These papers describes Face Recognition Process using PCA Algorithm and Euclidean distance.

1. Face Recognition Process
Amro El Namory
Esraa Adel
Misr Higher Institute for Computers, Mansoura. (Student).

2. CONTENTS:-
• What is Face Recognition ?
• How it works ?
• Steps of Face Recognition.
• Feature Extraction.
• Classification.
• Applications of Face Recognition.
• Advantage and Limitations of Face Recognition
• References.

3. WHAT IS FACE RECOGNITION ?
Face Recognition : is a process to
identify faces as a known or
Unknown face based on
face features.

4. HOW IT WORK?
Face Recognition software is based on the ability to
recognize faces.
Firstly, we must have a Database of faces and these
Database is trained to extract faces features.
Suppose we want to recognize a detected face of
unknown person, the software will extract the features
of the detected face and then compare these features
with the stored features in Database.
If the features are matched , the software will recognize
the detected face.

5. STEPS OF FACE RECOGNITION
Face Detection
Feature Extraction
Classification
Face Recognition

6. FLOW CHART SHOWS THE STEPS OF FACE
RECOGNITION AND HOW IT WORKS.
True
False
Start
Input Face
Size =
128*128
Feature Extraction
Resize to 128*128

7. Comparison Features with DB
Display Face
Matching
End
No Image
False
True

8. FEATURES EXTRACTION
Firstly , What is Features ?
♦ Features are used to describe the object prior to the task of
classification.
Then , What is Feature Extraction ?
♦ Feature Extraction is an operation on two dimensional images
that extract the features of these images and then produce a list
of descriptions , that calls Feature vector.
What are the types of Features ?
♦ Features are gleaned from :
1- The boundary properties of the shape.
2- The internal properties of the shape.

9. ♦ We extract the Features from internal properties of the shape
using the mean value method.
♦ After calculating the mean value of each image, Calculating the
deviation of each image from the mean.
♦ After Feature Extraction we use the PCA Algorithm to reduce the
Extracted Features.

10. PCA ALGORITHM
♦ Principal Component Analysis (PCA) is a useful statistical technique that
has found application in fields such as face recognition and image
compression.
♦ The Functionality of PCA is the reduction of features by retaining as much as
variation possible in the original data set.
Steps of PCA :
1- Convert image of training set to image vectors.
2- Normalize the Face Vectors.
3- Calculate the Eigenvectors.
4- Reduce Dimensionality.
5- Back to original dimensionality.
6- Represent Each Face Image a Linear Combination of all K Eigenvectors.

11. STEP 1 : CONVERT IMAGE OF TRAINING SET TO
IMAGE VECTORS.
M = Images = 16
1 2 3 4 5 6
9 10 11 12 13 14
7 8
15 16
Image
ColumnVector
Images converted to vector
Face vector space
𝑻𝒊

12. STEP 2 : NORMALIZE THE FACE VECTORS.
M = Images = 16
1 2 3 4 5 6
9 10 11 12 13 14
7 8
15 16
Mean
ImageImages converted to vector
Face vector space
It have two stages :
1- Calculate the Average Face Vector / Mean Image (Ψ).
2- Subtract Mean Image from each face image.
1- Calculate the Average Face Vector / Mean Image (Ψ).
Saving to
Features
(Ψ)
Ф𝒊

13. STEP 2 : NORMALIZE THE FACE VECTORS.
2- Subtract Mean Image from each face image.
Normalized
Image
Face vector space
Image
Mean
Image– =
(Ψ)
Ф𝒊

14. STEP 3 : CALCULATE THE EIGENVECTORS.
♦ Firstly we need to calculate the covariance vector C
from the following equation :
𝐶 =
1
𝑀
𝑛=1
𝑀
Φ 𝑛Φ 𝑛
𝑇
=
1
𝑀
𝐴. 𝐴 𝑇
Where 𝑨 = {Ф 𝟏, Ф 𝟐, Ф 𝟑, … … … ., Ф 𝟏𝟔} [𝐀 = 𝐍 𝟐
× 𝐌]
♦ Then, we need to find only K eigenvectors from the 𝑵 𝟐 eigenvectors,
where K ≤ M
𝒖𝒊

15. STEP 4 : REDUCE DIMENSIONALITY.
♦ Consider lower dimensional sub space, then, Calculate Covariance
matrix (L) of lower dimensional.
M = Images = 16
1 2 3 4 5 6
9 10 11 12 13 14
7 8
15 16
(Ψ)Ф𝒊
𝒗𝒊Face vector space
Lower dimensional Sub space
𝑳 = 𝑨 𝑻 𝑨
= 𝑴 × 𝑵2 𝑵2 × 𝑴
= 𝑴 × 𝑴
𝝁𝒊

16. STEP 5 : BACK TO ORIGINAL DIMENSIONALITY.
𝒗𝒊 𝝁𝒊
𝒖𝒊 = 𝑨𝒗𝒊
(Ψ)Ф𝒊
The K selected eigenface
𝐂 = 𝑨𝑨 𝑻

17. STEP 6 : REPRESENT EACH FACE IMAGE A LINEAR
COMBINATION OF ALL K EIGENVECTORS.
(Ψ)Ф𝒊
The K selected eigenface
M = Images = 16
1 2 3 4 5 6
9 10 11 12 13 14
7 8
15 16
𝜴𝒊 =
𝝎 𝟏
𝒊
𝝎 𝟐
𝒊
𝝎 𝟑
𝒊
.
.
.
𝝎 𝑲
𝒊
Each face from Training set can be
represented a weighted sum of
the K Eigenfaces + the Mean face
Mean Image A weight vector 𝛀𝐢 which
is the eigenfaces
representation of the 𝒊 𝒕𝒉
face. We calculated each
faces weight vector.
Face vector space

18. EUCLIDEAN DISTANCE
♦ One of the most common metrics
used is the Euclidean distance measure.
♦ To measure the similarity of pattern samples in
the geometric pattern space.
♦ The Euclidean metric is widely used mainly
because it is simple to calculate.

19. EUCLIDEAN DISTANCE
♦ Consider two vectors (X and Y) that we wish to
find the Euclidean distance between them d(X, Y) .
Euclidean Distance
X
Y
x
y
𝒅 =
𝒊=𝟏
𝑴
(𝑿𝒊 − 𝒀𝒊) 𝟐
i =1,....., M
where M is the dimensionality of the vector.

20. EUCLIDEAN DISTANCE
For the two-dimensional we get :
𝒅 = (𝑿 𝟏 − 𝒀 𝟏) 𝟐+(𝑿 𝟐 − 𝒀 𝟐) 𝟐
Alternative distance metrics include : the sum of the modulus
of the differences between the measurements.
𝑳 𝟏 =
𝒊=𝟏
𝑴
|𝑿𝒊 − 𝒀𝒊|

21. EUCLIDEAN DISTANCE
In application, usually we have a description of a texture
sample X.
We want to find which element of a database best matches
that sample.
In terms of Euclidean distance, the difference d between the
M descriptions of a sample, X, and the description of a
known texture, Y, is d as given before.
𝒅 =
𝒊=𝟏
𝑴
(𝑿𝒊 − 𝒀𝒊) 𝟐
The classifier must decide which type of class category
they match most closely.

22. APPLICATIONS OF FACE RECOGNITION

23. • Image quality.
• Image size.
• Face angle.
• Processing and storage.
• Convenience and Social
acceptability, All you need is
your picture taken for it to
work.
• Face recognition is easy to
use and in many cases it can
be performed without a
Person even knowing.
• Face recognition is also one
of the most inexpensive
biometric in the market and
Its price should continue to
go down.
ADVANTAGE AND LIMITATIONS OF FACE
RECOGNATION
Advantage Disadvantage

24. REFERENCES
www.slideshare.com
www.wikipedia.com