Eigenface for Eigenface for Face RecognitionFace RecognitionPresenter: Trn c MinhPresenter: Trn c Minh OutlineOutlineOverviewOverviewEigenfaces for RecognitionEigenfaces for RecognitionConclusion OverviewOverviewFace Representation Face RepresentationTemplate-based approaches Template-based approachesFeature-based approaches Feature-based approachesAppearance-based approaches Appearance-based approachesFace Detection Face DetectionUtilization of elliptical shape of human headUtilization of elliptical shape of human head ( (applicable onl to front viewsapplicable onl to front views ! "#$ ! "#$%anipulation of images in &face space' "($ %anipulation of images in &face space' "($Face !enti"cation Face !enti"cation)erformance a*ected b scale+ pose+ illumination+)erformance a*ected b scale+ pose+ illumination+ facial e,pression+ and disguise+ etc- facial e,pression+ and disguise+ etc- Face spaceFace spaceAn image is a point in a high dimensional space An image is a point in a high dimensional spaceAn . , % image is a point in R An . , % image is a point in R.% .%/e can de0ne vectors in this space as we did in the 12 case /e can de0ne vectors in this space as we did in the 12 case+ = OutlineOutlineOverviewOverviewEigenfaces for RecognitionEigenfaces for RecognitionConclusion Eigenfaces #pproachEigenfaces #pproachn the language of infor$ation theor%&& n the language of infor$ation theor%&&E*icient encoding followed b comparing one faceE*icient encoding followed b comparing one face encoding with a database of models encodedencoding with a database of models encoded similarl similarl Eigenfaces #pproach Eigenfaces #pproach (Contd.)(Contd.)n $athe$atical ter$s&&' n $athe$atical ter$s&&'Find the principal components of the faceFind the principal components of the face distribution+ or the eigenvectors of the covariancedistribution+ or the eigenvectors of the covariance matri, of the set of face images+ called eigenfaces matri, of the set of face images+ called eigenfacesEigenfaces are a set of features that characterizeEigenfaces are a set of features that characterize the variation between face images the variation between face imagesEach training face image can be represented inEach training face image can be represented in terms of a linear combination of the eigenfaces+ soterms of a linear combination of the eigenfaces+ so can the new input image can the new input image3ompare the feature weights of the new input3ompare the feature weights of the new input image with those of the 4nown individuals image with those of the 4nown individuals E,ample for eigenfaceE,ample for eigenfaceEigenfaces loo( so$ewhat li(e generic faces' Ma)or *tepsMa)or *teps(- (- 5nitialization6 ac7uire the training set of face images5nitialization6 ac7uire the training set of face images and calculate the eigenfaces+ which de0ne the faceand calculate the eigenfaces+ which de0ne the face space space1- 1- 8iven an image to be recognized+ calculate a set of8iven an image to be recognized+ calculate a set of weights of theweights of the M M eigenfaces b pro9ecting it ontoeigenfaces b pro9ecting it onto each of the eigenfaces each of the eigenfaces:- :- 2etermine if the image is a face at all b chec4ing if2etermine if the image is a face at all b chec4ing if the image is su*icientl close to the face space the image is su*icientl close to the face space;- ;- 5f it is a face+ classif the weight pattern as either a5f it is a face+ classif the weight pattern as either a 4nown person of as un4nown 4nown person of as un4nown#- #- (Optional! 5f the same un4nown face is seen several(Optional! 5f the same un4nown face is seen several times+ update the eigenfaces < weight patterns+times+ update the eigenfaces < weight patterns+ calculate its characteristic weight pattern andcalculate its characteristic weight pattern and incorporate into the 4nown faces incorporate into the 4nown faces Calculating EigenfacesCalculating Eigenfaces=et of training images(is a column vector=et of training images(is a column vector of size! of size!Average face of the training set6 Average face of the training set6Each training image di*ers from the average face b6 Each training image di*ers from the average face b6A total number ofpairs of eigenvectors andA total number ofpairs of eigenvectors and eigenvaluesof the covariance matri,eigenvaluesof the covariance matri, ( (C C6 6matri,! E7- ((! matri,! E7- ((!where( where(A A6 matri,! 6 matri,!3omputationall 5ntractable 3omputationall 5ntractable > >1 2, ,......,M n21 N11MnnM= = n n= nn11MT Tn nnC AAM== =1 2[ , ,......, ]MA = 2 2N N 2N M 2N Calculating EigenfacesCalculating EigenfacesFor 3omputational Feasibilit For 3omputational FeasibilitOnlOnl MM - ( - ( eigenvectors areeigenvectors are meaningful meaningful (!(! Eigenvectorsand associated eigenvaluesofEigenvectorsand associated eigenvaluesof 66 E7- (1! E7- (1!Therefore+are the eigenvalues of + are theTherefore+are the eigenvalues of + are the associated eigenvalues associated eigenvaluesE7- (:! E7- (:!The associated eigenvalues allow us to ran4 theThe associated eigenvalues allow us to ran4 the eigenvectors according to their usefulness ineigenvectors according to their usefulness in characterizing the variation among the images characterizing the variation among the images2M N Tn n nAA A A =nATC AA =n1Mn nk k nkA == = +sing Eigenfaces for +sing Eigenfaces for !enti"cation!enti"cation3onstruction of ?nown 5ndividuals@ Face3onstruction of ?nown 5ndividuals@ Face 3lasses 3lasses-- 5mages of 4nown individuals are pro9ected onto &face-- 5mages of 4nown individuals are pro9ected onto &face space' b a simple operation+space' b a simple operation+ where iA(+ 1+ BB+ % where iA(+ 1+ BB+ % represents therepresents the i ith individual+th individual+ andand kk A(+ 1+ BB+A(+ 1+ BB+ MM represents the weight coe*icientrepresents the weight coe*icient of eigenvector- The pattern vector of theof eigenvector- The pattern vector of the i ithth individual individual

-- 5f an individual has more than one image+ ta4e the-- 5f an individual has more than one image+ ta4e the average of the pattern vectors of this person average of the pattern vectors of this person( )Tik k i = k1 2 '[ , ,......, ]i i i iM = +sing Eigenfaces for +sing Eigenfaces for !enti"cation ,Cont!'-!enti"cation ,Cont!'-8iven a new image 8iven a new image -- )ro9ect onto face space+ and get its pattern vector-- )ro9ect onto face space+ and get its pattern vector -- 2etermine whetheris a face image6 -- 2etermine whetheris a face image6E7- (;!E7- (;!5f C a prede0ned threshold + it is a face imageD5f C a prede0ned threshold + it is a face imageD otherwise+ not otherwise+ not-- 3lassif either as a 4nown individual or as un4nown6-- 3lassif either as a 4nown individual or as un4nown6 E7- (#! E7- (#!5fC a prede0ned5fC a prede0ned threshold + is identi0ed as thethreshold + is identi0ed as the k kth face classDth face classD otherwise+ it is identi0ed as un4nown otherwise+ it is identi0ed as un4nown1 2 '[ , ,......, ]M ='2 21 ( )Mn nn == 2 2( )k k = 'min{ , 1, 2,......, '}k kk M = = OutlineOutlineOverviewOverviewEigenfaces for RecognitionEigenfaces for RecognitionConclusion #!vantages#!vantagesEase of implementation Ease of implementation.o 4nowledge of geometr or speci0c.o 4nowledge of geometr or speci0c feature of the face re7uired feature of the face re7uiredEittle preprocessing wor4 Eittle preprocessing wor4 .i$itations.i$itations=ensitive to head scale =ensitive to head scaleApplicable onl to front view Applicable onl to front view8ood performance onl under controlled8ood performance onl under controlled bac4ground (not including natural scenes! bac4ground (not including natural scenes! ReferenceReference(- (- & &Eigenfacesforrecognition'+%-Tur4andA-Eigenfacesforrecognition'+%-Tur4andA- )entland+)entland+JournalofCognitiveNeuroscience,JournalofCognitiveNeuroscience, vol.3, No.1, 1991 vol.3, No.1, 19911- 1- & &Face recognition using eigenfaces'+ %- Tur4 andFace recognition using eigenfaces'+ %- Tur4 and A- )entland+A- )entland+ Proc. IEEE Conf. on Comuter !isionProc. IEEE Conf. on Comuter !ision an" Pattern #ecognition an" Pattern #ecognition+ pages #FG-#H(+ (HH( + pages #FG-#H(+ (HH(:- :- Eindsa-5-=mith-AtutorialonprincipalEindsa-5-=mith-Atutorialonprincipal components analsis+ Februar 1II1 components analsis+ Februar 1II1$. $. IlkerAtala%M.&c'(esis)*ace #ecognition+singIlkerAtala%M.&c'(esis)*ace #ecognition+sing EigenfacesIstan,ul'ec(nical+niversit%-EigenfacesIstan,ul'ec(nical+niversit%- Januar% 199. Januar% 199.#- #- 2imitri)issaren4o+Eigenface-basedfacial2imitri)issaren4o+Eigenface-basedfacial recognition+ Feb IG+ 1II: recognition+ Feb IG+ 1II: De$oDe$o Than( %ouThan( %ou