LETTERS
International Journal of Recent Trends in Engineering, Vol 2, No. 2, November 2009
51
Face Recognition based on TwoDimensional
PCA on Wavelet Subband
Kishor S Kinage
1
and S. G. Bhirud
2
1
D J Sanghvi College of Engineering /Electronics & Telecomm. Department, Mumbai, India
Email: kskinage@gmail.com
2
VJTI/Computer Engineering Department, Mumbai, India
Email: sgbhirud@yahoo.com
Abstract—In this paper a new face recognition technique
based on TwoDimensional Principal Component Analysis
(2DPCA) on Wavelet Subband is proposed. We extract
image features of facial images from various wavelet
transforms (Haar, Daubechies, Coiflet, Symlet, Biothogonal
and Reverse Biorthogonal) by decomposing face image in
subbands 1 to 8. These features are analyzed by 2DPCA and
Euclidean distance measure. A series of experiments based
on ORL database were then performed to evaluate the
performance. The results show that for the entire wavelets,
subband 3 give the best accuracy and is computationally
most efficient. 7th order Symlet is found to be the best
among all.
Index Terms—PCA, 2DPCA, wavelet, face recognition
I.
I
NTRODUCTION
In recent years, face recognition has received more and
more attention due to its benefit of being a passive, non
intrusive system to verify personal identity in a natural
and friendly way. It has many potential application areas
ranging from access control, mug shots searching,
security monitoring, and surveillance systems. Face
recognition is among the most challenging tasks in
pattern recognition research due to its scientific
challenges and potential applications.
There have been a lot of methods proposed for
overcoming the difficulty of face recognition[1]. Methods
of face recognition can be divided into two approaches
namely, feature geometry based and subspace analysis
techniques. In feature geometry based approach,
recognition is based on the relationship between human
facial features such as eye(s), mouth, nose and face
boundary. Subspace analysis approach attempts to
capture and define the face as a whole. The face is treated
as a twodimensional pattern of intensity variation. The
original image representation is highly redundant, and the
dimensionality of this representation could be greatly
reduced when only the face pattern is of interest.
The most popular among the techniques used for
frontal face recognition/verification are the subspace
methods. The classification is usually performed
according to a simple distance measure in the
multidimensional space. PCA[2][3][4], ICA[5], and
LDA[6] are wellknown approaches to face recognition
that use feature subspaces. PCA based methods suffer
from two limitations, namely, poor discriminatory power
and large computational load. Recently, Yang et al.[7]
proposed 2DPCA for face recognition. Unlike Eigenface
and Fisherface, 2DPCA is based on 2D image matrices
rather than 1D vectors so as the image matrix does not
need to be transformed into a vector prior feature
extraction. 2DPCA is easier to evaluate and less time is
required to determine the corresponding eigenvectors.
In view of the limitations in existing PCA based
approach, this paper proposes new face recognition
technique based on 2DPCA on Wavelet Subband. We
extract image features of facial images from various
wavelet transforms (Haar, Daubechies, Coiflet, Symlet,
Biothogonal and Reverse Biorthogonal) by decomposing
face image in subbands 1 to 8. These features are
analyzed by 2DPCA and Euclidean distance measure. A
series of experiments based on ORL database[8] were
then performed to evaluate the performance. The
recognition rates and processing time are compared
among various wavelet filters in 8 subbands. The results
show that for all the wavelets subband 2 and 3 give the
best accuracy and are computationally most efficient. 7th
order Symlet is found to be the best among all.
The remainder of the paper is organized as follows:
next section describes wavelet transformation and the
filters. Section III describes the concept of PCA and
2DPCA. A face recognition system based on the
proposed method is discussed in section IV. Experimental
results are presented in section V. Finally, conclusions
are given in section VI.
II.
W
AVELET
T
RANSFORM
Wavelet Transform is a popular tool in image
processing and computer vision, because of its ability to
capture localized timefrequency information of image
extraction. The decomposition of the data into different
frequency ranges allows us to isolate the frequency
components introduced by intrinsic deformations due to
expression or extrinsic factors (like illumination) into
certain subbands. Waveletbased methods prune away
these variable subbands, and focus on the subbands that
contain the most relevant information to better represent
the data[9].
1D Continuous Wavelet Transform (CWT) can be
defined as follows:
( )
∫
∞
∞−
= ttf
s
sCWT
s τ
ψτ
,
)(
1
),(
(1)
( )
⎟
⎠
⎞
⎜
⎝
⎛
−
= dt
s
t
s
t
s
τ
ψ
τ
1
,
is basis function.
© 2009 ACADEMY PUBLISHER
LETTERS
International Journal of Recent Trends in Engineering, Vol 2, No. 2, November 2009
52
(a) (b)
Figure 1. (a) Two level 2D DWT on an image, (b) Three level 2D
DWT on an image.
( )
t
ψ
is called mother wavelet. The parameters
s
and
τ
, are the scaling and shift parameter, respectively.
DWT is a sampled version CWT. Two Dimensional
Discrete Wavelet Transform for
nm×
image is
defined as follows:
∫
∞
∞−
⎟
⎠
⎞
⎜
⎝
⎛
−= dxk
x
xfkjDWT
j
2
)(
2
1
),( ψ
(2)
where
j
is the power of binay scaling and
k
is a
constant of the filter.
The 2D DWT is computed by successive lowpass and
highpass filtering of the image. By applying 2D DWT on
an image, the image is decomposed into four subbands
LL, LH, HL, HH subbands, corresponding to
approximate, horiozontal, vertical, and diagional features
respectively. The subband denoted by LL is
approximately at half the original image. While the
subbands HL and LH contain the changes of images or
edges along vertical and horizontal direstions,
respectively. The subband HH contains the detail in the
high frequency of the image. Figure 1 shows various
subbands in 2level and three level decomposition of
wavelet. Figure 2 shows wavelet decomposition for
images in the database at level 2. Decomposed face
images in database at subband LL2 and LL3 are shown in
figure 3 and figure 4 respectively.
Figure 2. Wavelet decomposition at level 2
Figure 3. Decomposed face images at subband LL2. (size 30X25)
Figure 4. Decomposed face images at subband LL3.(16X14)
III.
PCA
AND
2D
PCA
Principal Component Analysis (PCA) has been proven
to be an effective facebased approach. Sirovich and
Kirby[3] first proposed using KarhunenLoeve(KL)
transform to represent human faces. In their method,
faces are represented by a linear combination of weighted
eigenvector, known as eigenfaces. Turk and Pentland[2]
developed a face recognition system using PCA.
However, PCAbased methods suffer from two
limitations, namely, poor discriminatory power and large
computational load. In PCA the 2D image information
must be previously transformed into 1D vectors, which
results in high dimensional image space. Because of large
size of image vectors it becomes difficult to compute
covariance matrix of face image increasing the
computational complexity.
Yang et al, proposed a new technique 2DPCA which is
based on 2D image matrices rather than 1D vectors so the
image matrix does not need to be transformed into a
vector prior to feature extraction. Instead, an image
covariance matrix is constructed directly using the
original image matrices and its eigenvectors are derived
for image feature extraction. Let
),.....,2,1( MiI
i
=
denotes the image matrix (
nm
×
)
of the image. The covariance matrix is represented by
( )
( )
∑
=
−−=
M
j
j
T
j
IIII
M
C
1
1
(3)
where
I
denotes the mean of all sample images. It
can be verified that
C
is a nonnegative
nn
×
matrix.
Extract the feature as follows:
CXXXJ
T
=)(
(4)
Then, optimal projection axes are selected by
maximizing the following criterion:
)(maxarg,...,
1
XJXX
d
=
(5)
Where
X
is a unitary column vector, besides, we have
),...,1,(),,(,djijiXX
ji
==δ
(6)
Where,
δ
is a Kronecker’s delta function. The optimal
projection axes,
d
XX,...,
1
, which are also eigenvectors
of the covariance matrix
C
corresponding to the first
d
largest eigenvalues, are orthonormal with each other.
Finally, a
dm
×
feature matrix of the face image is
obtained by projecting it onto the optimized projection
axes:
jiji
XIY
=
,
(7)
Where,
Mi,...,2,1
=
, and
dj,...,2,1=
© 2009 ACADEMY PUBLISHER
LETTERS
International Journal of Recent Trends in Engineering, Vol 2, No. 2, November 2009
53
Figure 5 and Figure 6 show wavelet subband LL2 and
LL3 images projected in 2DPCA subspace.
IV.
T
HE
P
ROPOSED
M
ETHOD
By applying DWT on an image, we gain three benefits
(1) Dimensionality Reduction, which will lead to less
computational complexity, (2) Multiresolution Data
approximation and (3) Insensitive Feature extraction.
In view of the limitations in PCA and 2DPCA we
proposed a face recognition system as shown in Figure 7
[10][11]. For a given set of training face images, feature
vectors of faces are extracted through 2D wavelet at
appropriate LL subband. The reduced image data is then
sent to the 2DPCA process for finding the principal
component and reducing the dimensional space of the
image which is stored into the library. For a given testing
face image, feature vector is extracted through
appropriate 2D wavelet decomposition. The features are
extracted using 2DPCA and faces can be classified by
measuring the Euclidian distance between mean values of
training images in each class and the testing images.
Figure 5. Subband LL2 face images projected in 2DPCA
Figure 6. Subband LL3 face images projected in 2DPCA
Figure 7: Block diagram of the proposed face recognition system.
F
Figure 8. Sample face images from ORL face database.
V.
E
XPERIMENTAL
R
ESULTS
The experiment is performed using ORL face database
from AT&T (Olivetti) Research Laboratories,
Cambridge. The database contains 40 individuals with
each person having ten frontal images. Figure 8 shows
some of the sample face images from this database. There
are variations in facial expressions such as open or closed
eyes, smiling or nonsmiling, and glasses or no glasses.
All images are 8bits grayscale of size 112x92 pixels. We
select 200 samples ( 5 for each individual ) for teaining.
The remaining 200 samples are used as the test set.
In our face recognition experiments, we extract image
features of facial images from 49 wavelet transforms
(Haar, Daubechies, Coiflet, Symlet, Biothogonal and
Reverse Biortogonal) by decomposing face image in LL
subbands at 8 levels(1 to 8). The wavelets used are haar1,
db1 to db10, coif1 to coif5, sym1 to sym10, bio1.1, 1.3,
1.5, 2.2, 2.4,2.6, 3.1, 3.3, 3.5, 4.4, 5.5, 6.8, rbio1.1,
rbio1.5, 2.2, 2.4, 2.6, and 2.8. Table I depicts some
sample results for db4, sym7 and bio1.4 wavelets.
VI.
C
ONCLUSION
We propose a face recognition scheme that combined
wavelet transform and 2DPCA. We compared the
recognition performances of various wavelets at 8 levels,
1 to 8. Accuracy with only 2DPCA is 85% where as the
average accuracy of 2DPCA with wavelet in subbands 2
and 3 is 94.5%. Experimental result shows that our
approach increased the recognition accuracy.
Performance of the system is best in subband 2 and 3,
which is the midfrequency range. 7th order Symlet gives
the highest accuracy, because Symlet is nearly
symmetrical wavelet.
In the future work, we plan to carry out further
experiments with curvelets which is better at handling
curve discontinuities.
TABLE I.
RECOGNITION
ACCURACY
IN
PERCENTAGE
AND
TIME
REQUIRED
FOR
THREE
SAMPLE
WAVELETS,
DB4,
SYM7
AND
BIOR1.3
db4 Sym7 Bio1.3
Lev
el
Rec.
Acc.
Time Rec.
Acc.
Time Rec.
Acc.
Time
1 94.00 7.00 94.50 7.98 94.00 6.87
2 94.50 5.79 95.00 6.92 94.50 5.54
3 94.50 5.64 95.00 6.73 95.00 5.42
4 92.00 5.92 95.00 6.95 93.50 5.50
5 90.00 6.21 87.00 7.39 86.00
6.01
6 85.00 6.71 80.50 7.71 81.50 6.39
7 82.50 7.14 78.00 8.31 77.00 6.48
8 75.50 7.21 76.00 8.75 74.00
6.84
© 2009 ACADEMY PUBLISHER
LETTERS
International Journal of Recent Trends in Engineering, Vol 2, No. 2, November 2009
54
Figure 9: Plot of Level of Decomposition vs Recognition Accuracy.
Figure 10: Plot of Level of Decomposition vs Recognition Time
(Training and testing ) in seconds.
R
EFERENCES
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[2] Matthew Turk and Alex Pentland, “Eigenfaces for
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eigenface approach.
[3] L. Sirovich and M. Kirby, “LowDimensional Procedure
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[4] M. Kirby and L. Sirovich, “Application of the KL
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[8] ORL face databases,
http://www.uk.research.att.com/pub/data/orl_faces.zip
[9] DaoQing Dai and Hong Yan,
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Wavelets and Face
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