Discriminative Projection Selection Based Face Image Hashing

Transcription

1 IEICE TRANS. INF. & SYST., VOL.Exx D, NO.xx XXXX 00x LETTER Dscrmnatve Projecton Selecton Based Face Image Hashng Cagatay KARABAT a), Student Member and Hakan ERDOGAN, Nonmember SUMMARY Face mage hashng s an emergng method used n bometrc verfcaton systems. In ths paper, we propose a novel face mage hashng method based on a new technque called dscrmnatve projecton selecton. We apply the Fsher crteron for selectng the rows of a random projecton matrx n a user-dependent fashon. Moreover, another contrbuton of ths paper s to employ a bmodal Gaussan mxture model at the quantzaton step. Our smulaton results on three dfferent databases demonstrate that the proposed method has superor performance n comparson to prevously proposed random projecton based methods. key words: face mage hashng, bometrc securty, prvacy Fg. Basc steps of the bometrc hashng methods. Introducton In recent years, bometrcs has acheved wde-spread usage n varous applcatons. In most of these applcatons, bometrc templates are stored n databases and/or smart cards, thus rasng questons such as data securty and prvacy. Varous bometrc hashng methods, whch mostly depend on random projectons, are proposed to protect the bometrcs data []-[5] n the lterature. See Fgure for an llustraton of the bascs steps of such bometrc hashng methods. Ngo et al.[], [] employ feature extracton methods.e. Prncple Component Analyss PCA), Fsher Lnear Dscrmnant FLD), Wavelet transformaton, Wavelet Transform wth PCA, Wavelet Transform wth Fourer Melln Transform etc.) to the face mages and then make and use a random projecton RP) matrx for reducng the dmenson of the feature vectors. Fnally, they employ bnary quantzaton to obtan face mage hash vectors. We mprove upon ths method n our work. In ths work, we develop a new face mage hashng method based on a proposed technque that we call dscrmnatve projecton selecton to reduce verfcaton errors. Ths technque selects the rows of an RP matrx, whch s a user dependent dmenson reducton matrx, by usng the Fsher crteron [6]. Moreover, we employ Gaussan mxture model at the quantzaton step to obtan more dstnct face mage hash vectors for each user. Manuscrpt receved June 7, 0. The author s wth TUBITAK BILGEM Center of Research for Advanced Technologes on Informatcs and Informaton Securty) The author s wth the Faculty of Engneerng and Natural Scences, Sabanc Unversty The author s wth the Faculty of Engneerng and Natural Scences, Sabanc Unversty a) E-mal: cagatay@uekae.tubtak.gov.tr DOI: 0.587/transnf.E0.D.. The Proposed Bometrc Verfcaton Method In ths secton, we ntroduce a bometrc verfcaton system whch employs the proposed face mage hashng method based on the dscrmnatve projecton selecton technque.. Enrollment Stage There are three man steps at the enrollment stage: ) Feature extracton, ) Dmenson reducton, 3) Quantzaton... Feature Extracton At the feature extracton phase, we use two sets of data: tranng set and others set. The tranng set has tranng face mages of regstered users, I, j R m n, =,..., K where K denotes number of users and j=,..., L where L denotes number of tranng mages per user. We lexcographcally re-order them and obtan tranng face vectors, x, j R mn). The others set contans randomly selected face mages whch do not belong to any regstered users Ĩ s R m n, s =,..., M where M denotes the number of face mages belongng to the others set. We agan lexcographcally re-order them and obtan face vectors, x s R mn) of the others set. We apply PCA to the face mages n the tranng set for feature extracton. y, j = Ax, j µ), ) where A R q mn) s the PCA matrx traned usng the face mages n the tranng set, y, j R q s the PCA coeffcent vector belongng to the j th tranng mage of the th user and µ s the mean face vector. We project the face mages n the others set onto the PCA subspace as follows: ỹ s = A x s µ), ) where ỹ s R q s the PCA coeffcent vector belongng to Copyrght c 00x The Insttute of Electroncs, Informaton and Communcaton Engneers

2 IEICE TRANS. INF. & SYST., VOL.Exx D, NO.xx XXXX 00x the s th mage of the others set. We use these PCA coeffcent vectors n the dscrmnatve projecton selecton technque to fnd the most valuable features, whch maxmze the dstance between the face mages of a user n the tranng set and the face mages n the others set, n the lowerdmensonal subspace... Dmenson Reducton At the dmenson reducton phase, we generate an RP matrx, T R l q, for each user to reduce the dmenson of her feature vector. The RP matrx elements are dentcally and ndependently dstrbuted..d) and generated from a Gaussan dstrbuton wth zero mean and unt varance by usng a random number generator RNG) wth a seed derved from the user s secret key. We apply the Gram-Schmdt GS) procedure to obtan an orthonormal projecton matrx R R l q to have more dstnct projectons. Then, we project the PCA coeffcent vectors of the th user onto a lowerl-dmensonal subspace. z, j = R y, j, 3) where z, j R l s the ntermedate face mage hash vector belongng to the j th tranng mage of the th user. To determne the competng hash vectors, we also project the others set usng the RP matrx as follows: z s = R ỹ s, 4) where z s R l s the ntermedate face mage hash vector of the s th face mage of the others set and R s the orthonormal random projecton matrx of the th user. The proposed dscrmnatve projecton selecton technque selects the rows of the matrx R usng the Fsher crteron [6] and creates the dscrmnatve random projectons. Thus, we am to ncrease dscrmnablty due to mappng the PCA coeffcent vectors nto a more dscrmnant subspace. Fsher crteron s a feature selecton method and n ths case the features are the features obtaned after the random projecton of a PCA coeffcent vectory, namely: zk)=r T,ky, 5) for k=,...,l, where zk) s a scalar value and r T,k R q denotes the k th row of R. The k th feature for the th user s j th mage s z, j k) and the same feature for the s th element of the others set s z s k) whch are the k th elements of the correspondng vectors defned n Equatons 3) and 4). The features are already uncorrelated due to the GS procedure whch ensures r T,k r,m= 0 for k m. We defne e k [ z, k),...,z,l k) ], 6) whch s a collecton of the k th dmenson or bt poston) coeffcents of the ntermedate hash vectors belongng to the th user for each k=,...,l. Frst, we compute the sample mean value, ˆµ,k, of each e k vector for each bt poston k=,...,l as follows: ˆµ,k = L L j= e k j), 7) where e k j) s the jth element of the vector e k whch s defned n Equaton 6). Then, we compute the sample standard devaton, ˆσ,k, of each e k vector for each bt poston k=,...,l as follows: ˆσ,k = L L j= e k j) ˆµ,k ). 8) Smlarly, we collect together the k th dmenson values of the ntermedate hash vectors of the others data set as q k [ z k),..., z M k)] 9) for all k=,...,l. Frst, we compute the sample mean value, ˆµ,k, of each q k for each bt poston k=,...,l as follows: ˆµ,k = M M q k s), 0) where q k s) s the s th element of the vector q k whch s defned n Equaton 9). Next, we compute the sample standard devaton, ˆσ,k, of each q k for each bt poston k=,...,l as follows: ˆσ,k = M s= M q k s) ˆµ,k) s=. ) By applyng the Fsher crteron, we try to select the rows that have hgher contrast between genune user s data and the others set. In other words, we am to reduce the dstance between the genune user s dfferent face mage hash vectors whle at the same tme we am to maxmze the dstance between the th user s data and the others set. We compute the Fsher score for each row of R as follows: η k)= ˆµ,k ˆσ,k ˆµ,k ) + ˆσ,k ). ) We use these Fsher scores obtaned for each dmenson k to rank the rows of the random projecton matrx R. We defne r T,k to be the kth row of R. That s R = r T,.. r T,l. 3) We choose top rankng rows from the random projecton matrx. Let c be the ndex vector whch ranks the rows of the matrx n a descendng manner from towwherew

3 LETTER 3 s the number of desred rows. That s, c ) s the row ndex of R that has the hghest Fsher score, c ) s the ndex wth the second hghest score and so on. Thus, we obtan the dscrmnatve random projecton matrx ˆR R w q and the ndex vector, c, whch contans the ndces of topwrows for each user. We defne ˆr T, ˆR =.., 4) ˆr T,w where ˆr,p = r,c p) for p=,...,w. We only store the ndex vector, c, for the th user n the database for verfcaton at the test stage. Next, we project the PCA coeffcents, whch belong to the tranng face mages of the th user, onto a lowerwdmensonal subspace by usng the calculated ˆR as follows: f, j = ˆR y, j, 5) where f, j R w s the raw face mage hash vector belongng to the j th tranng mage of the th user. Ngo et.al [], [] uses FLD as a feature extracton method whch s appled before the random projecton step n the algorthm. Ther FLD transform s not user specfc and ams to dscrmnate face mages belongng to dfferent users n the database. In our case, we employ the Fsher crteron for projecton selecton for bometrc verfcaton. Therefore, n our case, the projecton selecton s user-specfc and ams to dscrmnate the clamed user s bometrc hash vector from all other possble ones that may come from other face mages. In our case, other face mages may even be from outsde the database whch s more realstc n a real scenaro. Our others set s chosen from another database for ths purpose. The projecton selecton s done after the random projecton step. FLD can reduce dmenson at most to K dmensons, where K s the number of users n the database, due to the maxmal rank of the between class covarance matrx. However, n our method, we do not have such a lmtaton snce the selecton s done by rankng the Fsher crtera obtaned from each projecton. In summary, there are fundamental dfferences between usng FLD as a dmenson reducng feature extracton method and usng the Fsher crtera for selecton of random projectons that best separate the clamed dentty from all others.. Quantzaton In ths subsecton, we dscuss the quantzaton methods used n ths work. We employ two dfferent quantzaton methods: ) Bnary quantzaton BQ) [], [] and ) The proposed Gaussan mxture model GMM) based quantzaton method. In our smulatons, we employ these quantzaton methods separately to show the performance of the system... Bnary Quantzaton Method wth a Fxed Threshold Ths technque s employed n Ngo et al. s method [], []. The raw face mage hash vector f, j elements are bnarzed wth respect to a pre-determned fxed threshold as follows: { f f λ, j k)=, j k) µ, 6) 0 Otherwse. where the threshold µ s chosen as the sample mean value of elements of the vector f, j and k=,...,w. The computed reference face mage hash vectorsλ, j R w are stored n the database... The Proposed GMM Based Quantzaton Method To the best of our knowledge, there s no face mage hashng method employng GMM n the quantzaton step. GMM s one of the most wdely used data clusterng methods n the lterature [7]. Let us assume that we have a set of numbers whch are obtaned by collectng the k th elements of raw face mage hash vectors and we want to bnarze the element of ths set. Snce our am s to make bnarzaton, we ft two Gaussan dstrbutons to the hstogram of the k th elements of the raw face mage hash vectors by usng the GMM. Then, we choose the average of the mean values of these two Gaussan dstrbutons as an optmum threshold for partton of these two dstrbutons. We repeat t for each bt locaton k =,..., w separately. In other words, we employ bmodal GMM to fnd an optmum threshold for each bt poston for bnarzaton. Let f, j k) denote the k th bt of f, j R w, we defne the vector d k as the collecton of all k th dmenson values of the raw mage hashes n the database. d k [ f, j k) : =,..., K, j=,..., L ] R r, 7) where k=,...,w, r=k L, K s the number of users and L s the number of tranng mages per user. Assume that the elements of the vector d k are observatons of a sngle random varable d. p d Ψ k) = S α k s p d θs) k, 8) s= whereα k s s a mxture weght, S s= αk s = where S = due to bnarzaton,ψ k = { α k,αk,θk,θk } and p d Ψ k ) s a one-dmensonal Gaussan densty wth ts own parameters θ k s= { µ k s,σ k s} as follows: p ) d θ k s = e d µk s) / σ k s) ), 9) π σ k s whereµ k s andσ k s denote mean varance for the s th component of the GMM respectvely for s={, }. We fnd an optmum threshold for each bt poston as follows: T k = µk +µk, 0) where T k denotes the optmum threshold for the k th bt poston of the raw face mage hash vector f, j,, j. Note that,

4 4 IEICE TRANS. INF. & SYST., VOL.Exx D, NO.xx XXXX 00x the GMM s traned usng the whole tranng set for each bt poston. Thus, the GMM parameters are not user dependent. Fnally, the elements of f, j are bnarzed wth respect to the optmum system-level thresholds as follows: { f f λ, j k)=, j k) T k, ) 0 Otherwse. where k =,...,w. The computed reference face mage hash vectorsλ, j R wx are stored n the database..3 Test Stage At the test stage, a clamer clams that she s the th user and sends her face mage and her secret key to the system. The system computes her test face mage hash vector by usng her face mage, her secret key to generate a RP matrx) and the ndex vector, c, whch belongs to the th user. Recall that ndex vectors and the reference face mage hash vectors of the regstered users are stored n the database; however, the secret keys are not stored n the database. Then, the Hammng dstance [8] s computed between the test face mage hash vector and the reference face mage hash vectors whch belong to the th user and were generated at the enrollment stage. If t s below the pre-determned dstance threshold, the clamer s accepted; otherwse, the clamer s rejected. We smulate two scenaros n our experments. These scenarous are descrbed n detal below.. Key-Unknown Scenaro: In ths scenaro, an unauthorzed mpostor has nether the secret key nor the face mage template belongng to the genune user. Note that the ndex vectors of the users are stored n the database. Therefore, whenever a clamer clams that she s the th user and sends her face mage and a secret key to the system, the system computes a test face mage hash vector by usng the data sent by the clamer and the ndex vector, c, whch belongs to the th user.. Key Stolen Scenaro: In ths scenaro, an unauthorzed mpostor acqures the secret key of the th genune user but does not have the clamed person s face mage. When an mpostor sends her face mage and the secret key of the th user to the system, the system computes a test face mage hash vector by usng the data sent by the mpostor and the ndex vector c that belongs to the th user whch s stored n the database. 3. Smulaton Results In ths secton, we dscuss our expermental results. We test the performance of the proposed method on AT&T [9], AR [0] and the Sheffeld prevously UMIST) face databases []. AT&T database has 400 dfferent face mages correspondng to 40 dstnct people. AR database has 30 face mages belongng to 0 dfferent people s faces. The Sheffeld database has 564 dfferent face mages belongng to 0 dfferent people. Besdes, we randomly select 04 face mages from Carnege Mellon Unversty database [] and create the others set. We compare the performance of the proposed method to the Ngo et al. s PCA+RP and FLD+RP methods that were ntroduced n [], [] as shown n Table. We automatcally select face mages for tranng and test sets and evaluate the performance of the proposed method and Ngo et al. s methods [], []. We use 04-length PCA coeffcent vectors for the face mages belongng to the tranng, test and others sets n the smulatons. In our experments, pre-processng technques such as eye algnment, head regon maskng, lghtng adjustment are not appled to the face mages. In our smulatons for both scenaros; for mpostor tests, each face mage n the test set s compared aganst each face mage of all other users n the tranng set. The faled mposter test results n False Acceptance error. For the genune tests, each face mage n the test set s compared aganst all face mages of the same user n the tranng set. The faled genune test results n False Rejecton error. The detaled nformaton on the data sets used n the experments are gven n Table. The proposed Table Data sets and Expermental Set-up Database Number of Face Images Tran set AR 30 mages from The frst 7 mages 0 people AT&T 400 mages from The frst 5 mages 40 people Sheffeld 564 mages from The frst 8 mages 0 people Test set The last mages The rest 5 mages The followng 8 mages method has better performance n terms of equal error rate EER) n comparson to the Ngo et al. s methods [], [] whereas Ngo et al. s PCA+RP and FLD+RP methods have comparable performances wth each other as shown n Table. As the length of face mage hash vector decreases, the proposed method shows better mprovement snce the proposed dmenson reducton matrx better preserves the Mss probablty n %) DET plots for the AT&T Database Ngo PCA+RP Ngo FLD+RP The Proposed Method wth BQ The Proposed Method wth GMM False Alarm probablty n %) Fg. DET plots for the methods wth 56 bt face mage hash vector length for key stolen scenaro - AT&T database

5 LETTER 5 Length of Face Hash Vector Table [], [] EER %) of Ngo et al. s Method [], [] PCA+RP) EER Performances of the Proposed Face Image Hashng Method and Ngo et al. s Methods EER %) of Ngo et al. s Method [], [] FLD+RP) EER %) of The Proposed Method wth Bnary Quantzaton Method wth Fxed Threshold EER %) of The Proposed Method wth GMM Based Quantzaton Method Scenaro 64 bt %.9 % 0.46 % 3.83 %.73 Key Unknown AT&T 8 bt % 7.36 % 8.5 %.3 %.57 Key Unknown AT&T 56 bt % 5.8 % 5.50 %.80 %.5 Key Unknown AT&T 5 bt % 3.79 % 4.7 %.48 %.0 Key Unknown AT&T 64 bt % 6.93 % 8.3 % 4.40 % 3.58 Key Stolen AT&T 8 bt % 3.97 % 6.73 %.0 %.4 Key Stolen AT&T 56 bt %.76 % 4.50 % 0.80 % 0.3 Key Stolen AT&T 5 bt %.34 % 3.55 % 0.5 % 9.73 Key Stolen AT&T 64 bt % 3.63 % 3.34 % 9.08 % 8.96 Key Unknown AR 8 bt % 8.4 % 8.05 % 8.67 % 8.7 Key Unknown AR 56 bt % 5.8 % 3.93 % 7.8 % 8. Key Unknown AR 5 bt %.38 %.9 % 8.33 % 8.57 Key Unknown AR 64 bt % 8.7 % 8.5 % 8.07 % 8.46 Key Stolen AR 8 bt % 7.7 % 7.56 % 8.06 % 8.05 Key Stolen AR 56 bt % 5.50 % 6.44 % 9.0 % 8.83 Key Stolen AR 5 bt % 4.89 % 5.04 % 0.95 % 0.4 Key Stolen AR Database 64 bt % 7.09 %.00 % 5.75 % 6.3 Key Unknown Sheffeld 8 bt % 6.38 % 9.0 % 3.33 % 4.03 Key Unknown Sheffeld 56 bt % 5.05 % 4.93 %.45 %.05 Key Unknown Sheffeld 5 bt % 4.97 % 4. % 0.44 %.0 Key Unknown Sheffeld 64 bt %.40 % 4.50 % 9.38 % 0.68 Key Stolen Sheffeld 8 bt %.9 % 4.30 % 7.5 % 9.7 Key Stolen Sheffeld 56 bt %.53 %.0 % 6.96 % 7.80 Key Stolen Sheffeld 5 bt % 3.47 %.55 % 9.7 % 8. Key Stolen Sheffeld par-wse dstances between feature vectors n the reduced dmenson subspace n comparson wth the tradtonal random projecton matrx. The best results are usually obtaned wth 8 or 56 bts. Besdes, we plot the detecton error trade-off DET) curves [3] for key stolen scenaro of the 56 bt face mage hash length wth the AT&T database n Fgure. Ngo et al. [], [] employs bnary quantzaton method wth a fxed threshold for all bts. Ths method may be suboptmal n some cases. The proposed GMM-based quantzaton method reduces EER most of the tme n comparson to the bnary quantzaton snce t fnds approxmately optmum threshold values for each bt poston. 4. Concluson In ths paper, we propose a novel face mage hashng method for a bometrc verfcaton system. The proposed method s based on dscrmnatve projecton selecton dependng on Fsher crtera. Another novelty of the proposed method s to employ bmodal GMM n the quantzaton step. The smulatons demonstrate that the proposed method has better performance n comparson wth the random projecton based face mage hashng methods proposed n the lterature. References Vdeo Tech., vol.6, no.6, June 006. [] D.C.L.Ngo, A.B.J. Teoh, A. Goh, Egenspace-based face hashng, Proc. of the Internatonal Conference on Bometrc Authentcaton ICBA) n LNCS, vol. 307, pp , Hong Kong, July 004. [3] C. Karabat, H.Erdogan, A Cancelable Bometrc Hashng for Secure Bometrc Verfcaton, Proc. IEEE IIH-MSP 009, pp , Kyoto, Japan, 009. [4] A. Lumn, L. Nann, An Improved BoHashng for Human Authentcaton, Proc. of the Pattern Recognton, vol.40, no.3, pp , March 007. [5] A.Kong, K.H. Cheung, D. Zhang, M. Kamel, J. You, An Analyss of BoHashng and Its Varants, Proc. of the Pattern Recognton, vol.39, no.7, pp , 007. [6] G. J. McLachlan ed., Dscrmnant Analyss and Statstcal Pattern Recognton, John Wley&Sons, Inc., 99. [7] R.O. Duda and P.E. Hart ed., Pattern Classfcaton and Scene Analyss, John Wley&Sons, Inc., 973. [8] R.W. Hammng, Error Detectng and Error Correctng Codes, Proc. Bell Sys. Techn. Journal, vol.9, no., pp.47-60, 950. [9] Cambrdge Unversy AT&T face database, [0] A.M.Martnez and R.Benavente, The AR Face Database, CVC Techncal report #4, June 998. [] Danel B. Graham and Ngerl M. Allnson, Face Recognton: From Theory to Applcatons, Proc. NATO ASI Seres F, Computer and Systems Scences, Vol. 63. H. Wechler, P.J.Phlps, V.Bruce, F. Fogelman-Soule and T.S. Huang ed.), pp , 998. [] Carnege Mellon Unversty Face Database, [3] A. Martn, G. Doddngton, T. Kamm, M. Ordowsk, and M.A. Przybock, The det curve n assessment of detecton task performance, n Proc. of Eurospeech Rhodes, Greece, Sept., 997, pp [] D.C.L.Ngo, A.B.J. Teoh, A.Goh, Bometrc Hash: Hgh Confdence Face Recognton, Proc. IEEE Trans. on Crc. and Sys. for