This document discusses face recognition using principal component analysis (PCA) and Gaussian-based PCA. It begins with an introduction to face recognition and PCA. The document then describes the PCA algorithm, including the training and recognition phases. It also discusses Gaussian filters and their use for image smoothing. The proposed method applies Gaussian filtering before PCA to enhance accuracy. Experimental results on a database of face images show Gaussian-based PCA produces closer matches and lower Euclidean distances, indicating more accurate recognition compared to normal PCA. In conclusion, preprocessing images with Gaussian filtering before PCA improves face recognition performance.

1. International Journal of Electronics and Communication Engineering & Technology (IJECET),
INTERNATIONAL JOURNAL OF ELECTRONICS AND
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME
COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)
ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 4, Issue 4, July-August, 2013, pp. 244-251
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IJECET
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Application of Gaussian Filter with Principal Component Analysis
Algorithm for The Efficient Face Recognition
Shashikant Sharma1, Kota Solomon Raju2
1Faculty/Electronics
2Principal
& Communication, BKBIET, Pilani, Rajasthan, India
Scientist/Digital System Group/CSIR-CEERI, Pilani-333031, India
1shashikant.sharma@bkbiet.ac.in, 2solomon@iitr.ernet.in
ABSTRACT: The selection of appropriate algorithm is an important target for any application.
In this paper Face recognition has been performed using Principal component analysis (PCA)
and Gaussian based PCA. PCA extracts the relevant information from complex data sets and
provides a solution to reduce dimensionality. PCA is based on Euclidean distance calculation
which is minimized by applying Gaussian Filter to enhance the accuracy for Face recognition.
The experiments shows that the proposed method (PCA) can effectively reduced the
computational complexity. Gaussian based PCA shows more accurate result as normal PCA for
face recognition.
KEYWORDS: Covariance Matrix, Eigen values, Euclidean distance, Gaussian Filter, PCA
algorithm
I.
INTRODUCTION
A Face recognition system is a computer application for automatically identifying or verifying
an individual by using a digital image. Some face recognition algorithm identifies facial features
by extracting exclusive characteristics from an image. An algorithm may analyze the relative
position, shape or size of nose, eyes, cheekbones and jaws. These features are then used to
identify other images with corresponding matching features. The most popular face
recognition algorithm includes Principal component analysis using Eigen faces, Linear
Discriminate Analysis using Fisher faces .It is usually employed in high security system which
includes Biometrics such as Fingerprints or eyes iris recognition system. Kirby and Sirovich [1]
showed that any face image can be efficiently represented along the Eigen faces (Eigen vectors)
coordinate space. Turk and Pentland [2] presented the well known Eigen faces method for face
recognition based on PCA. Face recognition system can be classified into two broad categories
[3]:
Firstly, finding a person within a large database of faces [6] e.g. in a database (Face recognition
which is not done in Real time). Secondly, identifying a particular individual in Real time e.g.
Location Tracking system.
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October 18-20, 2013
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2. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME
II.
PRINCIPAL COMPONENT ANALYSIS
PCA is a useful technique for face recognition and image compression. It is highly useful for
finding patterns in case of high dimensional data .It includes standard deviation, Eigen values
and Eigen vectors as well as covariance. PCA algorithm is highly robust includes parallelism
and is relatively very simple. There are various approaches to face recognition ranging from
the principal component analysis approach or Eigen faces. Prediction can be done through
feature matching. PCA has been called one of the most valuable results from applied linear
algebra. It is a dimensionality reduction technique based on extracting the desired number of
principal component of the multidimensional data. Face recognition system consist of two
phases [4]:


Training phase (feature extraction)
Recognition phase (feature matching)
A. Training Phase
1. The first step in the proposed algorithm is to read the images from database of still images.
2. Gaussian filtering is done to remove the noise from the images in the preprocessing step.
3. Each image in the database is represented as a row in a matrix D. The values in each of
these rows represent the pixels of the database image ranging from 0 to 255 for an 8-bit
grayscale image:
⋯
⋮
⋱
⋮
=
⋯
Where m=Size of original image (The image has total m pixels), n=Number of original Images.
4. Average of the matrix D is calculated to normalize the matrix D. The average of matrix D
is a row vector in which every element is the average of every Database image pixel values
respectively.
avg=(x1,x2,… … … … … , xm)
Where
= ∑
, i=1,2,3,…..,m-------------- (1)
5. Next, the matrix is normalized by subtracting each column of matrix “avg” from each
column of matrix D:
−
⋯
−
⋮
⋱
⋮
=
−
⋯
−
6. We then want to compute the covariance matrix of , which is ×
or × . But here
we use × , because it reduces the size of the covariance matrix and calculated as:
S=
×
--------------------------
(2)
7. Next step is to calculate the Eigen vectors of original matrix thus we need to calculate
the Eigen vectors of the covariance matrix S, let us say Eigen vectors of the covariance matrix
are C, the size of C is same as S.
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B K Birla Institute of Engineering & Technology (BKBIET), Pilani, India
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3. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME
8. Then we calculate the Eigen vectors of the original matrix after the calculation of C as
follows:
=
×
9. Each face is then projected to face space while calculating the projection of the image as:
= ×
B. Recognition Phase
1. First of all we read the test image from the test database.
2. This image is sent the preprocessing segment (Gaussian Filter) to remove the
noise.
3. Reshape the image into row vector having number of columns equal to the
product of number of rows and columns of the test image.
4. The test image is then normalized by subtracting the average image from the test image;
normalized matrix is stored in “t_avg”.
5. Next, we calculate the projection of test image to project the face on face space as follows:
test_projection= t_avd × V ------------(3)
4. We then calculate the Euclidean distance between the test projection and each of the
projections in the database:
( )=
Where i=1, 2,…., n and
database
∑
(
_
(1, ) −
( , ))
m= total number of pixels in a image n= number of images in the
5. Finally, we decide which database image is recognized by the test image by selecting
minimum Euclidean distance from the Euclidean distance vector “ED”. (Size of the Euclidean
Distance vector is 1 x no. of faces.)
III.
GAUSSIAN FILTER
Gaussian filters are the class of linear smoothening filters which are used for the Image
Smoothening. The weights of the Gaussian filter are chosen according to the shape of the
Gaussian function. The Gaussian smoothing filter is a very good filter for removing noise drawn
from a normal distribution. The zero-mean Gaussian function for 1-D is:
( )=
-----------(4)
For image processing, the two-dimensional zero-mean discrete Gaussian function,
(, )=
(
)
--------- (5)
is used as image smoothening filter. Where the ‘ ’, Standard deviation or Gaussian Spread
Parameter determines the width of Gaussian.
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4. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME
IV.
PROPOSED SYSTEM ARCHITECTURE
The propose system read the database images from the stored location. The preprocessing has
been done on the images after reading. The proposed system creates a database and stores all
the preprocessed images in this database and finally system creates a database matrix and the
system perform all the operations on the database matrix. The Principle Component Analysis
technique has been applied on the images of the database system.
The proposed system uses the test images stored in the database, read test image.
Preprocessing is done after reading the test image. The system implement Principal
Component Analysis algorithm on the test image.
Now system compares the test image from the database images one by one using Euclidean
distance. Finally system provides the result that shows the test image and recognized image
from database. The system flow chart is shown in Fig. 1.
Read the database
images
Preprocessing on the
database images
Create database
matrix
PCA
Read the Test image
Preprocessing on the
Test image
Algorithm
Select Minimum
Euclidean Distance
PCA
Algorithm
Output Display
Fig. 1: System Flow Chart
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5. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME
V.
EXPERIMENTAL RESULTS
The set of input database and test database images used in Algorithm are:
DATABASE IMAGES:
1.bmp
2.bmp
3.bmp
4.bmp
3.bmp
4.bmp
5.bmp
6.bmp
7.bmp
8.bmp
TEST IMAGES:
1.bmp
9.bmp
17.bmp
2.bmp
10.bmp
18.bmp
5.bmp
6.bmp
7.bmp
8.bmp
11.bmp
12.bmp
13.bmp
14.bmp
15.bmp
16.bmp
19.bmp
20.bmp
21.bmp
22.bmp
23.bmp
24.bmp
A. Results
Test image: 8.bmp Recognized Image: 3.bmp
Algorithm: PCA
Euclidean Distance: 4.335313*106
Test image: 8.bmp Recognized Image: 8.bmp
Algorithm: Gaussian PCA
Euclidean Distance: 1.0600*106
Test image: 10.bmp Recognized Image: 7.bmp Test image: 10.bmp Recognized Image: 5.bmp
Algorithm: PCA
Algorithm: Gaussian PCA
6
Euclidean Distance: 2.414793*10
Euclidean Distance: 1.0600*106
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6. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME
Test image: 6.bmp
Algorithm:PCA & GPCA
Recognized Image: 6.bmp
Euclidean Distance: 0.00
Table 1: Results of PCA methods
Test
Recognized Index
Index
ED (PCA)
Recognized Index
(PCA)
ED (GPCA)
(GPCA)
1
4.bmp
3.6885*106 4.bmp
2.1269*106
2
2.bmp
1.7175*106 2.bmp
1.2360*106
3
2.bmp
3.7526*106 1.bmp
2.5351*106
4
2.bmp
3.7963*106 2.bmp
1.0452*106
5
5.bmp
2.2853*106 3.bmp
0.9894*106
6
6.bmp
0.0000
0.0000
7
3.bmp
1.9317*106 3.bmp
0.9147*106
8
3.bmp
4.3353*106 8.bmp
1.0600*106
9
4.bmp
2.6730*106 4.bmp
1.0389*106
10
7.bmp
2.4148*106 5.bmp
1.1538*106
11
3.bmp
2.4923*106 3.bmp
0.9513*106
12
3.bmp
1.9791*106 3.bmp
0.8867*106
13
6.bmp
2.4792*106 6.bmp
0.7096*106
14
1.bmp
1.8833*106 1.bmp
0.4249*106
15
6.bmp
2.4867*106 6.bmp
1.4022*106
6.bmp
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7. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME
16
1.bmp
2.2740*106 4.bmp
1.0608*106
17
3.bmp
2.9281*106 8.bmp
1.6903*106
18
1.bmp
3.7535*106 1.bmp
1.9031*106
19
3.bmp
2.2228*106 3.bmp
0.9280*106
20
2.bmp
2.8989*106 2.bmp
1.1081*106
21
1.bmp
1.1613*106 1.bmp
0.3220*106
22
3.bmp
2.1236*106 3.bmp
1.4902*106
23
8.bmp
2.5454*106 8.bmp
1.0738*106
24
3.bmp
2.0392*106 3.bmp
0.5632*106
Table 2: Comparative analysis of PCA and GPCA
Fig. 2: Comparative Graph of PCA Method
VI.
CONCLUSION
In this paper Principal component analysis (PCA) is implemented in MATLAB recognize the
test image from the database images. Minimum Euclidean distance has been calculated using
PCA algorithm. Gaussian filter is applied on the images before processing them and PCA
algorithm is applied on the filtered images. The results of PCA and Gaussian based PCA are
compared. As the Gaussian base PCA gives close results with lower minimum Euclidean
Distance.
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8. International Journal of Electronics and Communication Engineering & Technology (IJECET),
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REFERENCES
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[3] S. Lawrence, C. Giles, A. Tsoi, and A. Back, “Face recognition: A Convolutional Neural
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Resilient Back propagation Algorithm”,IJETA,vol.2,issue11,pp: 223-228,2012
[7]Jin-Xin Shi,Xiao-Feng Gu,” The comparison of iris recognition using principal component
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BIOGRAPHY
Shashikant Sharma was born in Jaipur, Rajasthan, India in 1987. He
received the B.Tech degree in Electronics and Communication Engineering
from ICFAI UNIVERSITY, Dehradun, India in 2009. He is pursuing his M.
Tech in Electronics & Communication at National Institute of Technical
Teachers Training & Research (NITTTR), Chandigarh, India. His current
research interests focus on Signal Processing, Image Processing, and
Reconfigurable System Designing.
Dr. Kota Solomon Raju has been working as Principal Scientist in Digital
Systems Group, CSIR -Central Electronics Research Institute (CSIR - CEERI),
Pilani, Rajasthan, India. He received the Bachelor of Engineering degree in
1997 from Andhra University, Master of Engineering in 2003 from Birla
Institute of Technology and Science (BITS), Pilani and Ph.D in 2008 from
department of Electronics and Computer Engineering, IIT Roorkee, India.
Dr. Solomon is an advanced electronic systems design engineer. His
research work focused on reconfigurable computing systems (RCS),
advanced embedded systems design and wireless sensor network (WSN) based embedded
systems design and included hardware/software codesign, parallelizing applications,
customized computing, and high-level synthesis, ad hoc networking, Zigbee based networking,
and other sensor based embedded systems, protocols design and CAD tools for electronic
systems design. Apart from above R&D he also teaches /delivers lectures in System Modeling &
Design languages, Wireless Sensor Network based embedded Systems Design and Real -time
systems design courses for the post graduate students. He has delivered fifteen invited talks in
international / national conferences /seminars/workshops. He is author and co-author of
more than 42 scientific papers, published in peer-reviewed international journals and
conferences, guided around 40 M.Tech dissertations so far and many B.Tech, M.Sc and MCA
theses. He has been guiding two Ph.D. students. He is a life member of the IETE, New Delhi.
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