Face recogntion Using PCA Algorithm

FACE RECOGNITIONUSING PCA

ALGORITHM

By Ashwini Awatare

Contents:- Introduction Face Recognition Face Recognition using PCA algorithm Strengths & WeaknessesApplicationsConclusionResources

Introduction

Facial recognition (or face recognition) is a type of biometric software application that can identify a specific individual in a digital image by analyzing and comparing patterns.

Facial recognition systems are commonly used for security purposes but are increasingly being used in a variety of other applications. For example, The Kinect motion gaming system, uses facial recognition to differentiate among players.

WHAT IS FACE RECOGNITION?“Face Recognition is the task of identifying an already detected face as a KNOWN or UNKNOWN face, and in more advanced casesTELLING EXACTLY WHO’S IT IS ! “

FACE DETECTION

FEATURE EXTRACTION

FACE RECOGNITION

All identification or authentication technologies operate using the following four stages:

Capture: A physical or behavioral sample is captured by the system during Enrollment and also in identification or verification process.

Extraction: unique data is extracted from the sample and a template is created.

Comparison: the template is then compared with a new sample.

Match/non-match: the system decides if the features extracted from the new Samples are a match or a non match.

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PCA ALGORITHM

STEP O : Convert image of training set to image vectors

A training set consisting of total M images

Each image is of size N x N

STEP 1: Convert image of training set to image vectorsA training set consisting of total M image

Image converted to vector

For each (image in training set)

Ti Vector

N x N Image

N

Free vector space

STEP 2: Normalize the face vectors1. Calculate the average face vector

A training set consisting of total M image

Image converted to vector

Free vector space

……

Calculate average face vector ‘U’

Ti

U

STEP 2: Normalize the face vectors1. Calculate the average face vectors

2. Subtract avg face vector from each face vectorA training set consisting of total M image

Image converted to vector

Free vector space

……

Calculate average face vector ‘U’

Then subtract mean(average) face vector from EACH face vector to get to get normalized face vector Øi=Ti-U

Ti

U

STEP 2: Normalize the face vectors1. Calculate the average face vectors

2. Subtract avg face vector from each face vectorA training set consisting of total M image

Image converted to vector

Free vector space

……

Øi=Ti-U

Eg. a1 – m1

a2 – m2

Ø1= . .

. .

a3 – m3

Ti

U

STEP 3: Calculate the Eigenvectors (Eigenvectors represent the variations in the faces )A training set consisting of total M image

Image converted to vector

Free vector space

……

To calculate the eigenvectors , we need to calculate the covariance vector C

C=A.AT

where A=[Ø1, Ø2, Ø3,… ØM] N2 X M

Ti

U

STEP 3: Calculate the Eigenvectors

A training set consisting of total M image

Image converted to vector

Free vector space

……Ti

U C=A.AT

N2 X M M X N2 = N2 XN2

Very huge matrix

STEP 3: Calculate the Eigenvectors

A training set consisting of total M image

Image converted to vector

Free vector space

……Ti

U C=A.AT

N2 X M M X N2 = N2 X N2

Very huge matrix

……

N2 eigenvectors

STEP 3: Calculate the Eigenvectors

A training set consisting of total M image

Image converted to vector

Free vector space

……Ti

U

……

N2 eigenvectors

But we need to find only K eigenvectors from the above N2 eigenvectors, where K<M

Eg. If N=50 and K=100 , we need to find 100 eigenvectors from 2500 (i.e.N2 ) VERY TIME CONSUMING

STEP 3: Calculate the Eigenvectors

A training set consisting of total M image

Image converted to vector

Free vector space

……Ti

U

……

N2 eigenvectors

SOLUTION

“DIMENSIONALITY REDUCTION”

i.e. Calculate eigenvectors from a covariance of reduced dimensionality

STEP 4: Calculating eigenvectors from reduced covariance matrix

A training set consisting of total M image

Image converted to vector

Free vector space

……Ti

U

……

M2 eigenvectors

New C=AT .A M XN2 N2 X M = M XM

matrix

STEP 5: Select K best eigenfaces such that K<=M and can represent the whole training set

Selected K eigenfaces MUST be in the ORIGINAL dimensionality of the face Vector Space

STEP 6: Convert lower dimension K eigenvectors to original face dimensionality

A training set consisting of total M image

Image converted to vector

Free vector space

……Ti

U

……

100 eigenvectors

ui = A vi

ui = ith eigenvector in the higher dimensional spacevi = ith eigenvector in the lower dimensional space

……

2500 eigenvectors

……

100 eigenvectors

= A

ui = A vi

ui

vi

Each 100 X 1 dimension

Each 2500 X 1 dimension

……

2500 eigenvectors

ui

Each 2500 X 1 dimensionyellow color shows K selected eigenfaces = ui

STEP 6: Represent each face image a linear combination of all K eigenvectors

w1 w2 w3 w4 …. wk

∑

w of mean face

We can say, the above image contains a little bit proportion of all these eigenfaces.

w1

Ω= w2

: wk

Calculating weight of each eigenfacesThe formula for calculating the weight is:

wi= Øi. Ui

For Eg. w1= Ø1. U1

w2= Ø2. U2

Recognizing an unknown face

r1

r2

: rk

Convert the input

image to a face vector

Normalize the face vector

a1 – m1

i a2 – m2

. .

. .

a3 – m3

Project Normalized

face onto the eigenspace

Weight vector of input image

w1

Ω= w2

: wk

Calculate Distance between input weight

vector and all the weight vector of

training set€=|Ω–Ωi|2

i=1…M

Is Distance €> threshold∂ ? UNKNOWN FACE

NOYES

RECOGNIZED AS

Input image of UNKNOWN FACE

StrengthsIt has the ability to leverage existing

image acquisition equipment. It can search against static images such

as driver’s license photographs. It is the only biometric able to operate

without user cooperation.

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Weaknesses

Changes in acquisition environment reduce matching accuracy.

Changes in physiological characteristics reduce matching accuracy.

It has the potential for privacy abuse due to non cooperative enrollment and identification capabilities.

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Applications..

ApplicationsAccess ControlFace DatabasesFace IDHCI - Human Computer InteractionLaw EnforcementDay CareVoter verificationBanking using ATM

ApplicationsMultimedia ManagementSecuritySmart CardsSurveillanceSecurity/CounterterrorismResidential Security

Conclusionan algorithm to recognize faces present in

the face database. The proposed algorithm uses

the concept of PCA and represents an improved version of PCA to deal with the problem of orientation and

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Sources:[1]http://whatis.techtarget.com/definition/facial-

recognition[2]http://en.wikipedia.org/wiki/Facial_recognition_system[3]http://sebastianraschka.com/Articles/

2014_pca_step_by_step.html[4]M. Lam, H. Yan, An analytic-to-holistic approach for

face recognition based on a single frontal view, IEEE Trans. Pattern Anal. Mach. Intel. 20 (1998) 673-686.

[5]Zhang, Automatic adaptation of a face model using action units for semantic coding of videophone sequences, IEEE Trans. Circuits Systems Video Technol. 8 (6) (1998) 781-795.

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