eigenfaces for face recognition

8/12/2019 Eigenfaces for Face Recognition

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Eigenfaces for Face RecognitionECE 533 Final Project Report, Fall 03

Min Luo, Department of Biomedical Engineeringu!apat Panitc"o#, Department of Electrical $ Computer Engineering

Abstract%Eigenface& approac" for face recognition i& implemented a& our final project'Face recognition "a& #een an acti(e area of re&earc" !it" numerou& application&

&ince late )*+0&' Eigenface approac" i& one of t"e earlie&t appearance#a&ed face

recognition met"od&, !"ic" !a& de(eloped #- M' .ur/ and ' Pentland 1)2 in)**)' ."i& met"od utilie& t"e idea of t"e principal component anal-&i& and

decompo&e& face image& into a &mall &et of c"aracteri&tic feature image& called

eigenface&' Recognition i& performed #- projecting a ne! face onto a lo!

dimen&ional linear 4face &pace defined #- t"e eigenface&, follo!ed #- computingt"e di&tance #et!een t"e re&ultant po&ition in t"e face &pace and t"o&e of /no!n

face cla&&e&' num#er of e6periment& !ere done to e(aluate t"e performance of

t"e face recognition &-&tem !e "a(e de(eloped' ."e re&ult& demon&trate t"at t"eeigenface approac" i& 7uite ro#u&t to "ead8face orientation, #ut &en&iti(e to &cale

and illumination' t t"e end of t"e report, a couple of !a-& are &ugge&ted to

impro(e t"e recognition rate' ."e report i& organied a& follo!&9 t"e fir&t partpro(ide& an o(er(ie! of face recognition algorit"m&: t"e &econd part &tate& t"e

t"eor- of t"e eigenface& approac" for face recognition: Part ;;; focu&e& on

implementation i&&ue&, &uc" a& &-&tem &tructure de&ign, interface and u&e of eac"

functional #loc/, etc': in Part ;


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le(el recognition At"at i&, to determine !"et"er or not t"e gi(en image repre&ent& a face,

a face categor- &"ould #e c"aracteried #- generic propertie& of all face&: and for t"e

&u#ordinatele(el recognition Ain ot"er !ord&, !"ic" face cla&& t"e ne! face #elong& to,detailed feature& of e-e&, no&e, and mout" "a(e to #e a&&igned to eac" indi(idual face'

."ere are a (ariet- of approac"e& for face repre&entation, !"ic" can #e roug"l- cla&&ified

into t"ree categorie&9 template#a&ed, feature#a&ed, and appearance#a&ed'."e &imple&t template-matching approac"e& repre&ent a !"ole face u&ing a &ingle

template, i'e', a D arra- of inten&it-, !"ic" i& u&uall- an edge map of t"e original face

image' ;n a more comple6 !a- of templatematc"ing, multiple template& ma- #e u&ed foreac" face to account for recognition from different (ie!point&' not"er important

(ariation i& to emplo- a &et of &maller facial feature template& t"at corre&pond to e-e&,

no&e, and mout", for a &ingle (ie!point' ."e mo&t attracti(e ad(antage of template

matc"ing i& t"e &implicit-, "o!e(er, it &uffer& from large memor- re7uirement andinefficient matc"ing' ;n feature-basedapproac"e&, geometric feature&, &uc" a& po&ition

and !idt" of e-e&, no&e, and mout", e-e#ro!& t"ic/ne&& and arc"e&, face #readt", or

in(ariant moment&, are e6tracted to repre&ent a face' Feature#a&ed approac"e& "a(e

&maller memor- re7uirement and a "ig"er recognition &peed t"an template#a&ed one& do'."e- are particularl- u&eful for face &cale normaliation and 3D "ead model#a&ed po&e

e&timation' ?o!e(er, perfect e6traction of feature& i& &"o!n to #e difficult inimplementation 152' ."e idea of appearance-basedapproac"e& i& to project face image&

onto a linear &u#&pace of lo! dimen&ion&' uc" a &u#&pace i& fir&t con&tructed #-

principal component anal-&i& on a &et of training image&, !it" eigenface& a& it&eigen(ector&' Later, t"e concept of eigenface& !ere e6tended to eigenfeature&, &uc" a&

eigene-e&, eigenmout", etc' for t"e detection of facial feature& 12' More recentl-,

fi&"erface &pace 1G2 and illumination &u#&pace 1+2 "a(e #een propo&ed for dealing !it"

recognition under (ar-ing illumination'Face detection i& to locate a face in a gi(en image and to &eparate it from t"e remaining

&cene' e(eral approac"e& "a(e #een propo&ed to fulfil t"e ta&/' Hne of t"em i& to utilie

t"e elliptical &tructure of "uman "ead 1*2' ."i& met"od locate& t"e "ead outline #- t"eCann-& edge finder and t"en fit& an ellip&e to mar/ t"e #oundar- #et!een t"e "ead

region and t"e #ac/ground' ?o!e(er, t"i& met"od i& applica#le onl- to frontal (ie!&, t"e

detection of nonfrontal (ie!& need& to #e in(e&tigated' &econd approac" for facedetection manipulate& t"e image& in 4face &pace 1)2' ;mage& of face& do not c"ange

radicall- !"en projected into t"e face &pace, !"ile projection& of nonface image& appear

7uite different' ."i& #a&ic idea i& uded to detect t"e pre&ence of face& in a &cene9 at e(er-

location in t"e image, calculate t"e di&tance #et!een t"e local &u#image and face &pace'."i& di&tance from face &pace i& u&ed a& a mea&ure of 4facene&&, &o t"e re&ult of

calculating t"e di&tance from face &pace at e(erpoint in t"e image i& a 4face map' Lo!

(alue&, in ot"er !ord&, &"ort di&tance& from face &pace, in t"e face map indicate t"epre&ence of a face'

Face identification i& performed at t"e &u#ordinatele(el' t t"i& &tage, a ne! face i&

compared to face model& &tored in a data#a&e and t"en cla&&ified to a /no!n indi(idual ifa corre&pondence i& found' ."e performance of face identification i& affected #- &e(eral

factor&9 &cale, po&e, illumination, facial e6pre&&ion, and di&gui&e'

."escaleof a face can #e "andled #- a re&caling proce&&' ;n eigenface approac", t"e

&caling factor can #e determined #- multiple trial&' ."e idea i& to u&e multi&cale


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eigenface&, in !"ic" a te&t face image i& compared !it" eigenface& at a num#er of &cale&'

;n t"i& ca&e, t"e image !ill appear to #e near face &pace of onl- t"e clo&e&t &caled

eigenface&' E7ui(alentl-, !e can &cale t"e te&t image to multiple &ie& and u&e t"e &calingfactor t"at re&ult& in t"e &malle&t di&tance to face &pace'


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of face image& in t"e training &et' ?o!e(er, t"e face& can al&o #e appro6imated u&ing

onl- t"e 4#e&t eigenface&%t"o&e t"at "a(e t"e large&t eigen(alue&, and !"ic" t"erefore

account for t"e mo&t (ariance !it"in t"e &et of face image&' ."e primar- rea&on for u&ingfe!er eigenface& i& computational efficienc-' ."e mo&t meaningful Meigenface& &pan an

Mdimen&ional &u#&pace%4face &pace%of all po&&i#le image&' ."e eigenface& are

e&&entiall- t"e #a&i& (ector& of t"e eigenface decompo&ition'."e idea of u&ing eigenface& !a& moti(ated #- a tec"ni7ue for efficientl- repre&enting

picture& of face& u&ing principal component anal-&i&' ;t i& argued t"at a collection of face

image& can #e appro6imatel- recon&tructed #- &toring a &mall collection of !eig"t& foreac" face and a &mall &et of &tandard picture&' ."erefore, if a multitude of face image&

can #e recon&tructed #- !eig"ted &um of a &mall collection of c"aracteri&tic image&, t"en

an efficient !a- to learn and recognie face& mig"t #e to #uild t"e c"aracteri&tic feature&

from /no!n face image& and to recognie particular face& #- comparing t"e feature!eig"t& needed to Aappro6imatel- recon&truct t"em !it" t"e !eig"t& a&&ociated !it" t"e

/no!n indi(idual&'

."e eigenface& approac" for face recognition in(ol(e& t"e follo!ing initialiation

operation&9)' c7uire a &et of training image&'

' Calculate t"e eigenface& from t"e training &et, /eeping onl- t"e #e&t M image&!it" t"e "ig"e&t eigen(alue&' ."e&e Mimage& define t"e 4face &pace' & ne!

face& are e6perienced, t"e eigenface& can #e updated'

3' Calculate t"e corre&ponding di&tri#ution inMdimen&ional !eig"t &pace for eac"/no!n indi(idual Atraining image, #- projecting t"eir face image& onto t"e face

&pace'

?a(ing initialied t"e &-&tem, t"e follo!ing &tep& are u&ed to recognie ne! face image&9

)' @i(en an image to #e recognied, calculate a &et of !eig"t& of t"e Meigenface- projecting t"e it onto eac" of t"e eigenface&'

' Determine if t"e image i& a face at all #- c"ec/ing to &ee if t"e image i&

&ufficientl- clo&e to t"e face &pace'3' ;f it i& a face, cla&&if- t"e !eig"t pattern a& eig"er a /no!n per&on or a& un/no!n'

I' AHptional Jpdate t"e eigenface& and8or !eig"t pattern&'

5' AHptional Calculate t"e c"aracteri&tic !eig"t pattern of t"e ne! face image, andincorporate into t"e /no!n face&'

Calculating Eigenfaces

Let a face image A6,- #e a t!odimen&ionalN#-N arra- of inten&it- (alue&' n image

ma- al&o #e con&idered a& a (ector of dimen&ion CN , &o t"at a t-pical image of &ie 5

#- 5 #ecome& a (ector of dimen&ion 5,53, or e7ui(alentl-, a point in 5,53

dimen&ional &pace' n en&em#le of image&, t"en, map& to a collection of point& in t"i&"uge &pace'

;mage& of face&, #eing &imilar in o(erall configuration, !ill not #e randoml- di&tri#utedin t"i& "uge image &pace and t"u& can #e de&cri#ed #- a relati(el- lo! dimen&ional

&u#&pace' ."e main idea of t"e principal component anal-&i& i& to find t"e (ector t"at #e&t

account for t"e di&tri#ution of face image& !it"in t"e entire image &pace' ."e&e (ector&define t"e &u#&pace of face image&, !"ic" !e call 4face &pace' Eac" (ector i& of lengt"

CN , de&cri#e& anN#-Nimage, and i& a linear com#ination of t"e original face image&'


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Becau&e t"e&e (ector& are t"e eigen(ector& of t"e co(ariance matri6 corre&ponding to t"e

original face image&, and #ecau&e t"e- are faceli/e in appearance, t"e- are referred to a&

4eigenface&'

Let t"e training &et of face image& #e ) , C, 3, K, M ' ."e a(erage face of t"e

&et if defined #- ==

M

n nM )

)

' Eac" face differ& from t"e a(erage #- t"e (ector= nn ' n e6ample training &et i& &"o!n in Figure )a, !it" t"e a(erage face

&"o!n in Figure )#' ."i& &et of (er- large (ector& i& t"en &u#ject to principal component

anal-&i&, !"ic" &ee/& a &et of M ort"onormal (ector&, n , !"ic" #e&t de&cri#e& t"e

di&tri#ution of t"e data' ."e kt" (ector, k i& c"o&en &uc" t"at

=

=M

n

n

T

kkM )

CBA

) A)

i& a ma6imum, &u#ject to

=

= otherwise

kl

k

T

l,0

,) A

."e (ector& k and &calar& k are t"e eigen(ector& and eigen(alue&, re&pecti(el-, of t"e

co(ariance matri6

=

==M

n

TT

nn AA

MC

)

) A3

!"ere t"e matri6 2'''1 C) MA = ' ."e matri6 C, "o!e(er, i&CN #- CN , and

determining t"e CN eigen(ector& and eigen(alue& i& an intracta#le ta&/ for t-pical image

&ie&' computationall- fea&i#le met"od i& needed to find t"e&e eigen(ector&'

;f t"e num#er of data point& in t"e image &pace i& le&& t"an t"e dimen&ion of t"e &pace ACNM < , t"ere !ill #e onl- )M , rat"er t"an CN , meaningful eigen(ector& At"e

remaining eigen(ector& !ill "a(e a&&ociated eigen(alue& of ero' Fortunatel-, !e can

&ol(e for t"e CN dimen&ional eigen(ector& in t"i& ca&e #- fir&t &ol(ing for t"e

eigen(ector& of andM#-Mmatri6%e'g', &ol(ing a ) 6 ) matri6 rat"er t"an a ),3+I 6

),3+I matri6%and t"en ta/ing appropriate linear com#ination& of t"e face image& n '

Con&ider t"e eigen(ector& n of AAT &uc" t"at

nnn

TAA = AI

Premultipl-ing #ot" &ide& #-A, !e "a(e

nnn

T AAAA = A5

from !"ic" !e &ee t"at nA are t"e eigen(ector& of TAAC= 'Follo!ing t"i& anal-&i&, !e con&truct t"eM#-Mmatri6 AAL T= , !"ere n

T

mmnL = ,

and find t"eMeigen(ector& n ofL' ."e&e (ector& determine linear com#ination& of t"e

Mtraining &et face image& to form t"e eigenface& n 9

MnA n

M

k

knkn ,'''''',),)

====

A


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>it" t"i& anal-&i& t"e calculation& are greatl- reduced, from t"e order of t"e num#er of

pi6el& in t"e image& A CN to t"e order of t"e num#er of image& in t"e training &et AM' ;n

practice, t"e training &et of face image& !ill #e relati(el- &mall A CNM < , and t"e

calculation& #ecome 7uite managea#le' ."e a&&ociated eigen(alue& allo! u& to ran/ t"e

eigen(ector& according to t"eir u&efulne&& in c"aracterieing t"e (ariation among t"e

image&'

Using Eigenfaces to Classify a Face Image

."e eigenface image& calculated from t"e eigen(ector& of L&pan a #a&i& &et !it" !"ic"

to de&cri#e face image&' & mentioned #efore, t"e u&efulne&& of eigen(ector& (arie&according t"eir a&&ociated eigen(alue&' ."i& &ugge&t& !e pic/ up onl- t"e mo&t

meaningful eigen(ector& and ignore t"e re&t, in ot"er !ord&, t"e num#er of #a&i&

function& i& furt"er reduced from MtoMAMM and t"e computation i& reduced a& acon&e7uence' E6periment& "a(e &"o!n t"at t"e RM pi6el#-pi6el error& in repre&enting

cropped (er&ion& of face image& are a#out !it"M))5 andMI0 1))2'

;n practice, a &mallerMi& &ufficient for identification, &ince accurate recon&truction of

t"e image i& not a re7uirement' ;n t"i& frame!or/, identification #ecome& a patternrecognition ta&/' ."e eigenface& &pan anMdimen&ional &u#&pace of t"e original CN

image &pace' ."eMmo&t &ignificant eigen(ector& of t"e Lmatri6 are c"o&en a& t"o&e

!it" t"e large&t a&&ociated eigen(alue&'

ne! face image i& tran&formed into it& eigenface component& Aprojected onto 4face

&pace #- a &imple operationBA =

nn AG

for n),KK,M' ."i& de&cri#e& a &et of point#-point image maltiplication& and&ummation&'

."e !eig"t& form a (ector 2,''',,1 DC) MT

= t"at de&cri#e& t"e contri#ution of

eac" eigenface in repre&enting t"e input face image, treating t"e eigenface& a& a #a&i& &et

for face image&' ."e (ector ma- t"en #e u&ed in a &tandard pattern recognition algorit"m

to find !"ic" of a num#er of predefined face cla&&e&, if an-, #e&t de&cri#e& t"e face' ."e

&imple&t met"od for determining !"ic" face cla&& pro(ide& t"e #e&t de&cription of aninput face image i& to find t"e face cla&& k t"at minimie& t"e Euclidian di&tance

CC BAkk

= A+

!"ere k i& a (ector de&cri#ing t"e kt" face cla&&' ."e face cla&&e& k are calculated

#- a(eraging t"e re&ult& of t"e eigenface repre&entation o(er a &mall num#er of face

image& Aa& fe! a& one of eac" indi(idual' face i& cla&&ified a& 4un/no!n, and

optionall- u&ed to created a ne! face cla&&'Becau&e creating t"e (ector of !eig"t& i& e7ui(alent to projecting t"e original face image

onto to lo!dimen&ional face &pace, man- image& Amo&t of t"em loo/ing not"ing li/e aface !ill project onto a gi(en pattern (ector' ."i& i& not a pro#lem for t"e &-&tem,"o!e(er, &ince t"e di&tance #et!een t"e image and t"e face &pace i& &impl- t"e

&7uared di&tance #et!een t"e meanadju&ted input image = and =

=D

)

M

i

iif ,

it& projection onto face &pace9C

C

f= A*


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."u& t"ere are four po&&i#ilitie& for an input image and it& pattern (ector9 A) near face

&pace and near a face cla&&: A near face &pace #ut not near a /no!n face cla&&: A3

di&tant from face &pace and near a face cla&&: AI di&tant from face &pace and not near a/no!n face cla&&'

;n t"e fir&t ca&e, an indi(idual i& recognied and identified' ;n t"e &econd ca&e, an

un/no!n indi(idual i& pre&ent' ."e la&t t!o ca&e& indicate t"at t"e image i& not a faceimage' Ca&e t"ree t-picall- &"o!& up a& a fal&e po&iti(e in mo&t recognition &-&tem&: in

t"i& frame!or/, "o!e(er, t"e fal&e recognition ma- #e detected #ecau&e of t"e &ignificant

di&tance #et!een t"e image and t"e &u#&pace of e6pected face image&'

Summary of Eigenface Recognition Procedure

."e eigenface& approac" for face recognition i& &ummaried a& follo!&9

)' Collect a &et of c"aracteri&tic face image& of t"e /no!n indi(idual&' ."i& &et&"ould include a num#er of image& for eac" per&on, !it" &ome (ariation in

e6pre&&ion and in t"e lig"ting A&a- four image& of ten people, &o M!I0'

' Calculate t"e AI0 6 I0 matri6 L, find it& eigen(ector& and eigen(alue&, and

c"oo&e t"eMeigen(ector& !it" t"e "ig"e&t a&&ociated eigen(alue& Alet M)0 int"i& e6ample'

3' Com#ine t"e normalied training &et of image& according to E7' A to produce t"e

AM)0 eigenface& D,'''''',), Mkk = '

I' For eac" /no!n indi(idual, calculate t"e cla&& (ector k #- a(eraging t"e

eigenface pattern (ector& 1from E7' A+2 calculated from t"e original Afour

image& of t"e indi(idual' C"oo&e a t"re&"old t"at define& t"e ma6imum

allo!a#le di&tance from an- face cla&&, and a t"re&"old t"at define& t"e

ma6imum allo!a#le di&tance from face &pace 1according to E7' A*2'5' For eac" ne! face image to #e identified, calculate it& pattern (ector , t"e

di&tance k to eac" /no!n cla&&, and t"e di&tance to face &pace' ;f t"e

minimum di&tance


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indicate& t"at t"e function create& or update& t"e file: a #idirectional arro! mean& t"e file

i& fir&t read #- t"e function, and later modified or updated #- it' ."e&e file& "elp t"e

Con&tructEigenface&= and Cla&&if-Ne!face= function& communicate !it" eac" ot"er ina !ell organied !a-'

Figure 1. -&tem Flo!c"art. ."e &7uare& and parallogram& repre&ent function& and file& re&pecti(el-' n

arro! pointing out from a file to a function mean& t"e function read&8load& t"e file: an arro! pointing in t"eot"er direction indicate& t"at t"e function create&8update& t"e file: a #idirectional arro! mean& t"e file i&

fir&t read #- t"e function, and later modified8updated #- it' ."e&e file& "elp t"e Con&tructEigenface&= and

Cla&&if-Ne!face= function& communicate !it" eac" ot"er in a !ell organied !a-'

Functional Blocks

Eac" functional #loc/ "a& a corre&ponding 'm file "refer to the source code#' Detailed

de&cription of t"e functional #loc/& i& a& follo!&'

Load;mage&Aimagefilename9

Functionalit-9 load all training image& and return t"eir content& Ainten&it- (alue&

;nput parameter&9 imagefilename%a &tring t"at &tate& an image file name'

Hutput parameter&9 ;%a 3D matri6 !"o&e component& are t"e inten&it- (alue& oft"e training image&'

J&e9 ;Load;mage&Aimagefilename

P&eudocode9

if imagefilename is an empty string

do

(1 read all default training images into !" matri# I

Con&tructEigenface&

Cla&&if-Ne!face

eigenface&'mat

facecla&&e&'mat

noteOeigenface&'mat

undoJpdateEigenface&

Load;mage& trainingimage&'mat


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($ sa%e I to file &trainingimages.mat' in &.)rainingSet' directory Anote9

relati(e pat" i& u&ed t"roug"out t"e document, relati(e= in t"e &en&e t"at relati(e to t"e

location of t"e 'm &ource file&

(! *rite t+e file names of t+e default training images to te#t file

&note,eigenfaces.t#t' in &.Eigenfaces' directory

else Aa&&umingt"e file pat" and name are correct, i'e' t"e image file can #e openedand read properl-

do

(1 copy t+e image named imagefilename into &.)rainingSet' directory

($ load I from file &trainingimages.mat' in &.)rainingSet' directory

A3 read t+e image file named imagefilename At"e input parameter ande#tract its illuminant component (i.e. intensity into $" matri# Ine*

(- concatenate Ine* to I and sa%e t+e modified I to &trainingimages.mat'

t+us file &trainingimages.mat' gets updated

A5 append imagefilename Ai'e', name of t"e ne! training imageto t+e end

of te#t file &note,eigenfaces.t#t' in &.Eigenfaces' directory

(/ copy t+e test image from &.)estImage' directory to &.)rainingSet'direcotry

Note9 Load;mage&= function i& al!a-& called in t"e Con&tructEigenface&=

function' ."e input parameter of t"e latter i& pa&&ed to t"e former a& it& iput' ."e

3D matri6 ; returned #- Load;mage&= !ill #e u&ed for furt"er computation in

Con&tructEigenface&='

Con&tructEigenface&Aimagefilename9

Functionalit-9 A) con&truct or update eigenface&:

A con&truct or update face cla&&e&'

;nput parameter&9 imagefilename%a &tring t"at &tate& an image file name

Hutput parameter&9 &f%indicator of &ucce&&8failure of t"e e6ecution of t"efunction' ;f &f e7ual& to ), e6ecution &ucce&&full-: if &f e7ual& to 0, e6ecution

failure

J&e9 &fCon&tructEigenface&Aimagefilename

P&eudocode9

0 call function &oadImages' and get t+e illuminant components I of current

training images

0 construct eigenfaces 2 and face classes 34E56 7ased on I

sa%e 2 to file &eigenfaces.mat' in &.Eigenfaces' directory

sa%e 34E56 to file &faceclasses.mat' in &.Eigenfaces' directory

Note9 t"e input parameter of function Con&tructEigenface&= i& pa&&ed to function

Load;mage&= a& it& input !"en t"e former call& t"e latter' ."erefore, t"e t!o

&tatement& mar/ed !it" in a#o(e p&eudocode can #e re&tated a& follo!ing9

if imagefilename is an empty string

do

(1 construct t+e eigenfaces 2 7ased on t+e default training images

($ construct t+e face classes 34E56 7ased on t+e default training

images


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else Aa&&uming file pat" and name are correct, i'e' t"e image file can #e opened

and read properl-

do

(1 update current 2 according to t+e ne*ly added training image

($ update current 34E56 according to t+e latest added training

image>"en t"e input parameter i& an empt- &tring, Con&tructEigenface&= function

con&truct& t"e (er- fir&t (er&ion of eigenface&, and face cla&&e& #a&ed on t"e

default training image &et' Calling t"i& function !it" an empt- &tring a& t"e inputparameter i& a good t"ing to do onl- if it i& t"e fir&t time !e run t"e face

recognition program: ot"er!i&e, !e ma- lo&e u&eful information' &&uming !e

"a(e alread- run t"e face recognition program &e(eral time&, encountered a

num#er of ne! face&, and added t"e ne! face& to our training &et, ifCon&tructEigenface&= function i& called !it" an empt- input &tring, file& &uc" a&

trainingimage&'mat=, noteOeigenface&'t6t=, eigenface&'mat= and

facecla&&e&'mat= !ill all go #ac/ to t"eir initial (er&ion, in ot"er !ord&, updated

eigenface& and face cla&&e& #a&ed on t"e ne! training image& !ill #e mi&&ing and!"at !e "a(e are t"o&e containing onl- t"e default training image&= information'

."erefore, #e cautiou& !"en calling Con&tructEigenface&= function !it" anempt- &tring a& t"e input parameter'

Cla&&if-Ne!faceAimagefilename9

Functionalit-9 gi(en a te&t image, t"i& function i& a#le to determine

A) >"et"er it i& a face image

A ;f it i& a face image, doe& it #elong to an- of t"e e6i&ting face

cla&&e&Qa' ;f &o, !"ic" face cla&& doe& it corre&pond toQ

#' ;f not, Aoptionall- update t"e eigenface& according to t"ete&t image

;nput parameter9 imagefilename%a &tring t"at &tate& t"e name of t"e te&t image

Hutput parameter9 re&ult%indicator of t"e te&t image=& &tatu&

a' re&ult0, #ad file Acannot open t"e file

#' re&ult, te&t image i& not a face imagec' re&ult), te&t image i& a face image, and #elong& to one of

t"e e6i&ting face cla&&e&

d' re&ult), te&t image i& a face image, #ut doe& not #elong to

an- of t"e e6i&ting face cla&&e&

J&e9 re&ultCla&&if-Ne!faceAimagefilename

P&eudocode9if t+e test image file cannot 7e opened

do

(1 result89

($ return

(end if

predefine t*o t+res+olding %alues and


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pro:ect t+e test image onto face space

compute t+e distance 7et*een t+e test image and its pro:ection onto t+eface space

if ;A i& not a face image do

(1 result8


12/20

Flo!9 t"e &-&tem flo! i& illu&trated in Figure '

Figure $. System Flo*

Con&truct8updateeigenface& prior to

face identificationQ

Con&truct8update

eigenface&

.e&t image name

Cla&&if- t"e te&t image

N


13/20

I2. E#periment Results."e face recognition &-&tem !a& te&ted u&ing a &et of face image& do!nloaded from M;.

Media La# &er(er1))2' ll t"e training and te&ting image& are gra-&cale image& of &ie

)06)+' ."ere are ) per&on& in t"e face image data#a&e, eac" "a(ing G di&tinct

picture& ta/en under different condition& Ailluminance, "ead tilt, and "ead &cale'."e training image& are c"o&en to #e t"o&e of full "ead &cale, !it" "eadon lig"ting, and

uprig"t "ead tilt' ."e initial training &et con&i&t& of ) face image& of ) indi(idual&, i'e'

one image for one indi(idual AM)' ."e&e training image& are &"o!n in Figure 3a'Figure 3# i& t"e a(erage image of t"e training &et'

Figure !a. Initial )raining Images

Figure !7. 6%erage Face of Initial )raining Set

fter principal component anal-&i&, M)) eigenface& are con&tructed #a&ed on t"eM) training image&' ."e eigenface& are demon&trated in Figure I' ."e a&&ociated

eigen(alue& of t"e&e eigenface& are ))*'), )35'0, )G3'*, )*G'3, 30'3, 33', IG*'+,

550'0, G'+, +I3'5, )+)', in order' ."e eigen(alue& determine t"e 4u&efulne&& oft"e&e eigenface&' >e /eep all t"e eigenface& !it" nonero eigen(alue& in our e6periment,


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&ince t"e &ie of our training &et i& &mall' ?o!e(er, to ma/e t"e &-&tem c"eaper and

7uic/er, !e can ignore t"o&e eigenface& !it" relati(el- &mall eigen(alue&'

Figure -. Eigenfaces

."e performance of t"e eigenface& approac" under different condition& i& &tudied a&

follo!&'

Recognition !it" different "ead tilt&9

."e ro#u&tne&& of t"e eigenface& recognition algorit"m to "ead tilt i& &tudied #- te&ting face image& of eac" per&on t"at i& in t"e training &et, !it" different "ead tilt&%eit"er leftoriented or rig"toriented, a& &"o!n in Figure 5'

a. 7. c.

Figure @. )raining image and test images *it+ different +ead tilts.

a. training image 7. test image 1 c. test image $

;f t"e &-&tem correctl- relate& t"e te&t image !it" it& corre&pondence in t"e training &et,

!e &a- it conduct& a true-positi$eidentification AFigure& and G: if t"e &-&tem relate&

t"e te&t image !it" a !rong per&on AFigure +, or if t"e te&t image i& from an un/no!nindi(idual !"ile t"e &-&tem recognie& it a& one of t"e per&on& in t"e data#a&e, afalse-

positi$eidentifaction i& performed: if t"e &-&tem identifie& t"e te&t image a& un/no!n


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!"ile t"ere doe& e6i&t a corre&pondence #et!een t"e te&t image and one of t"e training

image&, t"e &-&tem conduct& afalse-negati$edetection'

."e e6periment re&ult& are illu&trated in t"e .a#le )9

)a7le 1> Recognition *it+ different +ead tilts

Num#er of te&t image& I

Num#er of truepo&iti(e identification& ))

Num#er of fal&epo&iti(e identification& )3

Num#er of fal&enegati(e identification& 0

a. 7. c.

Figure / (irfan). Recognition *it+ different +ead tiltssuccessD

a. test image 1 7. test image $ c. training image

a. 7.

Figure A (david).Recognition *it+ different +ead tiltssuccessD

a. test image 7. training image


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a. 7.

c. d.

Figure (foof).Recognition *it+ different +ead tiltsfalseD

a. test image 1 7. training image (irfan returned 7y t+e face recognition system

c. test image $ d. training image (stephen returned 7y t+e program

Recognition !it" (ar-ing illuminance9

Eac" training image A!it" "eadon lig"ting "a& t!o corre&ponding te&t image&%one

!it" lig"t mo(ed #- I5 degree& and t"e ot"er !it" lig"t mo(ed #- *0 degree&' Ht"er

condition&, &uc" a& "ead &cale and tilt, remain t"e &ame a& in t"e training image' ."ee6periment re&ult& are &"o!n in .a#le '

)a7le $> Recognition *it+ %arying illuminance

Num#er of te&t image& I

Num#er of truepo&iti(e identification& )

Num#er of fal&epo&iti(e identification& 3

Num#er of fal&enegati(e identification& 0

Figure * &"o!& t"e difference #et!een t"e training image and te&t image&'

Figure . )raining image and test images *it+ %arying illuminance.

a. training image 7. test image 1> lig+t mo%ed 7y -@ degrees c. test image $> lig+t mo%ed 7y 9

degrees

truepo&iti(e e6ample i& demon&trated in Figure )0, and a fal&enegati(e one i& &"o!n

in Figure ))'


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a. 7.

Figure 19 (stan). Recognition *it+ %arying illuminancesuccessD

a. test image lig+t mo%ed 7y -@ degrees 7. training image +ead


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a. 7.

Figure 1! (stan).Recognition *it+ %arying +ead scalesuccessD

a. test image 1 medium scale 7. test image $ small scale c. training image full scale

a. 7.

Figure 1- (pascal. Recognition *it+ %arying +ead scalefalseD

a. test image medium scale 7. training image (robert full scale

E6periment re&ult &ummar-9

From t"e e6periment& performed, a fairl- good recognition rate A%&'() i& o#tained !it"

(ar-ing illuminance, an accepta#le rate A%%'() !it" different "ead tilt&, and a poor oneA&'() !it" (ar-ing "ead &cale' ?o!e(er, it i& a long !a- to go #efore !e can confidentl-

dra! a conclu&ion on t"e roug"ne&&8&en&iti(it- of t"e eigenface& recognition approac" to

t"o&e condition&' Large ca&e &tud- need& carr-ing out in t"e &en&e t"at9 A) a largetraining &et i& re7uired, !"ic" con&i&t& of a large group of people, eac" "a(ing &e(eral

face image& in t"e data#a&e: A numerou& te&t& are nece&&ar-, !it" face image& of people

!"o are or aren=t in t"e data#a&e: A3 "o! doe& t"e &-&tem perform under com#ination&

of condition c"ange&, e'g' &imultaneou& c"ange& in "ead tilt and illuminance, etc'."re&"olding i&&ue i& not addre&&ed in 1)2' et, it doe& affect t"e performance of t"e

algorit"m' Larger t"re&"old (alue lead& to lo!er fal&enegati(e rate, #ut "ig"er fal&e

po&iti(e rate: and (ice (er&a' ;n ot"er !ord&, a good c"oice of t"re&"old (alue could !ell#alance fal&enegati(e and fal&epo&iti(e rate&, t"u& ma6imie good recognition rate'

2. Conclusion

n eigenfacea&ed face recognition approac" !a& implemented in MatLa#' ."i&met"od repre&ent& a face #- projecting original image& onto a lo!dimen&ional linear&u#&pace%face &pace=, defined #- eigenface&' ne! face i& compared to /no!n face

cla&&e& #- computing t"e di&tance #et!een t"eir projection& onto face &pace' ."i&

approac" !a& te&ted on a num#er of face image& do!nloaded from 1))2' Fairl- goodrecognition re&ult& !ere o#tained'


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Hne of t"e major ad(antage& of eigenface& recognition approac" i& t"e ea&e of

implementation' Fut"ermore, no /no!ledge of geometr- or &pecific feature of t"e face i&

re7uired: and onl- a &mall amount of !or/ i& needed regarding preproce&&ing for an-t-pe of face image&'

?o!e(er, a fe! limitation& are demon&trated a& !ell' Fir&t, t"e algorit"m i& &en&iti(e to

"ead &cale' econd, it i& applica#le onl- to front (ie!&' ."ird, a& i& addre&&ed in 1)2 andman- ot"er face recognition related literature&, it demon&trate& good performance onl-

under controlled #ac/ground, and ma- fail in natural &cene&'

.o impro(e t"e performance of t"e eigenface recognition approac", a couple of t"ing&

can #e done'

A) .o reduce t"e fal&epo&iti(e rate, !e can ma/e t"e &-&tem return a num#er of

candidate& from t"e e6i&ting face cla&&e& in&tead of a &ingle face cla&&' nd t"eremaining !or/ i& left to "uman'

A Regarding t"e pattern (ector repre&enting a face cla&&, !e can ma/e eac" face

cla&& con&i&t of &e(eral pattern (ector&, eac" con&tructed from a face image of t"e

&ame indi(idual under a certain condition, rat"er t"an ta/ing t"e a(erage of t"e&e(ector& to repre&ent t"e face cla&&'.

2I. References)' 4Eigenface& for recognition, M' .ur/ and ' Pentland, *ournal of Cogniti$e

Neuroscience+ $ol,+ No,%+ %..%' 4Face recognition u&ing eigenface&, M' .ur/ and ' Pentland,/roc, 0111 Conf,

on Computer 2ision and /attern 3ecognition, page& 5+5*), )**)

3' 4Face recognition for &mart en(ironment&, ' Pentland and .' C"oud"ur-,

Computer+ 2ol, 0ss,(+ 4eb, (555I' 4Face recognition9 Feature& (er&u& template&, R' Brunelli and .' Poggio, 0111

Trans, /attern Anal6sis and Machine 0ntelligence, %7"%5#8 %5)(-%57(+ %..5' 4?uman and mac"ine recognition of face&9 &ur(e-, R' C"ellappa, C' L'>il&on, and ' iro"e-,/roc, of 0111, $olume 9+ pages &57-&)5+ %..7

' 4Eigenface& (&' fi&"erface&9 Recognition u&ing cla&& &pecific linear projection,

P' N' Bel"umeur, U' P' ?e&pan"a, and D' U' Vriegman, 0111 Trans, /atternAnal6sis and Machine 0ntelligence+ %."&%%-&(5+ %..&

G' 4;llumination cone& for recognition under (aria#le lig"ting9 Face&, ' '

@eorg"iade&, D' U' Vriegman, and P' N' Bel"umeur, /roc, 0111 Conf, on

Computer 2ision and /attern 3ecognition+ pages 7(-7.+ %..9+' 4?uman face &egmentation and identification, ' ' iro"e-, Technical 3eport

CA3-T3-:.7+ Center for Automation 3esearch+ ;ni$ersit6 of Mar6land+ College

/ark+ MD+ %..*' 4utomatic recognition and anal-&i& of "uman face& and facial e6pre&&ion&9

&ur(e-, ' amal and P' ' ;-engar,/attern 3ecognition+ (7"%#8 :7-&&+ %..(

)0' 4Lo! dimen&ional procedure for t"e c"aracteriation of "uman face&, iro(ic",L' and Vir#-, M,*ournal of the


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