Face Recognition. Face Recognition. Why is Face Recognition. Automated Face Recognition Difficult? Why is it Difficult?

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1 Face Recogto Face Recogto If I ook at your face I mmedatey recogze that I have see t before Yet there s o mache whch, wth that speed, ca take a pcture of a face ad say eve that t s a ma; ad much ess that t s the same ma that you showed t before uess t s eacty the same pcture If the face s chaged; f I am coser to the face; f I am further from the face; f the ght chages I recogze t ayway ow, ths tte computer I carry my head s easy abe to do that he computers that we bud are ot abe to do that Query Image Recogzed Perso Rchard P Feyma, Dec 9, 959 here's Pety of Room at the Bottom A Ivtato to Eter a ew Fed of Physcs Why s Face Recogto Automated Face Recogto Dffcut? Why s t Dffcut? evere umato chage Varyg vewpot, umato, etc Face Recogto Defto: Gve a database of abeed faca mages Recogze a dvdua from a mage formed from ew ad varyg codtos (pose, epresso, ghtg etc) ub-probems: Represetato: How do we represet mages of faces? What formato do we store? Cassfcato: How do we compare stored formato to a ew sampe? earch

2 Goa: Represetato Compact, descrptve object represetato for recogto Represetatos: hape Represetato: Geerazed cyders, uperquadrcs Apperace Based Represetato for Recogto: Ordary mages statstcs oday: Apperace Based Recogto Appearace based recogto refers to the recogto of D objects from ordary mages ear odes PCA Egefaces, EgeImages FD Fsher ear Dscrmat Aayss ICA mages are a ear combato of mutpe sources utear odes Reevat esor ath PCA esorfaces ICA by Ae O Vasescu ear Agebra he agebra of vectors ad matrces radtoay of great vaue mage scece Fourer trasform Karhue-oeve trasform (PCA) Egefaces ear methods mode: ear operators over a vector space ge-factor ear varato mage formato he ear combato of mutpe sources (ICA) utear Agebra he agebra of hgher-order (>) tesors A ufyg mathematca framework for mage scece atura mages resut from the teracto of mutpe factors reated to scee geometry Iumato Imagg utear agebra ca epcty represet mutpe factors utear operators over a set of vector spaces utear agebra subsumes ear agebra as a speca case ear odes I Images k R pe R k A mage s a pot dmesoa space pe k 55 R k 55 pe 55

3 Image Represetato Image Represetato k k I ) ( k k by Ae O Vasescu pe vaue as represetg pe Image Represetato Image Represetato k O Bass atr, B vector of coeffcets, c by Ae O Vasescu Bc k k I ) ( k Represetato Represetato Fd a ew bass matr that resuts a compact represetato oy Eampe - Represetato Heurstc oy Eampe - Represetato Heurstc Cosder a set of mages of peope uder the same vewpot ad ghtg Each mage s made up of pes ad pe has the same vaue as pe for a mages pe pe pe ad st by Ae O Vasescu oy Eampe - Represetato Heurstc oy Eampe - Represetato Heurstc Cosder a set of mages of peope uder the same vewpot ad ghtg Each mage s made up of pes ad pe has the same vaue as pe for a mages pe pe pe ad st by Ae O Vasescu Bass atr, B oy Eampe - Represetato Heurstc oy Eampe - Represetato Heurstc Cosder a set of mages of peope uder the same vewpot ad ghtg Each mage s made up of pes ad pe has the same vaue as pe for a mages pe pe pe ad st Bc by Ae O Vasescu ew Bass atr, B ew bass

4 pe oy Eampe-Recogto ove for ad store the coeffcet matr C: c D, data matr C, coeffcet matr C B D Gve a ew mage, ew : pe pe c c 5 5 ew c ew B ew ew ew et, compare c ew a reduced dmesoaty represetato of ew agast a coeffcet vectors c Oe possbe cassfer: earest-eghbor cassfer Prcpa Compoet Aayss: Egefaces Empoys secod order statstcs to compute a prcped way a ew bass matr tatstca earg tatstcs: the scece of coectg, orgazg, ad terpretg data Data coecto Data aayss - orgaze & summarze data to brg out ma features ad carfy ther uderyg structure Iferece ad decso theory etract reevat fo from coected data ad use t as a gude for further acto Epressos Iumatos D Peope Vews Data Coecto Popuato: the etre group of dvduas that we wat formato about ampe: a represetatve part of the popuato that we actuay eame order to gather formato ampe sze: umber of observatos/dvduas a sampe tatstca ferece: to make a ferece about a popuato based o the formato cotaed a sampe Deftos Idvduas (peope or thgs) - - objects descrbed by data Idvduas o whch a epermet s beg performed are kow as epermeta uts, subjects Data Aayss Epermeta Uts: mages Observed Data: pe vaues mages are drecty measurabe but rarey of drect terest Data Aayss: etracts the reevat formato Varabes- - descrbe characterstcs of a dvdua Categorca varabe paces a dvdua to a category such as mae/femae Quattatve varabe measures some characterstc of the dvdua, such as heght, or pe vaues a mage

5 Varabes Respose Varabes are drecty measurabe, they measure the outcome of a study Pes are respose varabes that are drecty measurabe from a mage Respose vs Epaatory Varabes Pes (respose varabes, drecty measurabe from data) chage wth chages vew ad umato, the epaatory varabes (ot drecty measurabe but of actua terest) Epaatory Varabes, Factors epa or cause chages the respose varabe Pe vaues chage wth scee geometry, umato ocato, camera ocato whch are kow as the epaatory varabes he Prcpe Behd Prcpa Compoet Aayss Aso caed: - Hotteg rasform or the - Karhue- oeve ethod Fd a orthogoa coordate system such that data s appromated best ad the correato betwee dfferet as s mmzed PCA / Egemages: rovch & Krby 987 PCA for Recogto Egemages "ow Dmesoa Procedure for the Characterzato of Huma Faces" urk & Petad 99 "Face Recogto Usg Egefaces" urase & ayar 995 "Vsua earg ad recogto of D objects from appearace" IJoffe; Prcpe Compoet Aayss; 986 RCGozaas, PAWtz; Dgta Image Processg; 987 KKarhue; Uber eare ethode der Wahrschechkets Rechug; 946 oeve; Probabty heory; 955 PCA: heory PCA Defe a ew org as the mea of the data set Fd the drecto of mamum varace the sampes (e ) ad ag t wth the frst as (y ), Cotue ths process wth orthogoa drectos of decreasg varace, agg each wth the et as hus, we have a rotato whch mmzes the covarace y e e y PCA-Dmesoaty Reducto Cosder a set of mages, & each mage s made up of pes ad pe has the same vaue as pe for a mages [ ] st ad PCA chooses as the drecto of hghest varabty of the data, mamum scatter pe st as pe d as pe data matr, D c Each mage coeffcets D UV Bc c c s ow represeted by a vector of a reduced dmesoaty space (svd of D) B mmze the foowg fucto set B U E B B such that B B Idetty

6 he Covarace atr Defe the covarace (scatter) matr of the put sampes: ( µ)( (where µ s the sampe mea) µ µ µ) ( D )( D ) where [ µ µ ] µ µ µ µ PCA: ome Propertes of the Covarace/catter atr he matr s symmetrc he dagoa cotas the varace of each parameter (e eemet, s the varace the th drecto) Each eemet,j s the co-varace betwee the two drectos ad j, represets the eve of correato (e a vaue of zero dcates that the two dmesos are ucorreated) catter of matr: VD of a atr ( D ) UΣV by svd of ( D- ) ( D )( D ) UΣ U (svd of ) ( D )( D ) set B U set B U ook for: -B uch that: PCA: Goa Revsted [c c ] B [ ] correato s mmzed Cov(C) s dagoa ote that Cov(C) ca be epressed va Cov(D) ad B : CC B ( D )( D ) B B B eectg the Optma B Data Reducto: heory How do we fd such B? ( D µ )( D µ ) b λ b B ΛB B opt cotas the egevectors of the covarace of D Each egevaue represets the the tota varace ts dmeso hrowg away the east sgfcat egevectors B opt meas throwg away the east sgfcat varace formato Bopt [b bd]

7 PCA for Recogto [ ] Cosder the set of mages st ad PCA chooses as the drecto of hghest varabty of the data Data ad Egefaces Data s composed of 8 faces photographed uder same ghtg ad vewg codtos Gve a ew mage,, compute the vector of coeffcets assocated wth the ew bass, B ew c ew pe st as pe d as c B B B ew ew c ew et, compare a reduced dmesoaty represetato of ew agast a coeffcet vectors c Oe possbe cassfer: earest-eghbor cassfer Each mage beow s a coum vector the bass matr B pe by Ae O Vasescu by Ae O Vasescu Egemages Prcpa compoets (egevectors) of mage esembe pe k 55 ear Represetato: c c c9 55 pe pe k 55 c c 55 c ear Represetato: pe c8 55 pe pe 55 d Uc Uc Rug um: term terms 9 terms 8 terms Egevectors are typcay computed usg the guar Vaue Decomposto (VD) agorthm he Covarace atr PIE Database (Wezma) Defe the covarace (scatter) matr of the put sampes: ( µ)( µ) (where µ s the sampe mea)

8 EgeImages-Bass Vectors Each mage beow s a coum vector the bass matr B PCA ecodes ecodes the varabty across mages wthout dstgushg betwee varabty peope, vewpots ad umato by Ae O Vasescu PCA for Recogto - EgeImages Cosder a set of mages of peope uder fed vewpot & ghtg codto Each mage s made up of pes pe perso perso d as pe st as st as d as Reduce dmesoaty by throwg away the as aog whch the data vares the east he coeffcet vector assocated wth the st bass vector s used for cassfcto Possbe cassfer: ahaaobs dstace Each mage s represeted by oe coeffcet vector Each perso s dspayed mages ad therefore has coeffcet vectors by Ae O Vasescu pe perso perso pe

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