1. FACE RECOGNITION
By
Vaishali S. Bansal
M.Tech Computer
C.G.P.I.T. Bardoli
2. LEARNING OBJECTIVES
THE VERY BASICS :
What is face recognition?
Difference between detection & recognition !!!
The origin and use of this technology ?
What are the various approaches to recognize a face?
OUR SELECTED FACE RECOGNITION METHOD :
Introduction to PCA Based Eigen Face Recognition
Method.
3. 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 cases,
TELLING EXACTLY
WHO’S IT IS ! “
FEATURE
FACE DETECTION FACE RECOGNITION
EXTRACTION
7. STEP 0: Convert image of training set to image vectors
A training set consisting of total M images
Each image is of size NxN
8. STEP 1: Convert image of training set to image vectors
A training set consisting of total M image
foreach (image in training set)
{ 1
Image converted to vector
NxN Image
N
……
Ti } Vector
• Free vector space
9. STEP 2: Normalize the face vectors
1. Calculate the average face vectors
A training set consisting of total M image
Image converted to vector
Calculate average face vector „U‟
U
……
Ti
• Free vector space
10. STEP 2: Normalize the face vectors
1. Calculate the average face vectors
2. Subtract avg face vector from each face vector
A training set consisting of total M image
Image converted to vector
Calculate average face vector „U‟
U
…… Then subtract mean(average) face
Ti vector from EACH face vector to
get to get normalized face vector
Øi=Ti-U
• Free vector space
11. STEP 2: Normalize the face vectors
1. Calculate the average face vectors
2. Subtract avg face vector from each face vector
A training set consisting of total M image
Image converted to vector
Øi=Ti-U
U
…… Eg. a1 – m1
Ti
a2 – m2
Ø1= . .
. .
• Free vector space a3 – m3
12. STEP 3: Calculate the Eigenvectors (Eigenvectors represent the
variations in the faces )
A training set consisting of total M image
Image converted to vector
To calculate the eigenvectors , we
U need to calculate the covariance
…… vector C
Ti
C=A.AT
where A=[Ø1, Ø2, Ø3,… ØM]
• Free vector space
N2 X M
13. STEP 3: Calculate the Eigenvectors
A training set consisting of total M image
Image converted to vector
U
C=A.AT
……
Ti
N2 X M M X N2 = N2 X N2
Very huge
• Free vector space matrix
14. STEP 3: Calculate the Eigenvectors
A training set consisting of total M image
N2 eigenvectors
……
Image converted to vector
U
C=A.AT
……
Ti
N2 X M M X N2 = N2 X N2
Very huge
• Free vector space matrix
15. STEP 3: Calculate the Eigenvectors
A training set consisting of total M image
N2 eigenvectors
……
Image converted to vector
• But we need to find only K
• U eigenvectors from the above
…… N2 eigenvectors, where K<M
Ti
Eg. If N=50 and K=100 , we need to
find 100 eigenvectors from 2500
• Free vector space (i.e.N2 ) VERY TIME CONSUMING
16. STEP 3: Calculate the Eigenvectors
A training set consisting of total M image
N2 eigenvectors
……
Image converted to vector
• SOLUTION
• U
…… “DIMENSIONALITY REDUCTION”
Ti
i.e. Calculate eigenvectors from a
covariance of reduced
• Free vector space dimensionality
17. STEP 4: Calculating eigenvectors from reduced covariance
matrix
A training set consisting of total M image M2 eigenvectors
……
Image converted to vector
• New C=AT .A
• U
…… M XN2 N2 X M = M XM
Ti matrix
• Free vector space
18. 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
19. STEP 6: Convert lower dimension K eigenvectors to
original face dimensionality
A training set consisting of total M image
ui = A vi
ui = ith eigenvector in the
higher dimensional space
vi = ith eigenvector in the
lower dimensional space
Image converted to vector
100 eigenvectors
•
• U
……
Ti
……
• Free vector space
20. 2500 eigenvectors
ui
……
Each 2500 X 1 dimension
ui = A v i
=A
100 eigenvectors
vi
……
Each 100 X 1 dimension
21. 2500 eigenvectors
ui
……
Each 2500 X 1 dimension
yellow colour shows K selected eigenfaces = ui
22. STEP 6: Represent each face image a linear
combination of all K eigenvectors
w1
Ω= w2
:
w of mean face wk
∑
w1 w2 w3 w4 …. wk
We can say, the above image contains a little bit proportion of all these eigenfaces.
23. Calculating weight of each eigenface
The formula for calculating the weight is:
wi= Øi. Ui
For Eg.
w1= Ø1. U1
w2= Ø2. U2
24. Recognizing an unknown face
Input image of
UNKNOWN FACE
a1 – m1
Convert the r1
Normaloze the a2 – m2
input image to r2
a face vector face vector . .
: . .
rk a3 – m3
RECOGNIZED AS
Is Project Normalized
YES Distance face onto the
NO eigenspace
€>
threshold
∂? UNKNOWN FACE
w1
Calculate Distance between
Ω= w2
input weight vector and all the
:
weight vector of training set
wk
€=|Ω–Ωi|2
i=1…M Weight vector of
input image
