Pose Invariant Face Recognition using Hybrid DWT-DCT Frequency Features with Support Vector Machines

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1 Proceedngs of the 4 th Internatonal Conference on 7 th 9 th Noveber 008 Inforaton Technology and Multeda at UNITEN (ICIMU 008), Malaysa Pose Invarant Face Recognton usng Hybrd DWT-DCT Frequency Features wth Support Vector Machnes Jawad Nag,*, Syed Khaleel Ahed, and Farrukh Nag 3 Power Engneerng Centre, Research Manageent Centre Departent of Electroncs and Councaton Engneerng, College of Engneerng 3 Departent of Mechancal Engneerng, College of Engneerng Unverst Tenaga Nasonal, K 7, Jalan Kajang-Puchong, Selangor, Malaysa jawad@unten.edu.y, syedkhaleel@unten.edu.y, farrukh@unten.edu.y Abstract Face recognton s a challengng proble and up to date, there s no technque that provdes a robust soluton to all stuatons. Ths paper presents a hybrd approach to pose nvarant huan face recognton. The proposed schee s based on a cobnaton of the Dscrete Wavelet Transfor (DWT) and Dscrete Cosne Transfor (DCT) analyss on face ages. The DWT-DCT doan coeffcents are used for feature extracton usng sple statstcal easures and quantzaton. Ths approach reduces the denson of the orgnal face ages whle preservng the property of data dstrbuton n the feature subspace. A Support vector achne (SVM) classfer s used for classfyng DWT-DCT based feature vectors nto separate groups for recognton purposes. The hybrd DWT-DCT-SVM face recognton odel s evaluated n MATLAB on the Cabrdge ORL face database. Coparson of the proposed technque wth exstng face recognton schees proves that the cobnaton of DWT-DCT prove feature selecton perforance copared to other approaches. Keywords: Face recognton, Dscrete wavelet transfor, Dscrete cosne transfor, Support vector achne, Donant frequency features.. Introducton Face recognton has becoe an actve area of research n recent years anly due to ncreasng securty deands and ts potental coercal and law enforceent applcatons []. The last decade has shown draatc progress n ths area, wth ephass on applcatons such as huan-coputer nteracton (HCI), boetrc analyss, content-based codng of ages and vdeos, ntellgent ontorng, and dentfcaton felds []. Coonly researched face recognton ethods nclude geoetry, Egenfaces, neural networks and hdden Markov based ethods [3]. Huan face ages cannot be drectly used for classfer desgn. Ths s due to the hgh densonalty of the face vectors and redundant nforaton contaned n the face vectors, whch does not reveal donant characterstcs wthn face ages. Face recognton technques coonly used for feature extracton and densonalty reducton nclude Prncpal Coponent Analyss (PCA) and Lnear Dscrnant Analyss (LDA). The dsadvantage of PCA s that t treats nner-classes and outer-classes equally, and therefore, becoes senstve to probles assocated wth facal expressons. To overcoe ths proble any ethods have been put forward such as Fsherfaces, a cobnaton of PCA and LDA [4]. Recently, wavelets havng good qualtes n spatal and frequency doans have been consdered an deal tool for solvng face recognton probles [5,6]. In addton, the DCT a coonly used approach for age copresson has been prevously used for feature extracton of face ages []. Ths paper presents a novel approach for pose nvarant face recognton wth draatc reducton n coputatonal requreents. Ths approach s based on a hybrd cobnaton of the Dscrete Wavelet Transfor (DWT) and Dscrete Cosne Transfor (DCT) for feature selecton fro face ages. Support Vector Machnes (SVM) havng good generalzaton ablty, non-lnear dvdng hypersurfaces and hgh dscrnaton are used to classfy DWT-DCT based feature vectors for recognton purposes [6]. The hybrd DWT-DCT-SVM face recognton odel s evaluated n MATLAB on the ORL face database. 99

2 . Dscrete Wavelet Transfor The Dscrete Wavelet Transfor (DWT) s a very popular and coonly used tool for age analyss and, as such, has becoe the part of JPEG000 standard. The DWT decoposes a sgnal nto a set of bass functons called wavelets; decoposton s defned as the resoluton of a sgnal. The DWT then perfors a ult-resoluton analyss of a sgnal wth localzaton n both te and frequency doans [5]. DWT can be atheatcally expressed as follows: * j d j, k = x( n) hj ( n k) DWTx ( n) = () * j a, = ( ) ( ) j k x n g j n k where coeffcents d j,k refer to the detal coponents n the sgnal x(n), and a j,k refers to the approxaton coponents n the sgnal. The functons h(n) and g(n) represent the coeffcents of the hgh-pass and low-pass flters respectvely, whlst paraeters j and k refer to wavelet scale and translaton factors. For the case of ages, D-DWT s pleented as a set of flter banks, coprsng of a cascaded schee of hgh-pass and low-pass flters. The fnal result obtaned s a decoposton of the nput age nto four non-overlappng ult-resoluton sub-bands: LL, LH, HL and HH. The sub-band LL represents the coarse-scale DWT coeffcents whle the sub-bands LH, HL and HH represent the fne-scale of DWT coeffcents. To obtan the next coarser scale of wavelet coeffcents, the sub-band LL s further processed untl soe fnal scale N s reached. When N s reached 3N+ sub-bands consstng of the ultresoluton sub-bands LL N and LH y, HL y and HH y are coputed, where y ranges fro untl N. 3. Dscrete Cosne Transfor The Dscrete Cosne Transfor (DCT) s an algorth wdely used for age copresson, as t fors the bass for the nternatonal standard loss age copresson algorth known as JPEG. The DCT converts spatal doan sgnals nto eleentary frequency coponents by representng an age as a su of snusods of varyng agntudes and frequences [4]. Face ages havng hgh correlaton and redundant nforaton cause coputatonal burden n ters of processng speed and eory utlzaton. Therefore, the D blocked-dct segents an age nonoverlappng blocks and apples the DCT to each block, whch results n: low frequency and hgh frequency sub-bands. Most of the vsually sgnfcant sgnal energy les at low-frequency sub-band whch contans the ost portant vsual parts of the age. These coeffcents can be used as a type of sgnature that s useful for recognton tasks, such as face recognton. Hgh frequency coponents of the age are usually reoved through copresson, whch reduce data volue wthout sacrfcng age qualty. For an nput age, x, the D-DCT coeffcents for the transfored output age y, are coputed as follows: where, α q M N u= 0 v= 0 y( u, v) = αuαv x(, n) M N = ( + ) u π (n + ) v cos cos M N, v = 0, v N α u () (3) The nput age x, conssts of atrx havng N M pxels, where x(,n) s the ntensty of the pxel n row and colun n, and y(u,v) s the D-DCT coeffcent n row u and colun v. The age s reconstructed by applyng the D-IDCT operaton defned, as follows: M N u= 0 v= 0 = x(, n) = αuαv y( u, v) M N ( + ) u (n + ) v cos cos M N 4. Support Vector Machne (4) Support vector achnes (SVMs) were ntroduced by Vapnk n the late 960s on the foundaton of statstcal learnng theory [7]. In SVM, tranng s perfored n such a way as to obtan a quadratc prograng (QP) proble. The soluton to ths QP proble s global and unque. For eprcal data (x, y ),,(x, y ) R n {-,+} that are apped by φ: R n F nto a feature space, the lnear hyperplanes that dvde the nto two labeled classes s shown as: w φ ( x) + b = 0 w R b R (5) To construct an optal hyperplane wth axuargn and bounded error n the tranng data (soft argn), the followng QP proble s to be solved: n,,, u = 0 u M 00

3 Input Iage ORL Face Database DWT Feature Extracton DCT Classfcaton SVM Face Database Classfcaton Output Match No Match Fgure. Proposed hybrd face recognton odel n w, b w + C = ( w ( x) + b) ξ, =, y φ,..., (6) The frst ter n cost functon (6) akes axu argn of separaton between classes, and the second ter provdes an upper bound for the error n the tranng data. The constant C [0, ) creates a tradeoff between the nuber of sclassfed saples n the tranng set and separaton of the rest saples wth axu argn. A way to solve (6) s va ts Lagrange functon. Gven a kernel K(x, y ) = φ(x ) φ(x j ), the Lagrange functon of (6) s splfed to: w = ax α = = α = j= = j j ξ α α y y K( x, x ) y α φ( x ), α y = 0, 0 α C, j (7) (8) Fro eq. (5) t s seen that the optal hyperplane n feature space can be wrtten as the lnear cobnaton of tranng saples wth α 0. These nforatve saples known as support vectors, construct the decson functon of the classfer based on the kernel functon: f ( x) = sgn y α k( x, x, = j ) + b (9) Kernel functons n SVMs are selected based on the data structure and type of the boundares between the classes. The wdely appled kernel functon s the radal bass functon (RBF) kernel, whch s defned as: K x, x j ) = exp γ x x RBF ( j (0) where γ > 0 s the RBF kernel paraeter. The RBF kernel nduces an nfnte-densonal kernel space, and the kernel wdth paraeter γ controls the scalng of the appng. 5. Methodology A general overvew of the proposed hybrd face recognton odel developed s shown n Fgure. A hybrd cobnaton of the DWT and the DCT s used to extract features fro face ages, whch then undergo classfcaton usng SVM. Feature vectors obtaned fro DWT-DCT selecton are used as nputs for the SVM classfer. Classfcaton s carred out by valdatng the nput age wth a traned face database. Classfcaton results ncludng denttes of the closest atches and confdence scores contrbute to the output of the syste. To evaluate the perforance of the proposed ethod, the ORL face database s used. Ths database was developed at the Olvett Research Laboratory, Cabrdge, U.K. The ORL database contans 400 ages of 40 people.e., 0 dfferent ages for each person. Iages dffer wth respect to frontal vews for each person wth soe tolerance n pose and rotaton. The sze of each age s pxels n Btap fle forat wth 56 grey levels per pxel []. Three ndvduals fro the ORL face database wth fve dfferent ages are shown n Fgure. The hybrd face recognton odel presented n ths paper s developed usng MATLAB R008a v The DWT and DCT are pleented usng the MATLAB Wavelet and Sgnal Processng Toolboxes. A MATLAB lbrary for support vector achnes (LIBSVM) [] s used as the core of the ult-class SVM classfer. 0

4 Fgure. ORL face age database 5.. Feature Extracton For feature extracton face ages were frstly, preprocessed whch ncludes nose reoval, gray level odfcaton and equalzaton. The feature extracton ethod conssts of two stages: DWT and DCT. proposed work, D-DWT s used to extract the coeffcents of lowest frequency range n sub-bands. Therefore, the LL sub-band coponent havng the hghest age energy s selected for feature extracton. Secondly, the D-DCT of LL sub-band coponent s coputed. The D-DCT of each of the 8 8 pxels, 36 age sub-blocks s coputed usng 8 of 64 DCT coeffcents. The reanng coeffcents are dscarded. The age s then reconstructed by coputng the D- IDCT of each of the 36 blocks. Fgure 4(a) represents the LL sub-band age fro Level Haar wavelet decoposton. As shown n Fgure 4(b), only a few coponents are vsble after the D blocked-dct. The DC coponent and low frequency coponents are concentrated n top left corner of each age block. The resultng copressed age produced after D- IDCT coputaton s shown n Fgure 4(c). D-DCT (a) (a) (b) D-IDCT (b) (c) (d) (e) (f) (g) (h) () Fgure 3. D-DWT wavelet decoposton For DWT coputaton, the age s decoposed nto blocks. Each block then undergoes wavelet decoposton, producng an approxaton age and a sequence of detal ages. For the work carred out, Level Haar wavelet decoposton s eployed as deonstrated n Fgure 3. Haar wavelet decoposton of Level of Fgure 3(a) produces one approxaton and three orentaton detal ages as shown n Fgures 3(b), 3(c), 3(d) and 3(e).e., LL, HH, HL and HH subbands respectvely. Fgure 3(b) contans the an energy of the age concentrated on low frequency coponents whle the other three (3) sub-bands contan uch lesser energes. Slarly, for Level Haar wavelet decoposton the LL sub-band age (Fgure 3(b)) s decoposed, whch produces four ages as shown n Fgures 3(f), 3(g), 3(h) and 3(). In our (c) Fgure 4. D-DCT coputaton To buld DCT-feature vectors the average of soe entre DCT feature set was coputed for each of the 36 sub-blocks. The ost upper left DCT coeffcents.e., the DC coponent and frst fve AC coponents were selected n a zgzag order. Fro each face age 36 6 = 6 DCT-features were extracted, where 36 represents the nuber of DCT sub-blocks n the age and 6 s the nuber of the features n each sub-block. 5.. SVM Classfcaton Iage feature vectors obtaned fro DWT-DCT selecton are cobned to obtan the support vectors, satsfyng eq. (7). For solvng ult-class probles LIBSVM [] uses the One Aganst One or OAO ethod. In the tranng stage, a C-SVM classfer s used. It s known that, k(k-)/ classfers are needed, f k ndependent classes are requred. It s noted that f k cannot be represented as exponent of, k should be separated as the su of the exponent of. In ths experent, the ORL database conssts of 40 people, therefore, k = 40.e., a 40-class C-SVM odel s used. 0

5 Start of Recognton Engne Fnd optal SVM hyper-paraeters for SVM classfer usng Grd-Search Bad Cross-valdaton usng 70% Tranng data and 30% Testng data fro 50% ORL face data Cross-valdaton Accuracy C-SVM Traned Classfer Good 6.. Wavelet Decoposton Level The frst experent studes the effect of usng DWT for Haar wavelet decoposton on the recognton rate of the syste. Experental results carred out to copare perforance of dfferent wavelet decoposton levels wth ther recognton rates as llustrated n Table. Table. Recognton Rates for Dfferent Wavelet Decoposton Levels Decoposton level Evaluaton te (secs) Recognton rate (%) % ORL Testng data C-SVM Predcton As can be seen fro Table, Haar Level wavelet decoposton yelds a better recognton rate than Level decoposton. Ths s because the LL subband contans ost suffcent energy concentrated on low frequency coponents n contrast wth the LL sub-band contans, whch contans uch lesser energy wth reduced densons. No C-SVM Predcton Accuracy > 95% Yes No Classfcaton Result 6.. DCT Block Sze End of Recognton Engne Fgure 5. SVM classfcaton engne Classfcaton accuracy of the SVM was optzed usng the Grd-Search ethod for dfferent RBF kernel paraeters γ and cost paraeters C. Exponentally growng sequences of (C, γ) were used to dentfy best paraeters, where C = [ -5, -3,, 5 ] and γ = [ -5, - 3,, 3 ] were used for = 565 cobnatons. For each par of (C, γ) valdaton perforance was easured by tranng 70% classfer data and testng the other 30% classfer data. Based on the hghest 0- fold Cross-valdaton accuracy 99.6%, optal hyperparaeters, C = and γ = 0.8 were selected to ft the SVM classfer. The C-SVM classfcaton engne odeled for face recognton s llustrated n Fgure Experental Results Experents carred out nvolved splttng the ORL face database nto tranng and testng sets. For the purpose of tranng, 70% of the ORL face ages (80 ages) were used, whle the other 30% (0 ages) were used for testng the face recognton odel. All experental results obtaned were an average of 0 consecutve sulatons, wth dfferent sets beng used for tranng and testng each te. The second experent studes the effect of DCT block sze on the rate of recognton of the syste wth each DCT coeffcent beng used n the feature vector. Table ndcates that the best recognton rate obtaned s for the case of 6 6 DCT block sze. Table. Recognton Rates for Dfferent DCT Block Szes DCT block sze Recognton rate (%) x 4x DCT Feature Vector Sze 6x6 8x The thrd experent s concerned wth the coputatonal load, whch coes fro large szed DCT-feature vectors. The a of ths experent s to deterne f saller DCT-feature vectors can be used wthout sgnfcantly degradng syste perforance. For the chosen DCT block sze of 6 6 pxels, a total of 36 DCT coeffcents are coputed for every saple. Each of these coeffcents represent a separate denson n a 36-densonal feature space. By assessng the varance n each denson of ths space, t was possble to deterne whch of the coeffcents 03

6 contrbute ost to the fnal decson of the classfer. Results obtaned n Table 3 reveal that n spte of the draatc reducton fro 6 DCT-features to only, the recognton rates obtaned are essentally the sae. Ths experent deonstrates that good face recognton perforance s possble, even wth feature vectors that are draatcally reduced n sze relatve to the usual case for DCT-based analyss. Table 3. Recognton Rates for DCT Feature Vector Szes DCT feature vector sze Evaluaton te (secs) Recognton rate (%) For coparson purposes, face recognton results as reported by the respectve authors on the ORL face database are shown n Table 4. It can be seen that our proposed hybrd DWT-DCT-SVM face recognton approach outperfors other technques provng that the hybrd DWT-DCT cobnaton of feature selecton provdes ore accurate recognton. Table 4. Coparatve Results on ORL Face Database Method Recognton rate (%) Ref. Egenface [4] FsherFace (PCA + LDA) [4] Gabor Wavelet + KPCA + SVM [7] Dscrnant Wavelet + NFS 96.0 [8] DWT-PCA [6] DWT-SHMM [9] SVM [4] DCT-LDA [4] DWT-HMM [5] DWT-DCT-SVM Proposed 7. Concluson In ths paper a novel fraework for pose nvarant huan face recognton s presented. Ths fraework uses a hybrd cobnaton of the DWT and DCT to extract donant frequency features fro face ages. The DWT s used to capture ajor face features, whereas the DCT extracts the ost donant face nforaton fro the lower frequency coponents n the DCT frequency doan. Furtherore, SVM s adopted to classfy DWT-DCT based features for recognton purposes. The proposed DWT-DCT-SVM face recognton odel s evaluated n MATLAB on the ORL face database. Experental results obtaned reveal that the proposed DWT-DCT-SVM approach shows good accuracy and outperfors prevously proposed face recognton technques. Furtherore, a reduced feature space draatcally reduces the coputatonal requreents as copared wth standard DCT feature extracton ethods. akng our syste well suted for low-cost, real-te pleentaton. 8. References [] R. Chellappa, C. L.Wlson, and S. Srohey, Huan and achne recognton of faces: A survey Proceedngs of the IEEE, Vol. 83, No. 5, pp , May 995. [] J. Nag, S. K. Ahed, and F. Nag, A MATLAB based Face Recognton Syste usng Iage Processng and Neural Networks n Proc. of 4th Internatonal Colloquu on Sgnal Processng and ts Applcatons, pp , 008. [3] E. Hjelås, and B. K. Low, Face detecton: A survey Coputer Vson and Iage Understandng, Vol. 83, No. 3, pp , Sept. 00. [4] Zhang Yankun, and Lu Chongqng, Effcent face recognton ethod based on DCT and LDA Journal of Systes Engneerng and Electroncs, Vol. 5, No., pp -6, 004. [5] Vnayadatt V. Kohr and U. B. Desa, DWT-HMM Based Face Recognton n Proc. of Indan Conference on Coputer Vson and Iage Processng, pp , 998. [6] P. Ncholl, and A. Ara, DWT/PCA Face Recognton usng Autoatc Coeffcent Selecton n Proc. of the 4th IEEE Internatonal Syposu on Electronc Desgn, Test and Applcatons, pp , 008. [7] Guang Da, and Changle Zhou, Face Recognton Usng Support Vector Machnes wth the Robust Feature n Proc. of IEEE Internatonal Workshop on Robot and Huan Interactve Councaton, pp , 003. [8] Jen-Tzung Chen, and Cha-Chen Wu, Dscrnate wavelet faces and nearest feature classfers for face recognton IEEE Transactons on PAMI, Vol. 4, No., pp , 004. [9] P. Ncholl, A. Ara, D. Bouchaffra, and R. H. Perrott, Multresoluton Hybrd Approaches for Autoated Face Recognton n Proc. of the Second NASA/ESA Conference on Adaptve Hardware and Systes, pp , 007. [0] Dtry Brluk (00). Noralzed ORL face database. Face recognton artcles and deos. [Onlne]. Avalable: [] C.-C. Chang, and C.-J. Ln. LIBSVM: A lbrary for support vector achnes. [Onlne]. Avalable: 04