cap5415-computer vision lecture 20-face …bagci/teaching/computervision16/lec20.pdfcap5415-computer...

CAP5415-ComputerVisionLecture20-FaceRecognition,Haar Features,

LocalBinaryPatterns,andBoosting

[email protected]

Lecture20

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Reminders• ProjectDeadlines/Return

– 6December,from1pm– 4.30pm– 8December,from1pm– 4.30pm– Location:HEC221– 5minutesPowerpoint presentation+Demo– Return

• Your.ppt/pdfpresentationandcode.

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Lecture20

FaceDetectionandRecognition

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Lecture20

Detection Recognition “Sally”

• Whywasn’tMassachusetss BomberidentifiedbytheMassachusettsDepartmentofMotorVehiclessystemfromthevideosurveillanceimages?

• HewasenrolledinMADMVDatabase!

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DMV Face Recognition

System ?SlideCreditstoAnimetrics,Dr.MarcValliant,VP&CTO

• Today’sFRtechnologywillreliablyfindcontrolledfacialphoto inamugshot databaseofcontrolleddatabase.

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SlideCreditstoAnimetrics,Dr.MarcValliant,VP&CTO

ControlledFacialPhoto• Today’sFRtechnologywillreliablyfindcontrolledfacialphotoinamugshot databaseofcontrolleddatabase.

• However,thereareconfoundingvariablesinuncontrolledfacialphotos

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ControlledFacialPhoto• Today’sFRtechnologywillreliablyfindcontrolledfacialphotoinamugshot databaseofcontrolleddatabase.

• However,thereareconfoundingvariablesinuncontrolledfacialphotos– Resolution (not enough pixels)– Facial Pose – angulated– Illumination– Occluded facial areas

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FurtherDifficulties

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Threegoals

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FeatureComputation

• features must be computed as quickly as possible

FeatureSelection

• select the most discriminating features

Realtimeliness

• must focus on potentially positive image areas (that contain faces)

FaceDetection• Beforefacerecognitioncanbeappliedtoageneralimage,the

locationsandsizesofanyfacesmustbefirstfound.

• Rowley,Baluja,Kanade (1998) 10

Lecture20

FaceDetection/RecognitionusingMobileDevices

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Facedetection(cameraautomaticallyAdjustthefocusbasedondetectedFaces)

Auto-loginwithrecognizedfaces

FaceDetection

Feature-basedEye,mouth,..

Template-basedAAM,…

Appearance-BasedPatches,…

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Someoftherepresentativeworks

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Rectangle(Haar-like)Features

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“Rectangle filters”

Value =

∑ (pixels in white area) –∑ (pixels in black area)

FastComputationwithIntegralImages

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• This can quickly be computed in one pass through the image

(x,y)( ) ( )

( ) ( ) ( )( ) ( ) ( )

' , '

formal definition:, ', '

Recursive definition:, , 1 ,

, 1, ,

x x y yii x y i x y

s x y s x y i x y

ii x y ii x y s x y

≤ ≤

=

= − +

= − +

∑

0 1 1 11 2 2 31 2 1 11 3 1 0

IMAGE

0 1 2 31 4 7 112 7 11 163 11 16 21

INTEGRAL IMAGE

FeatureSelection

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• For a 24x24 detection region, the number of possible rectangle features is ~160,000!

FeatureSelection

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• For a 24x24 detection region, the number of possible rectangle features is ~160,000! PCA

LocalBinaryPatterns(LBP):AlternativeFeatures

• Gray-scaleinvarianttexturemeasure• Derivedfromlocalneighborhood• Powerfultexturedescriptor• Computationallysimple• Robustagainstmonotonicgray-scalechanges

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LocalBinaryPatterns(LBP):AlternativeFeatures

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(LBPfromdynamic/videotexture)

SimpleFRforMobileDevices

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(LBP:localbinarypatterns)

PrincipalComponentAnalysis(PCA)

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• Mappingfromtheinputsintheoriginald-dimensionalspacetoanew(k<d)-dimensionalspace,withminimumlossofinformation.


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• PCAisanunsupervisedmethod, itdoesnotuseoutput information.


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• PCAisanunsupervisedmethod, itdoesnotuseoutput information.

PCAcentersthesampleandthenrotatestheaxestolineupwiththedirectionsofhighestvariance.


• Theprojectionofx onthedirectionof wis

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z = w

Tx

Originalaxes

**

***

*

* **

****

*

*

*

** ***

*

**

Datapoints

FirstprincipalcomponentSecondprincipalcomponent



• Theprincipalcomponentusw1 suchthatthesample,afterprojectiononw1,ismostspreadoutsothatthedifferencebetweenthesamplepointsbecomesmostapparent.

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z = w

Tx




• Tohaveuniquesolution,

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z = w

Tx

||w1|| = 1




• Tohaveuniquesolution,• with

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z = w

Tx

||w1|| = 1

z1 = w1Tx

Cov(x) = ⌃




• Tohaveuniquesolution,• with• Then,

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z = w

Tx

||w1|| = 1

z1 = w1Tx

Cov(x) = ⌃V ar(z1) = w1

T⌃w1




• Tohaveuniquesolution,• with• Then,• SEEKw1 suchthatVar(z1)ismaximized!

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Lecture20

z = w

Tx

||w1|| = 1

z1 = w1Tx

Cov(x) = ⌃V ar(z1) = w1

T⌃w1

SolutionofPCA• WriteitasaLagrangeproblem,takederivativesw.r.t tow,then

wheremisthesamplemean

(=D diagonal)(S:spectraldecomp.)

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z = W

T (x�m)

Cov(z) = WTSW

XTX = WDWT

SolutionofPCA

• Letussaywewanttoreducedimensionalitytok<d,wetakethefirstkcolumnsofW(withthehighesteigenvalues).

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XTX = WDWT

SolutionofPCA

• Letussaywewanttoreducedimensionalitytok<d,wetakethefirstkcolumnsofW(withthehighesteigenvalues).

i=1,…k,t=1,...,N

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XTX = WDWT

zti = w

Ti x

t

(XTX)wi = �iwi

X = USVT

U = evec(XXT )

V = evec(XTXT )

S2 = eval(XXT )

Screeplot:AbilityofPCstoexplainvariationindata

• Enough PCs (principal components) to have a cumulative variance explained by the PCs thatis >50-70%

• Kaiser criterion: keep PCs with eigenvalues >1

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λ

λN

Recap:PCAcalculationsincartoon

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StepsinPCA:#1CalculateAdjustedDataSet

…ndims

datasamples

DataSet:D Meanvalues:M

-…

AdjustedDataSet:A

=Mi iscalculatedbytakingthemeanofthevaluesindimensioni


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StepsinPCA:#2CalculateCo-variancematrix,C,fromAdjustedDataSet,A

Co-varianceMatrix:C

n

n

Cij =cov(i,j)

Note:Sincethemeansofthedimensions intheadjusteddataset,A,are0,thecovariancematrixcansimplybewrittenas:

C=AAT/(n-1)


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Lecture20

StepsinPCA:#3CalculateeigenvectorsandeigenvaluesofC

Eigenvectors

Eigenvalues

Ifsomeeigenvaluesare0orverysmall,wecanessentially discardthoseeigenvaluesandthecorrespondingeigenvectors,hencereducingthedimensionality ofthenewbasis.

Eigenvectors

Eigenvalues

xx

MatrixEMatrixE


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StepsinPCA:#4Transformingdatasettothenewbasis

F=ETA

where:• Fisthetransformeddataset• ET isthetransposeoftheEmatrixcontainingtheeigenvectors• Aistheadjusteddataset

Notethatthedimensions ofthenewdataset,F,arelessthanthedatasetA

TorecoverAfromF:

(ET)-1F=(ET)-1ETA(ET)TF=AEF=A

*Eisorthogonal,thereforeE-1 =ET

HolisticFR:Eigenfaces

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Eigenfaces,fisherfaces,tensorfaces…..

GaborFeature-basedFR• EarlierFRmethodsaremostlyfeature-based.• Themostsuccessfulfeature-basedFRistheelasticbunchgraph

matchingsystemwithGaborfiltercoefficientsasfeatures:

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(scale)

GaborFeatures

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Scale(5) Orientation(8)

PCAonFaces:“Eigenfaces”

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Averageface

Firstprincipalcomponent

Othercomponents

Forallexceptaverage,“gray” =0,“white” >0,“black” <0

Eigenfaces example

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Trainingfaces

Eigenfaces example

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Top eigenvectors: u1,…uk

Mean: μ

Applicationtofaces

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• Representing faces onto this basis

Facereconstruction:

SimplestApproachtoFR

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− The simplest approach is to think of it as a template matching problem

− Problems arise when performing recognition in a high-dimensional space.

− Significant improvements can be achieved by first mapping the data into a lower dimensionality space.

FRusingeigenfaces

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FRusingeigenfaces

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− The distance er is called distance within face space (difs)

− The Euclidean distance can be used to compute er, however, the Mahalanobis distance has shown to work better:

2

1|| || ( )

Kk k

i iiw w

=

Ω−Ω = −∑

Mahalanobis distance

Euclidean distance

FaceDetection

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(iPhoto)

FaceDetection

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NikonS60

FaceDetection

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NikonS60finds12faces…

TheViola/JonesFaceDetector• Aseminalapproachtoreal-timeobjectdetection• Trainingisslow,butdetectionisveryfast• Keyideas

– Integralimages forfastfeatureevaluation– Boosting forfeatureselection– Attentional cascade forfastrejectionofnon-facewindows

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Lecture20

P.ViolaandM.Jones.Rapidobjectdetectionusingaboostedcascadeofsimplefeatures. CVPR2001.

P.ViolaandM.Jones.Robustreal-timefacedetection. IJCV57(2),2004.

TheViola/JonesFaceDetector-Training

• Initially,weighteachtrainingexampleequally• Ineachboostinground:

• Findtheweaklearner thatachievesthelowestweighted trainingerror• Raisetheweightsoftrainingexamplesmisclassifiedbycurrentweak

learner

• Computefinalclassifieraslinearcombinationofallweaklearners(weightofeachlearnerisdirectlyproportionaltoitsaccuracy)• Exactformulasforre-weightingandcombiningweaklearnersdependon

theparticularboostingscheme (e.g.,AdaBoost)

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P.ViolaandM.Jones.Rapidobjectdetectionusingaboostedcascadeofsimplefeatures. CVPR2001.

P.ViolaandM.Jones.Robustreal-timefacedetection. IJCV57(2),2004.

TheViola/JonesFaceDetector-Testing

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• Firsttwofeaturesselectedbyboosting:

Thisfeaturecombinationcanyield100%detectionrateand50%falsepositiverate

TheViola/JonesFaceDetector-Testing

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• A200-featureclassifiercanyield95%detectionrateandafalsepositiverateof1in14084

Notgoodenough!

Attentional Cascade

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FACEIMAGESUB-WINDOW

Classifier 1T

Classifier 3T

F

NON-FACE

TClassifier 2

T

F

NON-FACE

F

NON-FACE

•Westartwithsimpleclassifierswhichrejectmanyofthenegativesub-windowswhiledetectingalmostallpositivesub-windows•Positiveresponsefromthefirstclassifiertriggerstheevaluationofasecond(morecomplex)classifier,andsoon•Anegativeoutcomeatanypointleadstotheimmediaterejectionofthesub-window

vsfalse neg determined by

% False Pos

% D

etec

tion

0 50

0

100

Receiveroperatingcharacteristic

CascadedClassifiers(Boosting)

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input

Base-learners

Output

BoostingforFR

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Weak Classifier 1

BoostingforFR

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WeightsIncreased

BoostingforFR

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Weak Classifier 2

BoostingforFR

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WeightsIncreased

BoostingforFR

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Weak Classifier 3

BoostingforFR

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Final classifier is a combination of weak classifiers

AdaBoost Algorithm

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• Given ,• Initialize• For

– For each classifier that minimizes the error with respect to the distribution

• is the weighted error rate of classifier– If , then stop – Choose , typically – Update

• where is a normalized factor (choose so that Dt+1 will sum_x=1)

1 1( , ),..., ( , )m mx y x y , { 1, 1}i ix X y Y∈ ∈ = − +

11( ) , 1,..., ,D i i mm

= =

1,...,t T=: { 1, 1}th X → − +

tD

argmint

t th H

h ε∈

= ( )[ ( )]t t i t iD i y h xε = ≠∑

0.5tε ≥t Rα ∈ 11 ln

2t

tt

εαε−=

tε th

1( ) exp( ( ))( ) t t i t i

tt

D i y h xD iZα

+−=

tZ

BoostingforFR

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Lecture20

• Define weak learners based on rectangle features

1( ) ( )

T

t tt

H x sign a h x=

⎛ ⎞= ⎜ ⎟⎝ ⎠∑

Boosting&SVM• Advantages of boosting

– Integrates classification with feature selection– Complexity of training is linear instead of

quadratic in the number of training examples– Flexibility in the choice of weak learners, boosting

scheme– Testing is fast– Easy to implement

• Disadvantages– Needs many training examples– Often does not work as good as SVM

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References&SliceCredits

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• Animetrics,Dr.MarcValliant,VP&CTO• M. Turk, A. Pentland, "Eigenfaces for Recognition", Journal of Cognitive

Neuroscience, vol. 3, no. 1., 1991.• Y.FreundandR.Schapire,Ashortintroductiontoboosting,JournalofJapanese

SocietyforArtificialIntelligence,14(5):771-780,September,1999.• S.Li, et al. Handbook of Face Recognition, Springer.• Paul A. Viola and Michael J. Jones, Intl. J. Computer Vision

57(2), 137–154, 2004, (originally in CVPR’2001)• Some slides adapted from Bill Freeman, MIT 6.869, April 2005)• Friedman, J., Hastie, T. and Tibshirani, R. Additive Logistic Regression: a

Statistical View of Boostinghttp://www-stat.stanford.edu/~hastie/Papers/boost.ps

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