Journal of Intelligent Learning Systems and Applications, 2012, 4, 266-273
http://dx.doi.org/10.4236/jilsa.2012.44027 Published Online November 2012 (http://www.SciRP.org/journal/jilsa)
Face Representation Using Combined Method of Gabor
Filters, Wavelet Transformation and DCV and Recognition
Using RBF
Kathirvalavakumar Thangairulappan1*, Jebakumari Beulah Vasanthi Jeyasingh2
1Department of Computer Science, VHNSN College, Virudhunagar, India; 2Department of Computer Applications, ANJA College,
Sivakasi, India.
Received April 27th, 2012; revised July 19th, 2012; accepted July 26th, 2012
ABSTRACT
An efficient face representation is a vital step for a successful face recognition system. Gabor features are known to be
effective for face recognition. The Gabor features extracted by Gabor filters have large dimensionality. The feature of
wavelet transformation is feature reduction. Hence, the large dimensional Gabor features are reduced by wavelet trans-
formation. The discriminative common vectors are obtained using the within-class scatter matrix method to get a feature
representation of face images with enhanced discrimination and are classified using radial basis function network. The
proposed system is validated using three face databases such as ORL, The Japanese Female Facial Expression (JAFFE)
and Essex Face database. Experimental results show that the proposed method reduces the number of features, mini-
mizes the computational complexity and yielded the better recognition rates.
Keywords: Feature Extraction; Gabor Wavelet; Wavelet Transformation; Discriminative Common Vector; Radial
Basis Function Neural Network
1. Introduction
Face recognition is one of the most dynamic research
areas in the study of pattern recognition and computer
vision. A good face recognition methodology should con-
sider representation as well as classification issues [1]. In
the literature of face recognition, there are various face
representation methods based on global features, includ-
ing a great number of subspace-based methods and some
spatial-frequency techniques. Subspace-based methods,
such as principal component analysis (PCA) [2], Fisher’s
linear discriminant (FLD) [3] and independent compo-
nent analysis (ICA) [4], have been widely recognized as
the dominant and successful face representation methods.
The characteristics of the Gabor wavelets, especially
for frequency and orientation representations, are similar
to those of the human visual system, and they have been
found to be appropriate for texture representation and
discrimination. Yi-Chun Lee and Chin-Hsing Chen [5]
have proposed feature extraction for face recognition
based on Gabor filters and two-dimensional locality pre-
serving projections. Gabor wavelets have been success-
fully and widely applied to face recognition [6,7], face
detection [8], texture segmentation [9], handwritten nu-
merals recognition [10] and fingerprint recognition [11].
Chengjun Liu and Harry Wechsler [1] have applied the
Enhanced Fisher linear discriminant Model (EFM) to an
augmented Gabor feature vector derived from the Gabor
wavelet representation of face images to obtain a low-
dimensional feature representation with enhanced dis-
crimination power. In the Independent Gabor Features
(IGF) method, they have first derived a Gabor feature
vector from a set of down sampled Gabor wavelet repre-
sentation of face images, then reduce the dimensionality
of the vector by means of Principal Component Analysis
(PCA), and finally defined the independent Gabor fea-
tures based on the Independent Component Analysis [12].
Arindam Kar et al. [13] have presented a technique by
which high intensity feature vectors extracted from the
Gabor wavelet transformation of frontal face images, is
combined together with Independent Component Analy-
sis (ICA) for enhanced face recognition. Shen et al. [14]
have presented a frame work based on a combination of
Gabor wavelets and General Discriminant Analysis for
face identification and verification. Wing-Pong Choi et
al. [15] have proposed a simplified version of Gabor
wavelets (SGWs) and an efficient algorithm for extract-
ing the features based on an integral image.
*Corresponding author.

Face Representation Using Combined Method of Gabor Filters, Wavelet Transformation and DCV
and Recognition Using RBF
267
Cevikalp et al. [16] have proposed a face recognition
method called the Discriminative Common Vector (D-
CV), in which within-class scatter matrix of the sample is
used to obtain the discriminative common vectors. Am-
ong the so many popular methods for face recognition,
the wavelet transform is used almost as widely as the
subspace method [17]. Its ability to capture localized
time-frequency information of image motivates its use
for feature extraction. An approach based on a combina-
tion of the discrete wavelet transform and the Gabor filter,
is implemented in a breast cancer screening system. The
two-dimensional discrete wavelet transform is employed
to process the mammogram and obtain its HH high fre-
quency sub-band image. Then, a Gabor filter bank is ap-
plied to the latter at different frequencies and spatial ori-
entations to obtain new Gabor images [18].
Neural networks have been widely used for classifica-
tion and recognition tasks. Radial Basis Function Neural
Network is a special type of artificial neural network
suitable for classification, time-series forecasting and so
on. The mostly adopted network topology is radial basis
function neural network (RBFNN) due to a number of
advantages compared with other types of ANNs, such as
better prediction capabilities, simpler network structures,
and faster learning process [19]. A novel face recognition
approach based on kernel discriminative common vectors
(KDCV) and RBF network is proposed [20]. In this,
kernel DCV (KDCV) algorithm is employed to generate
DCV and is used as the hidden-layer units of the RBF
network for recognizing the patterns. Balasubramanian et
al. [21] have presented a method for automatic real time
face and mouth in video sequences recognition using
radial basis function neural networks (RBFNN).
In this paper, a face recognition system using the com-
bination of Gabor filter, wavelet transformation and
DCV has been proposed for feature extraction and then
radial basis function is used to recognize the extracted
features. The rest of the paper is structured as follows:
the next section describes feature extraction using Gabor
wavelet, wavelet transformation and the discriminative
common vector method. Section 3 presents the proposed
recognition process using radial basis function network.
Section 4 describes the data set and experiment results
along with discussions.
2. Feature Extraction
Feature extraction, in the sense of linear or nonlinear
transform of the data with subsequent feature selection is
commonly used for reducing the dimensionality of the
patterns. In the proposed work, Gabor filters and the
wavelet transformation are applied on the input patterns
to extract the important features and reduce the dimen-
sion and then discriminative common vectors are ob-
tained using within-class scatter matrix.
2.1. Gabor Wavelet Representation of Faces
In this work, Gabor features are used to represent the
face images. Gabor filters are defined as follows. In the
spatial domain, a 2D Gabor filter is a Gaussian kernel
function modulated by a sinusoidal plane wave [22,23] is
as follows:



 

,,,
2
22 22
,
expexp 2π,
π
cos sin
sin cos
fxy
f

x
yjf
xx y
yx y







x




 
(1)
where
f
is the central frequency of the sinusoidal
plane wave,

is the anti-clockwise rotation of the
Gaussian and the plane wave,

is the sharpness of the
Gaussian along the major axis parallel to the wave, and

is the sharpness of the Gaussian minor axis perpen-
dicular to the wave.
f



and
f


 are defined to
keep the ratio between frequency and sharpness constant.
To extract features from a face image, a set of Gabor
filters with different frequencies and orientations are re-
quired as,


,max ,,,,,2, π
8
u
uvuv
f
v
xy ff

 


0, ,1,0, ,1uUvV

 
where max
f
highest peak frequency, U and V are the
number of scales and orientations respectively. An image
can be represented by the Gabor wavelet transform with
the description of both the spatial frequency structure and
spatial relations. The number of Gabor filters to use is the
first issue to deal with for feature extraction from images.
This depends on the application. Normally 40 filters such
as 5 scales and 8 orientations as shown in Figure 1 are
used for face recognition. In this work, Gabor filters de-
signed with 5 scales and 8 orientations are used for fea-
ture extraction.
Image features can be extracted by convolving the in-
put image with Gabor filters. The Gabor representation
of a face image


Ix can be obtained by convolving
the image with the Gabor filters as defined by





,,
*
uv uv
GI  xx (2)
where


,uv
Gxdenotes the convolution result corre-
sponding to the Gabor filter at orientation u and scale v.
As a result, image


Ixcan be represented by a set of
Gabor wavelet coefficients

Face Representation Using Combined Method of Gabor Filters, Wavelet Transformation and DCV
and Recognition Using RBF
268

,uv
Gx,. Convolving the input
image with the 40 Gabor filters with 5 different scales
and 8 orientations results in the Gabor feature set. An
input face image and the Gabor feature representations
are shown in the Figure 2.
0, ,4;0, ,7uv
2.2. Wavelet Transform
Wavelet transformation results in strong representations
with regard to lighting changes and be capable of cap-
turing substantial facial features. A wavelet transform is
created by passing the image through a series of filter
bank stages. The filtered outputs are then down sampled
by a factor of 2 in the horizontal direction. Each of these
signals is then filtered by an identical filter pair in the
vertical direction. The decomposition of the image into 4
Figure 1. Gabor filters for 5 scales and 8 orientations.
Figure 2. An input face image and the Gabor feature rep-
resentation.
subbands is denoted by LL, HL, LH, and HH. Each of
these subbands can be thought of as a smaller version of
the image representing different image properties.
2.3. Discriminative Common Vector
In order to obtain a low-dimensional feature representa-
tion with enhanced discrimination power it is proposed to
construct discriminant features from the Gabor and wa-
velet coefficients using within-class scatter matrix me-
thod. A common vector for each individual class is ob-
tained by removing all the features that are in the direc-
tion of the eigenvectors corresponding to the nonzero
eigen values of within-class scatter matrix of all classes.
The new set of vectors, called the discriminative com-
mon vectors, is used for recognition.
Let the training set be composed of C classes, where
each class contains N samples. Let i
m
x
denotes the
sample from the class. Within-class scatter matrix of
the samples is constructed to obtain the feature vectors,
which is defined as
thm
thi
T
w
SAA (3)
where the matrix A is given by
112
1111 2
,, , ,,
C
NN
Axxxx C



 



(4)
where
j
i
x
is the i-th sample of the class j and μj is the
mean of samples in the jth class.
Let us define


1r
Q

 
S
, which is the set of or-
thonormal eigenvectors corresponding to the non-null
eigenvalues of w and r is the dimension of w. The
projection matrix can be expressed as
S
PQQ. Next
choose an input sample and project it on the null space of
in order to get the common vectors, defined as:
w
S
com
ii
m
i
m
x
xQQx (5)
where 1mN

 samples and classes. Cal-
culate the principal components of com (the eigen-vec-
tors k), which correspond to the non zero eigen-values
as defined as:
1i
S
C
w


T
opt com
arg max
w
J
WWS

 W


(6)
where is computed as
com
S
T
comcom com
SAA (7)
where com
A
is given by
1
comcom comcom com
C
Ax x 


 


 (8)
The Feature Vector of Training set is calculated as
Ti
i
Wx m (9)
Similarly, to recognize a test imagetest
x
, the feature

Face Representation Using Combined Method of Gabor Filters, Wavelet Transformation and DCV
and Recognition Using RBF
269
is given as follows.
vector of this test image is found by
Step 1. Generate random number to initialize the wei-
ghts of the RBF network.
T
test test
Wx (10)
Step 2. Enter the coefficients obtained from DCV. The above method is summarized as follows:
 Compute the nonzero eigenvalues and corresponding
eigenvectors of w S using the matrixT
A
A, where A
is computed using Equation (4).
Step 3. For each input pattern compute hidden layer
output using the Equation (12).
Step 4. Compute the output layer output using the
Equation (13).
 Choose an input sample from each class and project it
onto the null space of w S to obtain the common vec-
tors. Compute iStep 5. Find the error as the difference between de-
sired and actual output obtained.
com
x
using Equation (5).
 Compute the eigenvectors k wof com S, corresponding
to the nonzero eigenvalues, by using the Equations (6)
and (7).
Step 6. Adjust the hidden layer weights according to
Equation (14).
Step 7. Find output of the output layer.
 The feature vector for training set and test set is ob-
tained using Equations (9) and (10) respectively. Step 8. Compute sum of squared error of the network.
Step 9. Repeat steps 3-8 for all input patterns.
Step 10. Repeat steps 3-9 until the acceptable mini-
mum error level is reached.
3. Recognition by Radial Basis Function
Neural Network The proposed work is shown in Figure 3. The Entire
work is summarized as follows.
Radial Basis Function neural network (RBF) considered
for recognition contains three layers: input, hidden and
output. The number of nodes in the input layer corre-
sponds to the dimension of extracted feature vector. The
input neurons are normalized using the Equation (11),
where i
x
is the input vector. The normalized input
values are fed to each of the neurons in the hidden layer.
The basis function of the hidden layer neurons are con-
sidered to be Gaussian and the computed basis function
output are passed to the output layer.
thi
 For each training set face images, perform steps 2-5,
 Compute the Gabor filters using the Equation (1).
 Find the Gabor representation of the face images by
convolving the input face image and the Gabor filters
using the Equation (2).
 Reduce the dimension of the Gabor features by ap-
plying the wavelet transformation.
 Compute the DCV Coefficients for the computed
wavelet coefficients of step 4 using the within class
scatter matrix method.
The hidden layer output is computed as
 Train the RBF network for recognizing DCV coeffi-
cients using the algorithm in Section 3.1.

2
2
exp
j
x
X












(12)
 Repeat the steps 2-5 for the test set face images.
 Classify the DCV coefficients of test image using the
trained RBF network.
where

12
T
,,,
n
X
xx x is the normalized input vec-
tor,

is the center and

is the width.
The output layer output is computed as 4. Results and Discussions

1
k
ijij
j
ywX 

 (13) The proposed system is tested using the face databases
such as ORL, The Japanese Female Facial Expression
(JAFFE) and Essex Face database.
where is the number of hidden neurons,
k
j
i are the
weights connecting the hidden layer neuron j and output
layer neuron i. The weights are adjusted using the for-
mula,
w
The ORL face data base contains 40 faces and each
face has 10 different facial views representing various
expressions, small occlusion by glasses, different scale
and orientations. Hence, there are 400 face images in the
database and each 100 images of 20 persons are used for
training and another 100 images of the 20 persons are
used for testing. The resolution of all the images is 112 ×
92.




1ijj wtwtd yX     (14)
where

is a positive learning rate parameter.
3.1. Algorithm
Gabor wavelet representations such as the real part and The training algorithm of Radial Basis Function Network
 


 


2min*unitvec maxminunitvec
ii ii i
xx xxx (11)

Face Representation Using Combined Method of Gabor Filters, Wavelet Transformation and DCV
and Recognition Using RBF
270
Feature Extraction
Gabor Wavelet
Wavelet Transform
Discriminative Common Vector
Recognition by RBF
Extracted Features
Input Image
Figure 3. Proposed recognition system.
Figure 4. Real part of Gabor wavelet representation.
Figure 5. Magnitude part of Gabor wavelet representation.
the magnitude part of a sample image are shown in Fig-
ures 4 and 5 respectively. Different wavelets namely
Haar, Symlet, Daubechies and Coiflets are used during
wavelet transformation. The original, resultant large di-
mensional Gabor images and the reduced gabor images
after applying wavelet transformation along with their
sizes are shown in Figures 6(a)-(c). The recognition
rates along with training time and epoch obtained for
different wavelets are shown in Table 1 . The recognition
rates for different wavelets namely Haar, Sym4, Sym8,
Db4, Db6, Coif2, Coif4 are 98.7%, 97.0%, 96.67%,
97.33%, 96.33%, 97.00% and 96.37% respectively.
The Japanese Female Facial Expression contains 213
images of 7 facial expressions (6 basic facial expressions
+ 1 neutral) posed by 10 Japanese female models. Each
image has been rated on 6 emotion adjectives by 60
Japanese subjects. The actual dimension of the image is
256 × 256. The epoch, training time and recognition rate
obtained for JAFFE Database are listed in Table 2. The
highest recognition rate is 98.88% for Haar wavelet and
96.7% for Sym8. Lowest training time 18.01 seconds is
used when Sym8 wavelet is applied.
The Essex Face database is having faces of more than
(a)
(b)
(c)
Figure 6. (a) Original image with size 112 × 92; (b) Gabor
face representation with size 112 × 92; (c) Gabor + Wavelet
representation with size 28 × 23.
Table 1. Results of ORL Database.
Wavelet
Name Recognition Rate (%) Training Time in Seconds Epoch
Haar 98.7 9.28 324
Sym4 97.0 9.6 363
Sym8 96.67 10.12 352
Db4 97.33 9.79 339
Db6 96.33 10.38 361
Coif2 97.00 10.48 337
Coif4 96.37 11.97 348

Face Representation Using Combined Method of Gabor Filters, Wavelet Transformation and DCV
and Recognition Using RBF
271
150 male and female with 20 images per individual of
University of Essex, UK. The various results obtained on
Essex face database are presented in Table 3.
Two more feature extraction methods are carried out
in this work for comparative purpose. In the first method,
the features are extracted using the wavelet transforma-
tion and DCV. In the second method, the Gabor repre-
sentation for the face obtained are averaged then applied
to wavelet transformation and then to DCV method.
These two methods are tested on the ORL, JAFFE and
Essex face databases using different types of wavelets
and the results are shown in Table 4.
When comparing the previous works, the performance
of the proposed work is better than the other methods.
The recognition rate of hybrid method of wavelet, DCV
and RBF (WDR) is 97.3% for ORL dataset, where as the
wavelet face along with Neural Network yields the rec-
ognition rate of 93.5%. After combining the Gabor fea-
ture extraction with the WDR, the proposed method Ga-
bor, wavelet, DCV and RBF (GWDR) is yielded the im-
proved recognition rate as 98.7% for ORL, 98.88% for
JAFFE and 98.33% for ESSEX database.
The recognition rates of these methods are less when
compared with the proposed method which is a hybrid of
Gabor, wavelet transformation and DCV method. When
comparing these two methods, wavelet and DCV based
feature extraction yields better results than the hybrid
Table 2. Results of JAFFE database.
Wavelet
Name Recognition Rate (%) Training Time in Seconds Epoch
Haar 98.88 19.44 380
Sym4 98.7 18.22 344
Sym8 96.7 18.01 334
Db4 98 18.54 349
Db6 97.33 19.02 353
Coif2 98 19.31 359
Coif4 97.7 18.52 339
Table 3. Results of ESSEX database.
Wavelet
Name Recognition Rate (%) Training Time in Seconds Epoch
Haar 98.33 19.44 380
Sym4 98.4 18.22 324
Sym8 96.7 18.01 311
Db4 98.33 18.54 349
Db6 97 19.02 353
Coif2 98.11 19.31 364
Coif4 97.33 18.5 337
method of averaged Gabor, wavelet transformation and
DCV. The recognition rate obtained using the three face
databases on applying other methods are shown in Table
5. The recognition rates of the ORL, JAFFE and Essex
Table 4. Recognition rates.
Wavelet + DCV + RBF Averaged Gabor + Wavelet
+ DCV + RBF
Recognition Rate (%) Recognition Rate (%)
Wavelet
Name
ORLJAFFEESSEX ORL JAFFEESSEX
Haar 97.397.3 96.8 96.33 90.3391.33
Sym4 96.797 95 96 90 91
Sym8 95.095.7 95.4 96 90 89
Db4 96.096.7 95.33 94.33 89.3392
Db6 95.496.4 94.0 94.0 88 90.37
Coif2 96.1796 95.0 96.0 88.492
Coif4 95.0 95.3 94.67 96.33 89.192.7
Table 5. Comparison of recognition rates.
Method NameOR LMethod
Name JAFFE Method Name Essex
Eigen Faces 89.5%LDA + SVM 91.27% Wavelet +
HMM 84.2%
Direct LDA 90.8%MLA + NN 91.14 DWT + PCA86.1%
Eigen Faces +
NN 91.2%SVM 91.6% PZM 88.02%
Wavelet Face +
NN 93.5%Adaboost 92.4% Gabor + SHMM 88.7%
SOM + CN 96.5%PCA + SVM 93.43% DM 91.72%
HMM 97%MLA + NM 97% Fisher faces92.62%
Wavelet + DCV
+ RBF 97.3% Wavelet + DCV + RBF 97.3% Wavelet + DCV + RBF96.8%
Gabor +
Wavelet +DCV
+ RBF 98.7% Gabor +
Wavelet +
DCV + RBF 98.88% Gabor+
Wavelet +
DCV + RBF98.33%
95
95.5
96
96.5
97
97.5
98
98.5
99
99.5
HaarSym4Sym8Db4 Db6 Coif2Coif4
Wavelet Name
Recognition Rate in %
OR
L
JAFFE ESSEX
Figure 7. Comparison of recognition rates of three data-
bases for different wavele ts.

Face Representation Using Combined Method of Gabor Filters, Wavelet Transformation and DCV
and Recognition Using RBF
272
face databases for different types of wavelets are shown
in Figure 7.
5. Conclusion
The performance of a face recognition system depends
not only on the classifier, but also on the face representa-
tion. A face recognition system is devised with effective
face representation by the combined approach of Gabor
filter, wavelet transformation and discriminative com-
mon vectors and recognition by radial basis function
(RBF) neural network. The proposed system reduces the
number of features, minimizes the computational com-
plexity and yielded the better recofgnition rates for ORL
database, JAFFE face database and ESSEX database.
The recognition performance of the classification is im-
proved due to the hybrid technique used in the feature
extraction stage which provides necessary information
for classification.
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