face recognition using ica presentation

8/13/2019 face recognition using ica presentation

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PRESENTED BY:SADIA KHAN

HINA SALEEM

SIDRA KHANMADIHA BIBI


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FACES

Faces are integral to human interaction

Manual facial recognition is already usedin everyday authentication applications

ID Card systems (passports, health card, anddrivers license)

Booking stations

Surveillance operations


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Facial Recognition technology automates the recognition

of faces using one of two 2 modeling approaches: Face appearance 2D Eigen faces 3D Morphable Model

Face geometry 3D Expression Invariant Recognition

2D Eigenface

Principle Component Analysis (PCA) 3D Face Recognition 3D Expression Invariant Recognition

3D Morphable Model

Facial Recognition


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ICA finds the directions of

maximum independence


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Facial Recognition: Eigenface

Decompose face

images into a smallset of characteristicfeature images.

A new face iscompared to thesestored images.

A match is found if

the new faces is closeto one of theseimages.


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Create training set of faces and calculate the

eigenfaces

Project the new image onto the eigenfaces.Check if image is close to face space.

Check closeness to one of the known faces.

Add unknown faces to the training set and re-calculate

Facial Recognition: PCA - Overview


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Facial Recognition: PCA Training Set


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Facial Recognition: PCA Training

Find average of

training images.Subtract average face

from each image.

Create covariancematrix

Generate eigenfaces

Each original image

can be expressed as alinear combination ofthe eigenfaces facespace


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A new image is project into the facespace.

Create a vector of weights that describes this image.

The distance from the original image to thiseigenface is compared.

If within certain thresholds then it is a recognizedface.

Facial Recognition: PCA Recognition


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Independent component analysis (ICA) is a method for

finding underlying factors or components from multivariate

(multi-dimensional) statistical data. What distinguishes ICA

from other methods is that it looks for components that are

bothstatistically independent, and nonGaussian.

A.Hyvarinen, A.Karhunen, E.Oja

Independent Component Analysis

What is ICA?


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Blind Signal Separation (BSS) or Independent Component Analysis (ICA) is the

identification & separation of mixtures of sources with little prior

information.

Applications include:

Audio Processing Medical data

Finance

Array processing (beamforming)

Coding

and most applications where Factor Analysis and PCA is currently used. While PCA seeks directions that represents data best in a |x0- x|

2 sense,ICA seeks such directions that are most independent from each other.

Often used on Time Series separation of Multiple Targets

ICA


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Principle 1: Nonlinear decorrelation. Find the

matrix Wso that for any i j, the componentsyiand

yjare uncorrelated, and the transformed componentsg(yi)and h(yj)are uncorrelated, whereg and haresome suitable nonlinear functions.

Principle 2: Maximum nongaussianity. Find the

local maxima of nongaussianity of a linearcombination y=Wxunder the constraint that thevariance of x is constant.

Each local maximum gives one independent

component.

ICA estimation principles


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Given a set of observations of random variablesx1(t),

x2(t)xn(t), where tis the time or sample index, assume

that they are generated as a linear mixture of independent

components: y=Wx, where Wis some unknown matrix.Independent component analysis now consists of

estimating both the matrix Wand theyi(t), when we only

observe thexi(t).

ICA mathematical approach


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ICA Principal (Non-Gaussian is Independent)

Key to estimating A is non-gaussianity

The distribution of a sum of independent random variables tends toward a Gaussiandistribution. (By CLT)

f(s1) f(s2) f(x1) = f(s1+s2)

Where wis one of the rows of matrix W.

y is a linear combination of si, with weights given by zi.

Since sum of two indep r.v. is more gaussian than individual r.v., so zTs is more gaussianthan either of si. AND becomes least gaussian when its equal to one of si.

So we could take was a vector which maximizes the non-gaussianity of wTx.

Such a wwould correspond to a zwith only one non zero comp. So we get back the si.

szAswxwy TTT


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We need to have a quantitative measure of non-gaussianity for ICA Estimation.

Kurtotis : gauss=0 (sensitive to outliers)

Entropy : gauss=largest

Neg-entropy : gauss = 0 (difficult to estimate)

Approximations

where v is a standard gaussian random variable and :

224 }){(3}{)( yEyEykurt

dyyfyfyH )(log)()(

)()()( yHyHyJ gauss

222 )(48

1

12

1)( ykurtyEyJ

2)()()( vGEyGEyJ

)2/.exp()(

).cosh(log1)(

2uayG

yaa

yG


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Centering

x= x E{x}

But this doesnt mean that ICA cannt estimate the mean, but it just simplifiesthe Alg.

ICs are also zero mean because of:

E{s} = WE{x}

After ICA, add W.E{x} to zero mean ICs

Whitening We transform the xs linearly so that the x~are white. Its done by EVD.

x~ = (ED-1/2ET)x = ED-1/2ETAx = A~s

whereE{xx~} = EDET

So we have to Estimate Orthonormal Matrix A~

An orthonormal matrix has n(n-1)/2 degrees of freedom. So for large dim A we

have to est only half as much parameters. This greatly simplifies ICA.

Reducing dim of data (choosing dominant Eig) while doing whitening alsohelp.

Data Centering & Whitening


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0) Centring = make the signals centred in zero

xixi - E[xi] for each i

1) Sphering = make the signals uncorrelated. I.e. apply a transform Vto xsuch that Cov(Vx)=I // where Cov(y)=E[yyT] denotes covariance matrix

V=E[xxT]-1/2 // can be done using sqrtm function in MatLab

xVx // for all t (indexes t dropped here)

// bold lowercase refers to column vector; bold upper to matrix

Scope: to make the remaining computations simpler. It is known thatindependent variables must be uncorrelatedso this can be fulfilled

before proceeding to the full ICA

Computing the pre-processing steps for ICA


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Computing the rotation step

Fixed Point Algorithm

Input: X

Random init of W

Iterate until convergence:

Output: W, S

1)(

)(

WWWW

SXW

XWS

T

T

T

g

T

t

T

t

TGObj1

)()()( IWWxWW

0WXWXW

TTgObj

)(

where g(.) is derivative of G(.),

Wis the rotation transform soughtis Lagrange multiplier to enforce that

W is an orthogonal transform i.e. a rotation

Solve by fixed point iterations

The effect ofis an orthogonal de-correlation

This is based on an the maximisation of anobjective function G(.) which contains an

approximate non-Gaussianity measure.

The overall transform then

to take Xback to Sis (WTV)

There are several g(.)

options, each will work best

in special cases. See FastICA

sw / tut for details.


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Two architectures for performing ICA on images. (a) Architecture I forfinding statistically independent basis images. Performing sourceseparation on the face images produced IC images in the rows of U. (b)The gray values at pixel location i are plotted for each face image. ICA inarchitecture I finds weight vectors in the directions of statisticaldependencies among the pixel locations. (c) Architecture II for finding afactorial code. Performing source separation on the pixels produced afactorial code in the columns of the output matrix, U. (d) Each faceimage is plotted according to the gray values taken on at each pixellocation. ICA in architecture II finds weight vectors in the directions ofstatistical dependencies among the face images


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face recognition using ica presentation

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