Face Recognition Based on PCA Algorithm Using Simulink in...

International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)

Volume 3 Issue 7, July 2014

2303 ISSN: 2278 – 1323 All Rights Reserved © 2014 IJARCET

Face Recognition Based on PCA Algorithm Using Simulink in Matlab

Dinesh Kumar1, Rajni2.

1Mtech scholar department of ECE DCRUST Murthal Sonipat Haryana,

2Assistant Prof. Department of ECE DCRUST Murthal Sonipat Haryana

Abstract

The purpose of research work is to develop a computer system that can recognize a

person by comparing the individuals. As such we know reliable automatic face

recognition has become a realistic target of biometrics research. In this paper we

introduce a method for face recognition that is (PCA) principal component analysis. It

is easy and not costly as compare to other, like iris scan or finger print scan. In PCA we

only required 2-D frontal image of the person whose face to be recognize. This 2-D

frontal image is converted into 1-D matrix by concatenated of 2-D matrix. Face

recognition is very hot topic from a number of years because of its application.

Key terms: Face recognition, Principal Component Analysis, Eigen value, Eigenvector.

1 Introduction:

Face recognition is very interesting and popular from 50-60 years. In 1960s first semi-

automated system for face recognition is generated. In it some feature of face is extracted

(like ears, nose, eyes and mouth etc.). Then comparison is done between the reference data

and calculated distance and ratio to a common reference point. In 1970s specific marker

based technique was developed by Lesk, Goldstein and Harmon [1]. They used 21 specific

subjective markers for automate the recognition. These specifications were like hair color, lip

thickness, skin color, face shape and nose shape etc. But the problem with both the

techniques was that the measurement and locations were manually computed. Kirby and

Sirovich generate a technique called Principal Component Analysis in 1988. It is a standard

linear algebra technique for the problem of face recognition. Another the Eigen face

techniques were discovered by Turk and Pentland in 1991 [2]. There no further improvement

was done on it because it was environmental effect. In 2001 new technology came out and it

captured very good public’s attention. That approach captured surveillance image and

compared them to the database of digital photos. That was very better for security point of

view. Face recognition technique is increasing day by day and play major role in our life.

Now it is being used to identify missing children’s, passport fraud, identity fraud etc [3].

As we know human face is an extremely complex dynamic structure with characteristics

that can quickly and significantly change with time. The human ability to recognize face is

remarkable. In our lifetime we recognize thousands of faces, but after some time separation

we unable to recognize them. It is only due to the face variability. Face recognition is

playing very important role in our life and hot research area in the field of computer vision

[4]. It is very important research area because of its application. Security point of view face




recognition is very better technique. It is very useful in field of entertainment, law

enforcement, surveillance, smart cards (national ID, passport) and widely used in many

corporate and educational institutions. There are so many techniques for face recognition one

of them is Principal Component Analysis [5]. A face recognition system for automatically

identifying or verifying a person from a digital still and video image based on computer-

driven application. Generally face recognition works in two steps:

1.1. Face Detection 1. 2. Face Recognition

Face detection- For face detection we use a simple camera to take clear photo of a person.

Then we detect face from that image. After detect many face from image we make database

of it. And it is used for comparison with test image.

Face recognition- Test image face is also detect by using face detection technique. Then that

face is compared with the constricted database. On basis of that comparison we can say face

is known or not.

Image from camera

Figure 1 generally face detection and recognition

2. Mathematics representation of PCA Algorithm

For PCA algorithm we take a 2-D image of a person by using any camera. Then that 2-D

image is converted into 1-D by concatenation of the matrix. Suppose we take M images to

create database of N*N (rows of matrix *columns of image). In it Pj considered as pixel

values. PCA transforms a set of data obtained from possibly correlated variables into a set of

Face

detection &

create

database

Test

image

Recognition

of face

Comparison




uncorrelated variables called principle components. These may be equal or less than the

number of original variables [6].

Lets us consider a training database consists of N images which are of same size. The images

are normalized by converting each image matrix to equivalent image vector Zi. The training

set matrix Z is the set of images vectors with Training set

Z = [Z1 Z2 …..ZN] (1)

The mean face (µ) is the arithmetic average vector as given by:

µ = 1

𝑁 𝑍𝑘

𝑞𝑘=1 (2)

The deviation vector for each image Ωi is given by:

Ωi = Zi – µ where i = 1,2,…N (3)

Consider a difference matrix B= [Ω1, Ω2… ΩN] which having only the distinguishing

features for face images and removes the common features. To find eigenfaces we have to

calculate the Covariance matrix C of the training image vectors by [7]:

C=B.BT (4)

Due to large dimension of matrix C, we consider matrix N of size (Nt X Nt) which gives the

same effect with reduces dimension.

The eigenvectors of C (Matrix U) can be obtained by using the eigenvectors of N (Matrix V)

as given by:

Ui=BVi (5)

To find the weight of each eigenvector αi to represent the image in the Eigen face space, as

given by [8]:

αi = Ui T (Z -µ ) , i=1,2,……, N (6)

Weight matrix A = [µ1, µ2 …. µN] T

(7)

The Euclidean distance is used to find out the distance between two face keys vectors and it

is given by:

Euclidean distance = (𝑎𝑖 − 𝑏𝑖)2𝐷𝑖=1 (8)

On basis of that distance, we can say face is recognized or not.

3 Results

3.1 Face detection: - we take a 2-D image of any person, after that cropping is done. In cropping we

remove the unwanted part of image. Than that image is put into the Matlab program and by using B-

box we select the region of interest. Finally face is detected from the image.




Figure 2 detection of face in color and gray color.




3.2 Face Recognition

3.2.1 Analysis of Color database: For single Image database

For face recognition we use a image of size 512×512.

Figure 3 Colored images of six individual persons.

SR.

No.

Database Test Image Mean Eigen Value Euclidean

Distance

Theta

=C*Max(vector

Rast)

Result

1 Akc1 Ack1 0.4856 -0.2652 6.316274 3.3620 R




Result for Color Database with individual

3.2.2 Analysis of Color database: For Nine Images in database


Figure 4 Database with nine images 3of 3 individual each

2 Akc1 D2 0.4856 -0.2955 1.136893 3.3620 N. R

3 D2 D2 0.5140 -0.4303 5.215788 3.3620 R

4 D2 Par512 0.5140 -0.2037 2.298737 3.3620 N.R

5 Par512 Vk512 0.6652 -0.4693 1.249261 3.3620 N.R




Figure 5 Test images of size 512×512

Results for database with nine images

SR.

No.

Database Test

Image

Mean Eigen

Value

Euclidean

Distance

Theta

=C*Max(vector

Rast)

Result

1 D3 Ack1 0.5135 -0.6466 6.991376 1.5405 R

2 D3 amit 0.5135 -0.9227 6.3940913 1.5405 R

3 D3 D2 0.5135 -0.6769 1.2268813 1.5405 F

4 D3 Vk512 0.5135 -0.5602 1.2503594 1.5405 N.R

5 D3 par512 0.5135 -0.4503 1.0291825 1.5405 N.R

3.2.3. Analysis of Gray database: For single Image database


Figure 6 Gray images of six individual images




Result for Gray Database of individual Image

SR.

No.

Database Test

Image

Mean Eigen

Value

Euclidean

Distance

Theta

=C*Max(vector

Rast)

Result

1 Ak2 Ak2 0.3484 -0.4631 4.6123056 2.8788 R

2 Dk2 ak2 0.4557 -0.0766 -1.333633 2.8788 N.R

3 Par512b Par512b 0.7197 -0.2708 3.8894222 2.8788 R

4 Dk2 Par512b 0.4557 -0.3889 0.9743281 2.8788 N.R

3.2.4 Analysis of Database with nine Images: Database for four image


Figure 7 Database with nine images 3× 3 matrix form

Figure 8 Database with nine images 3× 3 matrix form




Result for Gray Database of individual Image

SR.

No.

Database Test

Image

Mean Eigen

Value

Euclidean

Distance

Theta

=C*Max(vector

Rast)

Result

1 Db3 Ak2 0.5114 -0.3294 7.667889 3.3620 R

2 Db3 Vk512b 0.5114 -0.6392 4.3078312 3.3620 R

3 Db3 Dk2 0.5114 -0.5499 8.855483 3.3620 R

4 Db3 Dk1 0.5114 -1.1804 5.872846 3.3620 R

5 Db3 par512b 0.5114 -0.1362 6.9711253 3.3620 R

Conclusion This paper presents a computer software system which can recognize a face.

PCA technique which is used for face recognition based on Simulink in Matlab. For face

recognition we use a image of size 512×512. Figure two and three shows the face detection.

Figure 4 shows colored images of six individual persons. These images are compared to each

other and result is shown in the table. In the figure 5, we use a database of nine images and in

the figure 6 test images are shown. Results after applied PCA algorithm are shown in the

table. Similarly gray color image are used and result for that is shown with help of table.

References

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