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slicenseandpassportcheck,bankingandcustoms
controlsystem,andotherfields[1].
Themainmethodsoffacerecognitiontechnologycanbesummeduptothreekinds:
basedongeometricfeatures,templateandmodelseparately.ThePCAfacerecognitionmethodbasedonK-Ltransformhasbeenconcernedsincethe1990s.Itissimple,fast.andeasytouse.Itcanreflectthepersonface'
scharacteristiconthewhole.Therefore,applyingPCAmethodinthefacerecognitionisunceasinglyimproving.
D.-S.Huangetal.(Eds.):
ICIC2008,LNCS5226,pp.561–568,
2008.©
Springer-VerlagBerlinHeidelberg2008
ThispaperputsforwardamethodoffacerecognitionbasedonRed-BlackwavelettransformandPCA.Firstly,usingtheimprovedimagehistogramequalization[2]todoimagepreprocessing,eliminatingtheimpactofthedifferencesinlightintensity.Sec-ondly,usingtheRed-Blackwavelettransformtowithdrawthebluesub-bandoftherelativestablefaceimagetoobscuretheimpactsofexpressionsandpostures.Then,usingPCAtowithdrawthefeaturecomponentanddorecognition.ComparingwiththetraditionalPCAmethods,thisonecanobviouslyreducecomputationalcomplexityandincreasetherecognitionrateandanti-noiseperformance.Theexperimentalresultsshowthatthismethodmentionedinthispaperismoreaccurateandeffective.
2Red-BlackWaveletTransform
Liftingwavelettransformisaneffectivewavelettransformwhichdevelopedrapidlytheseyears.ItdiscardsthecomplexmathematicalconceptsandthetelescopicandtranslationoftheFouriertransformanalysisintheclassicalwavelettransform.Itde-velopsfromthethoughtoftheclassicalwavelettransformmulti-resolutionanalysis.Red-blackwavelettransform[3-4]isatwo-dimensionalliftingwavelettransform[5-6],itcontainshorizontal/verticallifinganddiagonallifting.Thespecificprinciplesareasbellow.
2.1Horizontal/VerticalLifting
AsFig.1shows,horizontal/verticalliftingisdividedintothreesteps:
1.Decomposition:
Theoriginalimagebyhorizontalandverticaldirectionisdividedintoredandblackblockinacross-blockway.
2.Prediction:
Carryonthepredictionusinghorizontaland
the
verticaldirectionfourneighborhood'
sredblockstoobtainablackblockpredictedvalue.
Then,usingthedifferenceoftheblackblockactualvalueandthepredictedvaluetosubstitutetheblackblockactualvalue.Itsresultobtainstheoriginalimagewaveletcoefficient.AsFig.1(b)shows:
f(i,j)¬
f(i,j)-[f(i-1,j)+f(i,j-1)+f(i,j+1)+f(i+1,j)]/4
(imod2¹
jmod2)
(1)
3.Revision:
Usingthehorizontalandverticaldirectionfourneighborhood'
sblackblock'
swaveletcoefficienttorevisetheredblockactualvaluetoobtaintheapproximatesignal.AsFig.1(c)shows:
f(i,j)+[f(i-1,j)+f(i,j-1)+f(i,j+1)+f(i+1,j)]/8
(imod2=
(2)
Inthisway,theredblockcorrespondstotheapproximatinginformationoftheimage,andtheblackblockcorrespondstothedetailsoftheimage.
2.2DiagonalLifting
Onthebasisofhorizontal/verticallifting,wedothediagonallifting.AsFig.2shows,itisalsodividedintothreesteps:
Fig.2.Diagonallifting
Afterhorizontal/verticallifting,dividingtheobtainedred blockintotheblueblockandtheyellowblockinthediagonalcrossway.
Usingfouroppositeangleneighborhood'
sblueblocktopredict adatainordertoobtaintheyellowblockpredictedvalue.Thenthedifferenceoftheyellowblockactualvalueandthepredictedvaluesubstitutestheyellowblockactualvalue.Itsresultobtainstheoriginalimagewaveletcoefficientofthediagonaldirection.AsFig.2(b)shows:
f(i,j)-[f(i-1,j-1)+f(i-1,j+1)+f(i+1,j-1)+f(i+1,j+1)]/4
(imod2=1,jmod2=1)
(3)
Usingfouroppositeangleneighborhoodyellowblockwaveletco-efficienttorevisetheblueblockactualvalueinordertoobtaintheapproximatesignal.AsFig.2(c)shows:
f(i,j)-[f(i-1,j-1)+f(i-1,j+1)+f(i+1,j-1)+f(i+1,j+1)]/8
(imod2=0,jmod2=0)
(4)
Afterthesecondlifting,thered-blackwavelettransformisrealized.
AccordingtotheEquations,itcananalyzesomecorrespondingrelationsbetweenthered-blackwavelettransformandtheclassicalwavelettransform:
namely,theblueblockisequaltothesub-bandLLoftheclassicaltensorproductwavelets,theyellowblockisequaltosub-bandHHandtheblackblockisequaltosub-bandHLandLH.Experimentalresultsshowthatitdiscardsthecomplexmathematicalconceptsandequations.Therelativityofimagecanmostlybeeliminatedandthesparserrepresen-tationofimagecanbeobtainedbytheRed-Blackwavelettransform.
TheimageafterRed-Blackwavelettransformisshowedinthe
Fig.3(b),ontheleftcorneristhebluesub-bandblockimagewhichistheapproximateimageoforiginalimage.
Fig.3.Theresultofred-blackwavelettransform
3FeatureExtractionBasedonPCA[7]
PCAisamethodwhichanalysesdatainstatisticalway.Thismethoddiscoversgroupofvectorsinthedataspace.Usingthesevectorstoexpressthedatavarianceasfaraspossible.PuttingthedatafromtheP-dimensionalspacedowntoM-dimensionalspace(P>
>
M).PCA use K-L transform to obtain the minimum-dimensional imagerecogni-tionspaceoftheapproximatingimagespace.Itviewsthefaceimageasahigh-dimensionalvector.Thehigh-dimensionalvectoriscomposedofeachpixel.Thenthehigh-dimensionalinformationspace maps the low-dimensional characteristic subspace by K-Ltransform. It obtains a group of orthogonal bases through high-dimensionalfaceimagespaceK-Ltransform.Thepartialretentionoforthogonalbasescreatesthelow-dimensionalsubspace.Theorthogonalbasesreservediscalled “Principlecomponent”.Sincetheimagecorrespondingtotheorthogonalbasesjustlikeface,sothisisalsocalled“Eigenfaces”method.Thearithmeticoffeatureextractionarespecifiedasfollows:
Forafaceimageofm×
n,connectingitseachrowwillconstitutearowvectorwhichhasD=m×
ndimensions.TheDisthefaceimagedimensions.SupposingMisthenumberoftrainingsamples,
xjisthefaceimagevectorwhichisderivedfromthejthpicture,
sothecovariancematrixofthewholesamplesis:
M
s=å
(x-u)(x-u)T (5)
T j jj=1
Andtheμistheaverageimagevectorofthetrainingsamples:
å
j
u=1Mx
Mj=1
(6)
1 2
OrderingA=[x
-u,x
-u,L,x
-u],soS
=AATanditsdemisionisD´
D.(7)
T
AccordingtotheprincipleofK-Ltransform,thecoordinateweachieved is com-posed of eigenvector corresponding to nonzero
eigenvalueofmatrixComputingouttheeigenvalueandOrthogonal
normalizedvectorofmatrixD×
Ddirectlyisdiffi-cult.SoaccordingtotheSVDprinciple,itcanfigureouttheeigenvalueandeigen-vectorofmatrixthroughgettingtheeigenvalueandeigenvector
ofmatrix
li(i=1,2,L,r)is r nonzero eigenvalue of matrix
vi:
is the
eigenvector corre-sponding toli
so the orthogonal normalized
lieigenvectorofmatrix isasbel-low:
This is the eigenvector of Arranging its eigenvalues
accordingtothesize:
l1³
l2³
L³
li,itscorrespondingeigenvectoris
mi. In this way, each face image can project on the sub-space
composedof,
m1m2…mr.Inordertoreducethedimension,itcan
selecttheformerdeigenvectorsassub-space.Itcanselectdbiggesteigenvectorsaccordingtotheenergyproportionwh