Post on 04-Jun-2018
transcript
8/13/2019 face recognition using ica presentation
1/31
PRESENTED BY:SADIA KHAN
HINA SALEEM
SIDRA KHANMADIHA BIBI
8/13/2019 face recognition using ica presentation
2/31
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
8/13/2019 face recognition using ica presentation
3/31
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
8/13/2019 face recognition using ica presentation
4/31
ICA finds the directions of
maximum independence
8/13/2019 face recognition using ica presentation
5/31
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.
8/13/2019 face recognition using ica presentation
6/31
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
8/13/2019 face recognition using ica presentation
7/31
Facial Recognition: PCA Training Set
8/13/2019 face recognition using ica presentation
8/31
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
8/13/2019 face recognition using ica presentation
9/31
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
8/13/2019 face recognition using ica presentation
10/31
8/13/2019 face recognition using ica presentation
11/31
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?
8/13/2019 face recognition using ica presentation
12/31
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
8/13/2019 face recognition using ica presentation
13/31
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
8/13/2019 face recognition using ica presentation
14/31
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
8/13/2019 face recognition using ica presentation
15/31
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
8/13/2019 face recognition using ica presentation
16/31
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
8/13/2019 face recognition using ica presentation
17/31
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
8/13/2019 face recognition using ica presentation
18/31
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
8/13/2019 face recognition using ica presentation
19/31
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.
8/13/2019 face recognition using ica presentation
20/31
8/13/2019 face recognition using ica presentation
21/31
8/13/2019 face recognition using ica presentation
22/31
8/13/2019 face recognition using ica presentation
23/31
8/13/2019 face recognition using ica presentation
24/31
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
8/13/2019 face recognition using ica presentation
25/31
8/13/2019 face recognition using ica presentation
26/31
8/13/2019 face recognition using ica presentation
27/31
8/13/2019 face recognition using ica presentation
28/31
8/13/2019 face recognition using ica presentation
29/31
8/13/2019 face recognition using ica presentation
30/31
8/13/2019 face recognition using ica presentation
31/31