Dual Tree Complex Wavelet Transform for Face Recognition Using PCA Algorithm

Transcription

1 B.Dhamenda,INDIA / Intenatonal Jounal of Reseach and Computatonal echnology, Vol.5 Issue.4 ISSN: , Dec, Dual ee Complex Wavelet ansfom fo Face Recognton Usng PCA Algothm Dhamenda B 1 Naveen kuma B 2 Suntha.M 3 Sunanda.K 4 Asst. Pof. Dept. of E.C.E Asst. Pof. Dept. of E.C.E Asst. Pof. Dept. of E.C.E Asst.Pof. Dept of ECE CJIS, Waangal, JNU, INIDA CJIS, Waangal, JNU, INIDA CJIS, Waangal, JNU, INIDA KIS, Waangal, KU, INIDA dhama.sep29@gmal.com naveenget426@gmal.com bommasunthaavkuma@gmal.com sunanda.mtech@gmal.com Abstact In ths pape the sutablty of Dual ee Complex Wavelet ansfom fo Face Recognton s studed. In contast to the dscete wavelet tansfom (DW), the desgn of Dual ee Complex Wavelet ansfom poses good dectonal popetes fo dagonal featues and s ugged to shft Invaance. hese featues of D-CW motvated to study the sutablty fo Face Featue Extacton and Recognton, as the featues of face ae oented n dffeent dectons. In ths wok the mage s decomposed usng D-CW to poduce eght complex sub-bands and the featues ae extacted fom the magntude of low fequency band (LL) usng Pncpal Component analyss (PCA). ORL database s used, as the database conssts of vaaton n pose and expesson. Recognton ate acheved on ORL database usng D-CW s satsfactoy. In ths pape pose poblem s addessed usng Complex Wavelets [9-10][13] and PCA to extact Multscale featues towads secue Face Recognton system. o ad the pocess of ecognton, neaest neghbohood classfe [16] s used; ths method fnds an mage to the class whose featues ae closest to t wth espect to the Eucldean nom. hs wok uses Dual tee Complex wavelet [15] tansfom manly to educe the computaton complexty. In the ORL face database [7] all the mages ae of sze 112x92, we woked on appoxmaton detals of fst level decomposton usng D- CW. he sze n fst level decomposton educes to 56x46. Keywods-Dual ee Complex Wavelet ansfom, PCA, and Eucldan Classfe. I. INRODUCION Bometcs compses methods fo unambguously ecognzng ndvduals based upon physcal and behavoal attbutes. Face ecognton s one of the bometc systems that takes mage o vdeo of a peson and compaes t wth mages n database to gant access to secue aeas. Many eseaches showed that the featues extacted fom face mages ad n desgnng obust secuty/authentcaton systems. Successful face ecognton system [1] s poposed utlzng Egen face appoach. hs method s conventonal, consdes fontal and clea faces fo mplementng the system, but n eal tme faces may not be fontal and devce ntnsc captue (llumnaton vaaton) popetes pose dffcultes n the pocess of detecton. hus n secuty and othe compute vson applcatons, pose and vaaton n llumnatons plays a ctcal ole. Conventonal Face featue extacton suffes manly fom a) Pose vaaton, b) Expesson vaaton, c) Resoluton vaaton and d) Illumnaton poblems Fgue.1. Dffeent poses of a subject fom ORL face database. Pncpal Component Analyss (PCA) s used to extact featues [1, 2, 3]. Egenface appoach s used fo low dmensonal epesentaton of faces by applyng Pncpal Component Analyss (PCA). he system functons by pojectng face mages onto a featue space that spans the sgnfcant vaatons among known face mages. he sgnfcant featues ae known as egenfaces because they ae egenvectos (pncpal components) [1]. he pefomance of the poposed algothm s vefed on avalable databases on the ntenet, such as ORL face database [7]. ORL face database conssts of 400 mages of 40 ndvduals; each subject has 10 mages n dffeent poses. Sample mages of the database shown n Fg.1. hs pape s oganzed nto sx sectons. In secton II we dscussed Dual ee Complex Wavelet ansfom, n secton III Featue Extacton and classfe, n secton IV poposed face ecognton system, n secton V, Expemental esults and concluson n the last secton. edto@jct.og all ghts eseved

2 II. DUAL REE COMPLEX WAVELE RANSFORM he dawbacks n DW can be elmnated by usng an expansve wavelet tansfom n place of a ctcally-sampled one. (An expansve tansfom s one that convets an N-pont sgnal nto M coeffcents wth M > N). D-CW povdes N mult scales, can be mplemented usng sepaable effcent Flte Banks as shown n Fg.2. Fgue.2. D- CW wokng pncple fo 1D sgnal Hee two sets of Flte banks ae used, conssts of low pass and hgh pass fltes. Down sample the nput sgnal by 2 though a flte of H(z) tansfe functon and agan though G(z) flte. he fltes should be Hlbet tansfom pas y t y t g h ( ) =H { ( )} (1) he fltes n the uppe and lowe DWs should not be the same, the fltes used n the fst stage of the dual-tee complex DW [4] should be dffeent fom the fltes used n the emanng stages. he sub band sgnals of the uppe DW can be ntepeted as the eal pat of a complex wavelet tansfom, and sub band sgnals of the lowe DW can be ntepeted as the magnay pat. Equvalently, fo specally desgned sets of fltes, the wavelet assocated wth the uppe DW can be an appoxmate Hlbet tansfom of the wavelet assocated wth the lowe DW. hen desgned, the dual-tee complex DW s nealy shft-nvaant and stong dectonal n contast wth the ctcally-sampled DW. he desgned flte complex wavelet should be analytc and t s ( t) : ( t) j ( t) (2) c h g he wavelet coeffcents w ae stoed as a cell aay. Fo j = 1..J, k = 1..2, d = 1..3, w{j}{k}{d} ae the wavelet coeffcents poduced at scale j wth an oentaton d. he dual-tee complex DW outpefoms well compaed to the ctcallysampled DW fo applcatons lke mage de-nosng and enhancement. D-CW fo mage povdes sx (d=1..6) dectonal hgh fequency sub bands and two (d=1, 2) low fequency sub bands as shown n fg 3. he 2-D wavelet s defned as ( ) y ( x, y) y ( x) y y = (3) whee y ( x) s complex analytc wavelet, gven as ( ) y ( x) = y ( x) + jy y (4) smlaly y ( x, y) = y ( x) y ( y) - y ( x) y ( y) + j éy ( x) y ( y) + y ( x) y ( y) ù ë û s eal and even and j s magnay and odd. he complex-wavelet coeffcent s defned as d ( k, l) d ( k, l) jd ( k, l) And ts magntude s c 2 2 d ( k, l) d ( k, l) d ( k, l) c When dc( k, l ) >0 And phase s gven as d (, ) actan c k l = q Whee = d ( k, l) d ( k, l) Key featues of D-CW ae c (8) (6) (7) 1. Bette dectonalty 2. Ant- alasng effect 3. Good shft-nvaant 4. Geomety of the mage featues etaned fom phase 5. Bette obustness fo smooth vayng 6. Low computaton compaed wth DW, 3 tmes that of maxmally decmated DW. Fgue.3. Decomposton of D-CW fo 2D mage

3 III. FEAURE EXRACION AND CLASSIFIER A. Pncpal Component Analyss A 2-D facal mage can be epesented as 1-D vecto by concatenatng each ow (o column) nto a long thn vecto. Let s suppose we have M vectos of sze N (= ows of mage columns of mage) epesentng a set of sampled mages. pj s epesent the pxel values. x = [p 1 : : : p N ] ; = 1,...., M he mages ae mean centeed by subtactng the mean mage fom each mage vecto. Let m epesent the mean mage. And let 1 M x M 1 m (9) w be defned as mean centeed mage w x m Ou goal s to fnd a set of e s whch have the lagest possble pojecton onto each of the w s. We wsh to fnd a set of M othonomal vectos e fo whch the quantty M 1 2 ( ew n) (10) M n 1 s maxmzed wth the othonomalty constant ee l k lk It has been shown that the e s and λ s ae gven by the egenvectos and egenvalues of the covaance matx C WW (11) whee W s a matx composed of the column vectos w placed sde by sde. he egenvectos coespondng to nonzeo egenvalues of the covaance matx poduce an othonomal bass fo the subspace wthn whch most mage data can be epesented wth a small amount of eo. he egenvectos ae soted fom hgh to low accodng to the coespondng egenvalues. he egenvecto assocated wth the lagest egenvalue s one that eflects the geatest vaance n the mage. hat s, the smallest egenvalue s assocated wth the egenvecto that fnds the least vaance. hey decease n exponental fashon, meanng that the oughly 90% of the total vaance s contaned n the fst5% to 10% of the dmensons. A facal mage can be pojected onto M ( M) dmensons by computng = [v 1, v 2,,, V M ] B. Classfe In ths wok we have used neaest neghbohood classfe [16] to ecognze the mage. hs classfe comes unde mnmum dstance classfes. It s also called as Eucldean classfe. In ths method the mnmum the dstance fom test featue vectos to tan featue vectos the coect the mage s. If X, Yj epesents test and tan mage featues then X Y X Y X Y X Y (12) j *Whee. epesents Eucldean nom Because of ts smplcty, t fnds an mage to the class whose featues ae closest to t wth espect to the Eucldean nom. IV. PROPOSED ALGORIHM he fst aspect of ths wok s to use Dual ee Complex Wavelet tansfom [9, 10, 13] whee multscale analyss and extacton of featues oented n dffeent dectons ae possble. he decomposton level of the wavelet tansfom s decded by the magey detals whch we need. In ths wok fst level decomposton s satsfactoy to peseve the detals. he Second and mpotant aspect of ths wok s to extact the featues fom mag(ll) usng PCA. D-CW Decomposton Featue Extacton usng PCA Image D-CW LL1 2 LL PCA LL LH 1 LH 2 HL1 HL2 HH 1 HH 2 Fgue.4. D-CW Featue Extacton (Poposed Algothm) he geneal pocedue of the poposed technque s as follows. As a fst step we wll take a test mage and fom a database of tanng mages excludng test mage. As next step Appoxmaton detals of all mages n database ncludng test mage ae calculated usng D-CW. he appoxmaton coeffcents of fst level decomposton ae complex numbes. hen we fomed new database wth magntudes of these complex numbes. Now the LL s pocessed usng PCA to extact the featues. Fg.4. shows all the steps of the poposed algothm and featue Extacton. hd aspect of ths wok, whch s the decson makng step to fnd sutable mage. Afte extactng featues fo all tan mages and test mage, neaest neghbohood classfe s used to ecognze the coect mage fom database. Face ecognton system wth poposed algothm s ugged to pose vaaton s shown n Fg.5.

4 ES IMAGE FACE DAABASE RAIN IMAGE Eucldean classfe s used to ad face ecognton whch can speed up the ecognton pocess. Expementaton s caed on openly avalable challengng face database. he ecognton ate s evaluated vayng the no. of featues and the coespondng ecognton ate s tabulated n able.1. and n Fg.7. he max ecognton ate epoted n ths wok s usng 100 featues. PROPOSED ALGORIHM PROPOSED ALGORIHM FEAURES DAABASE NAME RECOGNIION RAE (%) 1 ORL ORL ORL ORL CLASSIFIER 20 ORL ORL RESUL 100 ORL Fgue.5. Block dagam of face ecognton system able 1: Recognton Rate usng poposed Method on ORL face database. A. Database V. EXPERIMENAL RESULS In ths wok expementaton s caed on ORL face database [7]. he database conssts of 400 mages of 40 ndvduals n 10 dffeent poses. Sample mages fom ORL database ae shown n below fgue.6. Fgue.7. Recognton Rate vs. Featues fo ORL face database B. Expemental Results Fgue.6. ORL Face Database In ths pape Complex Wavelet s used to decompose the mage n to eght sub-bands. he eght sub-bands poduced ae oented n Hozontal, Vetcal, Dagonal dectons and ae complex n natue. Of all the sub-bands the emphass n ths wok s on LL band as the hstogam of ths band s smla to ognal mage. Pncpal Component Analyss s used to extact the featues fom the magntude of LL. VI. CONCLUSION o ameloate the Face ecognton task n ths wok Complex Wavelets ae utlzed n contast to DW. Complex wavelet decomposton of mage esulted n eght sub-bands and the featue extacton s caed on LL band usng pncpal component analyss. Maxmum Recognton ate epoted s 93.5 usng 100 featues extacted fom LL band. Futue wok ams at extactng featues fom the othe seven bands to utlze all the sub-bands featues n mpovng the face ecognton. ACKNOWLEDGMEN he authos would lke to thank M. I. W. Seles nck and hs teams at aco Polytechnc fo povdng complex wavelet tansfom Softwae.

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