face recogntion using pca algorithm
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TRANSCRIPT
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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