofv erypo orquality? inwhich ridgestructures arecompletely

corrupted?are sho wn inFigure ?? In orderto ensure that theperformance ofthe min utiae

?

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?a?

?b?

?c?

Figure?? Fingerprint regions? ?a?w ell?de?ned region? ?b?recov erablecorruptedregion? ?c?

unrecov erable corruptedregion?

extractionalgorithm willbe robustwithresp ectto the quality ofinput digital ?ngerprint

images? anenhancement algorithm which can improve theclarity ofthe ridgestructuresis

necessary?

A ?ngerprint expert is oftenable tocorrectly identifythemin utiaeby usingv arious

visualclues such as lo calridge orientation? ridgecontin uity? ridgetendency? etc?? aslong

asthe ridge andfurrow structures arenot corruptedcompletely? Itisp ossibleto dev elop

anenhancement algorithm that exploitsthese visual cluestoimprove the clarity ofridge

structures incorrupted ?ngerprint images? Generally? fora given digital?ngerprint image?

theregionof interest canbe dividedin to thefollo wingthree categories ?Figure???

? Well?de?nedre gion? where ridges andfurro ws areclearlydi?eren tiatedfrom one an?

other such thata minutiae extractionalgorithm is able toop eratereasonably?

?Rec overablec orruptedre gion? where ridgesandfurro ws arecorruptedbyasmall amount

ofcreases? sm udges?etc?But?they arestill visibleandthe neighb oring regionspro vide

su?cient informationab outthe trueridgeand furrow structures?

?

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? Unrec overablec orruptedre gion? whereridges and furro wsare corruptedby sucha

sev ere amount of noiseanddistortion thatno ridges andfurro ws arevisibleandthe

neighb oring regions donot pro vide su?cient information about the true ridgeand

furrow structures either?

We referto the ?rsttwo categories ofregions asrec over ableandthe last category asunrec ov?

er able? The goal ofanenhancementalgorithm isto impr ovethe clarityof ridgestructur esof

?ngerprint imagesin recov erableregions andto remove the unrecov erable regions?Since the

ob jective ofa ?ngerprint enhancement algorithmis toimprove the clarity ofridge structures

of input?ngerprint imagesto facilitatethe extraction ofridgesand minutiae?a ?ngerprint

enhancement algorithm should notresultin any spuriousridgestructures? This isv ery im?

p ortantb ecause spuriousridgestructure maychange theindividuality of input ?ngerprints?

Fingerprint enhancement canbe conductedon either?i? binaryridge images or?ii? gr ay?

levelimages?A binaryridgeimage is animage where alltheridgepixels areassignedav alue

? andnon?ridge pixels areassignedav alue ??The binary image canbe obtainedbyapplying

a ridgeextractionalgorithm ona gray?lev el?ngerprint image ????Sinceridges and furro ws

ina?ngerprint imagealternate andrun parallelto eachotherinalocalneighborhoo d?a

number ofsimpleheuristicscanbeusedtodi?erentiatethespuriousridgecon?gurations

fromthetrueridgecon?gurations inabinaryridgeimage????However?afterapplying

aridgeextractionalgorithmonthe originalgray?levelimages?information aboutthetrue

ridgestructuresisoftenlostdependingontheperformanceoftheridgeextractionalgorithm?

Therefore?enhancementofbinaryridgeimageshasitsinherentlimitations?

Inagray?level?ngerprintimage?ridgesandfurrowsinalocalneighborhoodforma

?

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sinusoidal?shapedplanewave which hasaw ell?de?ned frequencyand orientation?An umber

oftec hniques thattake adv an tage ofthis informationhaveb eenproposed to enhancegra y?

level ?ngerprint images ?????? ????? ?? ?? How ev er? theyusually assumethat thelocal ridge

orien tationscanbe reliablyestimated?In practice? thisassumption isnotv alidfor ?ngerprint

images ofpo orquality? which greatlyrestricts theapplicability of thesetec hniques? Hong

etal? ??? proposeda decomp ositionmethod toestimate the orientation?eld froma set of

?ltered imagesobtainedby applyinga bank ofGab or?lterson the input?ngerprint images?

Although this algorithmcan obtaina reliableorien tation estimateev enfor corruptedimages?

itiscomputationally expensive which makes itunsuitable foran on?linev eri?cationsystem?

We willpresenta fastenhancement algorithmwhich is ableto adaptivelyenhance theridge

and furrowstructures usingb oththe lo calridge orientation andlocalfrequency information?

Instead ofusinga computationalexpensive method toprecisely estimatethe local ridge

orien tation?a simple bute?cient method is used?In addition?since this algorithmis designed

tobe in tegrated in anonline system?a computationally e?cient?ltering tec hnique is used?

In thefollo wingsectionswe willdescribe in detail ourfast?ngerprintenhancement al?

gorithm? Section? addresses themainstepsofouralgorithm?Agoal?directedperformance

evaluationof theimplemented?ngerprintenhancementalgorithmon?ngerprintdatabases

isdescrib ed insection ??Section? contains thesummary anddiscussion?

?FingerprintEnhancement

A?ngerprint imageenhancement algorithmreceives aninput?ngerprintimage? appliesaset

ofintermediate steps ontheinputimage?and?nallyoutputsthe enhancedimage? Inorder

?

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tointro duceour ?ngerprint imageenhancement algorithm?a list of notations andsome basic

de?nitionsare givenb elo w?

??? Notation

A gr ay?level ?ngerprintimage?I? is de?nedasaN?N matrix? whereI?i?j? represents the

in tensity ofthepixel at theith row andj th column?We assume that all theimagesare

scanned ata resolution of???dotsp erinch?dpi?? which is theresolutionrecommendedby

FBI?The me anand variance ofa gra y?level?ngerprint image?I? arede?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 ??

?

? ???

respectiv ely?

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

ridgeorientation atpixel?i?j ?? Local ridgeorientation isusually sp eci?edforablock rather

than atevery pixel? animageisdivided in toa set ofw?w non?overlappingbloc ksanda

single lo cal ridgeorien tation isde?nedfor each bloc k?Notethat ina?ngerprint image?there

isnodi?erenceb etweena lo calridgeorien tationof ??

o

w

and???

o

? sincetheridges oriented

at??

o

andthe ridgesoriented at???

o

ina localneighborhood cannotbedi?erentiatedfrom

each other?

A frequencyimage?F?isaN?N image?where F?i?j?representsthelocalridgefrequency?

whichisde?nedasthefrequencyoftheridgeandfurrostructuresinalocalneighborhood

?

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Normalization

Orientation Image

Estimation

Frequency Image

Estimation

Region Mask

Generation

Filtering

Enhanced Image Input Image

Figure ??A ?owc hartof the proposed ?ngerprint enhancement algorithm?

alonga directionnormal to thelo cal ridgeorien tation? Theridge and furrow structures ina

local neighb orhood where minutiaeor singularp oints ???app ear do not formaw ell?de?ned

sinusoidal?shap edwav e?In such situations?thefrequencyis de?ned as theav eragefrequency

of its neighb ors? Like orien tation image? frequencyimage is speci?edbloc k?wise?

There gionmask?R? isde?nedasaN?N imagewithR?i?j?indicating thecategory

ofthe pixel?A pixel couldbeeither?i?anon?ridge?and?furr ow?unrecoverable? pixel ?with

v alue ?? or?ii?aridge?and?furr ow ?recov erable?pixel?withv alue ??? Region mask isalso

speci?edbloc k?wise?

??? Algorithm

The ?owc hart of the?ngerprintenhancementalgorithm is shown inFigure ?? Themain

steps ofthealgorithm include?

??Normalization? an input ?ngerprint image isnormalized so that it hasapre?sp eci?ed

meanandvariance?

?

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??Loc al orientation estimation? the orientationimageis estimatedfrom the normalized

input ?ngerprint image?

??Loc al fre quencyestimation? thefrequencyimageiscomputed from thenormalized

input ?ngerprint imageandthe estimatedorien tation image?

??Re gionmaskestimation? the region mask isobtainedby classifyingeach block inthe

normalizedinput ?ngerprintimage intoa recov erable ora unrecov erablebloc k?

?? Filtering?A bank of Gabor ?lters which is tunedto localridge orientationand ridge

frequency isapplied to theridge?and?furrow pixelsin thenormalized input ?ngerprint

imagetoobtainan enhanced ?ngerprint image?

???Normalization

LetI?i?j? denotethegray?lev elv alue atpixel?i?j ??M andV AR denote the estimatedmean

andv ariance ofI? respectively? andG?i?j? denote the normalizedgray?lev elv alueat pixel

?i?j ??Thenormalized imageis de?ned as follo ws?

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 thedesired meanandvariancev alues?respectively?Normalization

isapixel?wise operation? Itdo esnot changetheclarityof theridge andfurrowstructures?

Themainpurpose ofnormalization is toreducethev ariationsingray levelvalues along

?

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?a??b?

Figure?? The resultofnormalization? ?a?inputimage? ?b? normalizedimage?M

?

?

????V AR

?

? ?????

ridgesand furro ws? whichfacilitatesthe subsequent pro cessing steps? Figure? sho ws an

example ofimagenormalization?

??? OrientationImage

Theorientation imagerepresen tsan intrinsic property ofthe ?ngerprint imagesand de?nes

invariant coordinates for ridgesand furrows ina localneighb orhoo d? Byviewinga ?ngerprint

image as anoriented texture?an umb er ofmetho ds haveb een prop osedto estimatethe

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

square orientation estimationalgorithm? Giv enanormalized image?G? the mainstepsof

the algorithm areasfollows?

?? DivideG in tobloc ks ofsizew?w ???? ????

??Computethe gradients?

x

?i?j? and?

y

?i?j? at each pixel??i?j ?? Depending onthe

??

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computational requiremen t?thegradient operatormayv ary fromthe simpleSob el

op eratortothemore complex Marr?Hildreth operator?

??Estimate the local orien tationof each block centeredat pixel?i?j? using thefollowing

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? isthe least squareestimate ofthelo calridge orien tation atthe block

centered at pixel?i?j ??Mathematically? it represen ts thedirection thatisorthogonal

to thedominantdirection oftheFourier spe ctrum ofthew?wwindo w?

??Due to the presenceof noise?corrupted ridgeandfurrowstructures? min utiae?etc? in

theinputimage? theestimated localridgeorien tation???i?j?? may notalwa ysbea

correctestimate?Since local ridgeorientationvariesslo wlyina local neighborhood

where nosingularp oin tsapp ear?a lo w?pass?ltercanbeused tomodifythe incorrect

localridgeorientation?In ordertoperformthelow?pass?ltering?the orientationimage

needstobeconvertedin toacontinuousvector?eld?which isde?nedasfollows?

?

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 onen tsof thev ector ?eld?respectiv ely? With

theresultingv ector?eld? thelo w?pass ?lteringcan thenbep 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 with unitin tegralandw

?

?w

?

sp eci?es the

sizeof the?lter? Note thatthesmo othingoperation isp erformedatthe block level?

Thedefault size ofthe?lter is?? ??

??Compute thelocal ridgeorien tationat?i?j? using

O?i?j??

?

?

tan?

?

?

y

?i?j?

?

?

x

?i?j?

?? ????

With this algorithm?afairly smoothorientation ?eldestimate canbeobtained? Figure?

showsanexample of theorientation imageestimated withouralgorithm?

??? RidgeFrequency Image

Ina lo calneighborhoodwhere nominutiae andsingularp oin tsapp ear?thegray levelsalong

ridges andfurro ws canbemodeled asa sinusoidal?shap edwavealongadirectionnormalto

the localridge orientation?seeFigure ??? Therefore?lo calridgefrequency isanother intrinsic

propertyofa?ngerprintimage?LetGbethenormalized imageandObe theorientation

image?thenthesteps involv edinlocalridgefrequencyestimationareasfollows?

??

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?a??b?

Figure?? Comparison of orientation ?eldsby themethod proposed in???? andour metho d?

w? ??andw

?

? ??

X

α

x-signature

Oriented Window

Local Ridge Oirentation

Block

β

Figure ?? Oriented window and x?signature?

??

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?? DivideG intobloc ks of sizew?w ???? ????

??F or each block centeredat pixel?i?j ?? computeanoriented window of sizel?w ???? ???

that isde?ned in theridge coordinatessystem ?Figure???

??F oreach block cen tered atpixel?i?j ?? computethe x?signature?X ????X ???? ???X?l? ???

of theridges andfurro wswithin theorien tedwindo w?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 utiaeand singularp ointsapp earin theorien tedwindo w?thex?signature

formsa discretesinusoidal?shapewav e?which hasthe samefrequency as that of the

ridges andfurro wsin theoriented window?Therefore? the frequencyof ridgesand

furrows canbeestimated fromthex?signature? LetT?i?j?be theav eragen umb er of

pixelsb etw eentwoconsecutivep eaks in thex?signature?thenthe frequency? ??i?j ??

iscomputed as???i?j????T?i?j ?? If noconsecutivep eaks canbedetected from the

x?signature? thenthefrequency isassignedav alueof ??todi?erentiateitfrom the

v alidfrequencyvalues?

??F ora?ngerprintimagescanned ata ?xedresolution? thev alue ofthefrequency of

theridges andfurro ws inalo calneighborhoodliesinacertainrange?Fora???dpi

image?thisrangeis??????????? Therefore?if the estimatedv alueof the frequency is

outofthis range? thenthefrequencyis assignedav alue of?? toindicate thatanv alid

??

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frequencycan notbe obtained?

??Thebloc ksin which minutiaeand?orsingularp oints app earand?orridges andfurrows

arecorrupted do notformaw ell?de?ned sinusoidal?shap edwav e? Thefrequencyvalues

forthese bloc ks needtobe in terp olatedfromthe frequency ofthe neighb oring bloc ks

which haveaw ell?de?nedfrequency

?

? The

?

in terp olationisp erformed asfollo ws?

?i?F or each block cen teredat?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 discreteGaussian meanandvariance is? and?? respectiv ely?

andw

?

??is thesize ofthek ernel?

?ii?If there existsatleast oneblock withthefrequencyv alue of???then sw ap? and

?

?

and gotostep?i??

??Inter?ridges distancesc hange slowly ina local neighborhoo d?A low?pass?lter canbe

??