IOSR Journal of Computer Engineering (IOSR-JCE)

e-ISSN: 2278-0661, p- ISSN: 2278-8727Volume 16, Issue 2, Ver. VII (Mar-Apr. 2014), PP 59-63
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A Face Recognition Scheme Based On Principle Component
Analysis and Wavelet Decomposition

Ashish Sharma
1
, Dr.Varsha Sharma
2
, Dr.Sanjeev Sharma
3


1,2,3
School of Information Technology, RGTU, Bhopal-India

Abstract: In this paper, a new face recognition system based on Wavelet transform (HWT) and
Principal Component Analysis (PCA) is presented. The image face is preprocessed and detected. The
Haar wavelet is used to form the coefficient matrix for the detected face. The image feature vector is obtained by
computing PCA for the coefficient matrix of DWT. A comparison between the proposed recognition system
using DWT, PCA and Discrete Cosine Transform (DCT) is also made.
Keywords: Wavelet Transform, Principal Component Analysis.

I. INTRODUCTION
Face recognition is one of most successful applications in computer vision and pattern recognition and
the main objective of it is to recognize persons from pictures or video using a stored database of faces [1]. The
building of face recognition system is a sophisticated problem because the faces has a lot of variations and may
be located in a changed environment. Because of these reasons, the recognition of faces is a challenging
problem due to the wide variety of illumination, facial expression and pose variations. In developing a
face recognition system, we have to select suitable properties to represent a face under environmental changes.
Face recognition is used in many applications such as human computer interaction, biometrics and security
system [2].
In the recent years, wavelet analysis have generated a great interest in both theoretical and
applied mathematics, and the wavelet transform in particular has proven to be an effective tool for e.g. data
analysis, numerical analysis, and image processing [3].
The face recognition methods are categorized into holistic matching methods, feature-based
matching methods, and hybrid methods [4]. Holistic matching methods use the whole face region as the raw
input to a recognition system. It is reported in [4] that one of the methods used in representations of
the face region is Eigen faces, which are based on Principal Component Analysis (PCA). Using PCA,
many face recognition techniques have been developed: Eigen faces, which use a nearest neighbor classifier;
feature-line-based methods, which replace the point-to-point distance with the distance between a point and the
feature line linking two stored sample points; Fisher faces which use linear/Fisher discriminant analysis
(FLD/LDA); Bayesian methods, which use a probabilistic distance metric; and SVM methods, which use
a support vector machine as the classifier. Utilizing higher order statistics, independent-component
analysis (ICA) is argued to have more representative power than PCA, and hence may provide better
recognition performance than PCA [4]. For the other types of recognition, it can be referred to reference [4].
It is reported in [5] that dimension reduction is as important as the class separation in
applications like face recognition to make the face recognition system model based on the discrete
cosine transform (DCT) computationally efficient. DCT helps to separate the image into parts (or
spectral sub-bands) of differing importance (with respect to the image's visual quality). The DCT is
similar to the discrete Fourier transform: it transforms a signal or image from the spatial domain to the
frequency domain and represents an image as a sum of sinusoids of varying magnitude and frequencies.
In proposed model [5] of face recognition dimension reduction is achieved firstly through decimation algorithm
and then DCT is applied which exhibits large variance distribution in a small number of coefficients and
much of the signal energy lies in low frequencies; these appear in the upper left corner of the DCT [5].

II. WAVELET TRANSFORM
In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any
wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a
key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location
information. The first DWT was invented by the Hungarian mathematician Alfrd Haar. For an input
represented by a list of 2
n
numbers, the Haar wavelet transform may be considered to simply pair up input
values, storing the difference and passing the sum. This process is repeated recursively, pairing up the sums to
provide the next scale: finally resulting in 2
n
1 differences and one final sum.
A Face Recognition Scheme Based On Principle Component Analysis and Wavelet Decomposition
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Wavelets are functions that satisfy certain mathematical requirements and are used in representing data or other
functions. This idea is not new. Approximation using superposition of functions has existed since the early
1800s, when Joseph Fourier discovered that he could superpose sines and cosines to represent other functions.
However, in wavelet analysis, the scale that we use to look at data plays a special role. Wavelet algorithms
process data at different scales or resolutions. If we look at a signal with a large window, we would notice
gross features. Similarly, if we look at a signal with a small window, we would notice small features. The
result in wavelet analysis is to see both the forest and the trees, so to speak [6].
Using the classical wavelet decomposition, the image is decomposed into the approximation and details images,
the approximation is then decomposed itself into a secondlevel of approximation and details and so on (Press,
1992). Wavelet Packet Decomposition (WPD) is a generalization of the classical wavelet decomposition and
using WPD we decompose both approximations and details into a further level of approximations and details.
Theoretical backgrounds of the wavelet transform could be found in (Daubechies, 1992; Strichartz, 1994),
comprehensive description of the computerised realisation and source code could be found in (Press, 1992). We
will present only the main ideas related to the practical implementation..


Fig. 1 Wavelet Tree Decomposition

III. PRINCIPLE COMPONENT ANALYSIS
The Principal Component Analysis (PCA) is one of the most successful techniques that have been used in image
recognition and compression. PCA is a statistical method under the broad title of factor analysis. The purpose
of PCA is to reduce the large dimensionality of the data space (observed variables) to the smaller intrinsic
dimensionality of feature space (independent variables), which are needed to describe the data economically.
This is the case when there is a strong correlation between observed variables.
The jobs which PCA can do are prediction, redundancy removal, feature extraction, data compression, etc.
Because PCA is a classical technique which can do something in the linear domain, applications having linear
models are suitable, such as signal processing, image processing, system and control theory, communications,
etc. Face recognition has many applicable areas. Moreover, it can be categorized into face identication, face
classication, or sex determination. The most useful applications contain crowd surveillance, video content
indexing, personal identication (ex. drivers licence), mug shots matching, entrance security, etc. The main
idea of using PCA for face recognition is to express the large 1-D vector of pixels constructed from 2-D facial
image into the compact principal components of the feature space. This can be called eigen-space projection.
Eigen-space is calculated by identifying the eigenvectors of the covariance matrix derived from a set of facial
images(vectors).
A 2-D facial image can be represented as 1-D vector by concatenating each row (or column) into a long
thin vector. Lets suppose we have M vectors of size N (= rows of image columns of image) representing a
set of sampled images. p j s represent the pixel values

x
i
= [p
1
. . .p
N
]
T
, i =1........M

The images are mean centered by subtracting the mean image from each image vector. Let m represent
the mean image.
M
m = 1/M x
i

i=1
The eigenvectors corresponding to nonzero eigenvalues of the covariance matrix produce an
orthonormal basis for the subspace within which most image data can be represented with a small amount of
error. The eigenvectors are sorted from high to low according to their corresponding eigenvalues. The
eigenvector associated with the largest eigenvalue is one that reects the greatest variance in the image. That is,
the smallest eigenvalue is associated with the eigenvector that nds the least variance. They decrease in
exponential fashion, meaning that the roughly 90% of the total variance is contained in the rst 5% to 10% of
the dimensions [7].

A Face Recognition Scheme Based On Principle Component Analysis and Wavelet Decomposition
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Once the eigen faces have been computed, several types of decision can be made depending on the application.
What we call face recognition is a broad term which may be further specied to one of following tasks:
Identication where the labels of individuals must be obtained,
Recognition of a person, where it must be decided if the individual has already been seen,
Categorization where the face must be assigned to a certain class.
PCA computes the basis of a space which is represented by its training vectors. These basis vectors, actually
eigenvectors, computed by PCA are in the direction of the largest variance of the training vectors. As it has
been said earlier, we call them eigen faces. Each eigen face can be viewed a feature. When a particular face is
projected onto the face space, its vector into the face space describe the importance of each of those features in
the face. The face is expressed in the face space by its eigenface coecients (or weights). We can handle a
large input vector, facial image, only by taking its small weight vector in the face space. This means that we can
reconstruct the original face with some error, since the dimensionality of the image space is much larger than
that of face space.

IV. METHODOLOGY ADOPTED


Fig. 2 Flow Chart of the Methodology Adopted

V. RESULT AND DISCUSSION
Fig 3. Generated during the execution of the code for following method, the given image is a snapshot
which shows us the first step to select the training database path.


Fig 3. GUI of selecting Training DataBase

A Face Recognition Scheme Based On Principle Component Analysis and Wavelet Decomposition
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Fig 4. is generated during the second step, that is after selecting the training path, it popup a window to
select the test database path.


Fig. 4 GUI of selecting Testing DataBase

In the database images has been saved by numbers 1,2,3 etc. so fig 5 is the snapshot which ask the user
to select the particular number of image for which user want to perform face recognition. The given fig shows
that user selected image number 5.


Fig. 5 Selecting a Test Image

Fig.6 shows the test image according to the number given by the user.

Fig. 6 Test Image



A Face Recognition Scheme Based On Principle Component Analysis and Wavelet Decomposition
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In the Fig.7 the equivalent image matched with the test image selected by the user is showed.

Fig .7 Equivalent Image

150 face images of 50 person have been taken for the performance analysis of algorithm developed,
each image is different from the images of same person in terms of the face expression, few of them has been
shown here below.


Fig.8 database of test images

VI. CONCLUSION
The proposed face recognition system based on wavelet and PCA has been introduced and evaluated.
The simulation work has been carried out on MATLAB 7.8.1. The result of the method adopted found to be
better than the previous one.

REFERENCES
[1] Xiaoyang Tana, Songcan Chena, Zhi-Hua Zhou, Fuyan Zhang, 2006. "Face recognition from a single image per person: A survey,
Pattern Recognition", Vol. 39, 2006, pp. 1725 1745.
[2] Mohamed Rizon, Muhammad Firdaus Hashim, Puteh Saad, Sazali Yaacob, Mohd Rozailan Mamat, Ali Yeon Md Shakaff,
Abdul Rahman Saad, Hazri Desa and M. Karthigayan, 2006. "Face Recognition using Eigenfaces and Neural Networks",
American Journal of Applied Sciences, Vol. 2, No. 6, 2006, pp. 1872-1875.
[3] R. Sanjeev Kunte,R. D. Sudhaker Samuel, 2007. "Wavelet Descriptors For Recognition Of Basic Symbols In Printed
Kannada Text", International Journal of Wavelets, Multiresolution and Information Processing, Vol. 5, No. 2, 2007, pp. 351
367.
[4] S. T. Gandhe, K. T. Talele, and A.G.Keskar, 2008, "Face Recognition Using Contour Matching", IAENG International
Journal of Computer Science, Vol. 35, No. 2, 2008.
[5] M. Almas Anjum, M. Younus Javed, and A. Basit, 2006, "A New Approach to Face Recognition Using Dual Dimension
Reduction", International Journal of Signal Processing Vol. 2, No.1, 2006, pp1-6.
[6] Z. Zhang, M. Lyons, M. Schuster, S. Akamatsu. Comparison between geometry-based and Gabor-wavelets-based facial
expression recognition using multi-layer perceptron. 3rd. International Conference on Face & Gesture Recognition, pp.454
[7] J. R. Beveridge, K. Baek, B. A. Draper, K. She. PCA vs. ICA: a comparison on the FERET data set. Proceedings of the
International Conference on Computer Vision, Pattern Recognition and Image Processing, Durham, NC, March, 2002