This document discusses face recognition using Fisher face analysis (LDA). It provides an overview of LDA and how it is used for face recognition. LDA works by finding a linear transformation that maximizes between-class variance and minimizes within-class variance to achieve better class separation. The document outlines the LDA algorithm which involves computing within-class and between-class scatter matrices to find discriminant vectors that project faces into a space where classes are well separated. It also mentions the ORL face database is used and provides references for further information.

1. BY:-
Suraj Kumar(BT11CS008)
Saroj Paswan(BT11CS005)
FACE RECOGNITION
USING FISHER FACE ANALYSIS(LDA)

2. TOPICS OF DISCUSSION
 Face Recognition.
 Linear Discriminant Analysis(LDA).
 Class Separation using LDA.
 Algorithm used in LDA approach.
 Application of LDA.
 Database used.
 References.

3. FACE RECOGNITION
Face recognition system is a computer application for
automatically identify or verifying a person from a
digital image or video frame. In this system
automatically searching of faces from the face
databases, typically resulting in a group of facial
images ranked by computer evaluated similarity.

4. USE OF FACE RECOGNITION SYSTEM
Face recognition system is typically used in security system
and personal information access.
 SECURITY
 Airport, seaport, railway station etc.
 Find Fugitive.
 PERSONAL INFORMATION ACCESS
 ATM.
 Computer system.

5. FACE RECOGNITION ALGORITHM
 Linear Discriminant Analysis(LDA).
 Principle Component Analysis(PCA).

6. Linear Discriminant Analysis(LDA)
Linear discriminant methods group images of the
same classes and separates images of the different
classes. To identify an input test image, the projected
test image is compared to each projected training
image, and the test image is identified as the closest
training image.

7. To explain discriminant analysis, here we consider a classification
involving two target categories and two predictor variables.
The following figure shows a plot of the two categories with the
two predictor’s orthogonal axes:
Figure 1. Plot of two categories

8. The target variable may have two or more categories.
Images are projected from two dimensional spaces to
c dimensional space, where c is the number of classes
of the images. To identify an input test image, the
projected test image is compared to each projected
Training image.

9. Class Separation Using LDA
Linear discriminant analysis finds a linear
transformation (discriminant function) of the two
predictors, X and Y that yields a new set of
transformed values that provides a more accurate
discrimination than either predictor alone:
Transformed Target = C1*X + C2*Y

10. The following figure shows the partitioning done using the
transformation function:
Figure 2. Partitioning done using the transformation function

11. Maximizing the between class scatter matrix, while
minimizing the within-class scatter matrix, a transformation
function is found that maximizes the ratio of between-class
variance to within-class variance and find a good class
separation as illustrated as follows:
Figure 3. Class Separations in LDA

12. ALGORITHM USED IN LDA
In Linear discriminant analysis we provide the following steps to
discriminant the input images:
STEP-1:
We need a training set and at last one image in the test set.
These examples should represent different frontal views of
subjects with minor variations in view angle. They should
also include different facial expressions, different lighting,
background condition and only the face regions. It is
assumed that all images are already normalized to m × n
arrays.

13. b
b


 



 2

1

2

 


N
2
 2
a
a
a
1
2
b
N

1

2

 


N

c
c
c
e
e
 
 
  
 
 
 
  2
 
1
 
 2
 
 
 
 
 2
N
2
 d
d
d
1
2
e
N
 
1
 
  2

 
 
 
 N

f
f
f
representing faces

14. STEP-2:
For each image and sub image, starting with the two
dimensional m × n array of intensity values I(x, y), we
construct the vector expansion Φ R m× n. This vector
corresponds to the initial representation of the face. Thus
the set of all faces in the feature space is treated as a high-dimensional
vector space.

15. STEP-3:
By defining all instances of the same person’s face as being in
one class and the faces of different subjects as being in
different classes for all subjects in the training set, we
establish a framework for performing a cluster separation
analysis in the feature space. we compute the within-class
and between-class scatter matrices.

16. Now with-in class scatter matrix ‘Sw’ and the between class
scatter matrix ‘Sb’ are defined as follows:
푵풋 (휞풊
Sw = Σ풄 Σ풋=ퟏ 풊=ퟏ
풋 − 흁풋) (휞풊
풋 − 흁풋)푻 ------ (1)
푗, the 푖푡ℎ. samples of class j, 휇푗 is the mean of class j, c is the number
Where , Γ푖
of classes, 푁푗 is the number of samples in class j.
풄 (흁풋 − 흁) (흁풋 − 흁)푻 ---------------- (2)
Sb = Σ풋=ퟏ
Where, μ represents the mean of all classes.

17. mean of class
a b h
a b h
    
1 1 1
 
1     2 2 2
  
m where M
 
 
      2 2 2

, 8
N N N
M
a b h
Then subtract it from the training faces
a m b m c m d m
a m b m c m d m
           
1 1 1 1 1 1 1 1
       
  2 2    2 2        2 2   2 2

 a b c d
, , , ,
m m m m
       
       
  a  m        N 2 N 2   b  m   c  m N 2 N 2 N 2 N 2   d  m
N 2 N
2

e m f m
e m f
g m h m
   
 
    
       
     
          
     
              
1 1 1 1
2 2
m g m h m
e ,
f
g h
m m
 
  e  m
 N 2 N
2
 2 2 2 2 2 2
1 1 1 1
2 2 2 2 2 2
, , m m
f m g m h m
N N N N N N

18. The subspace for LDA is spanned by a set of vectors w=[푎 푚, 푏푚, …,
ℎ푚], Satisfying
w = arg max = mod
푤푇 푆푏 푤
푤푇 푆푤 푤
-----(3)
The with-in class scatter matrix represents how face images are distributed
closely with-in classes and between class scatter matrix describes how
classes are separated from each other. When face images are projected into
the discriminant vector w.
Face images should be distributed closely with-in classes and should
be separated between classes, as much as possible. In other words, these
discriminant vectors minimize the denominator and maximize the
numerator in equation (3).

19. The testing phase of LDA is as shown as in figure.
Face Database Training Set
Testing Set
Projection of Test
Image
LDA(Feature
Extraction)
Feature Vector Feature Vector
Classifier
(Euclidean distance)
Decision making

20. APPLICATION OF LDA
Linear discriminant analysis techniques used in statistics,
pattern recognition and machine learning to find a linear
combination of features which characterized or separates
two or more classes of objects.
DATABASE USED
ORL Database, All the files are in PGM format. The size of
each image is 92×112 pixels. with 256 grey levels per
pixel.
Fig. 4. One of ORL face database with ten different expressions.

21. REFERENCES
 [1] [Online]. Available:
http://www.animetrics.com/technology/frapplications.html
http://en.wikipedia.org/wiki/Facial_recognition_system
http://vis-www.cs.umass.edu/~vidit/IndianFaceDatabase
http://www.originlab.com
 [2] B. J. Oh, Face Recognition using Radial Basis Function Network based on
LDA. World Academy of Science, Engineering and Technology 7 2005
 [3] R. Duda and P. Hart, Pattern Classification and Scene Analysis.
 [4] R. Chellappa, C. Wilson, and S. Sirohey, Human and Machine Recognition
of Faces: A Survey, Proc. IEEE, vol. 83, no. 5, pp. 705- 740, 1995.
 [5] ORL face database: AT &T Laboratories, Cambridge,U.K..[Online].
Available: http://www. cam-orl.co.uk / facedatabse.html.

22. THANKS…