Support Vector Machines With Constraints for Sparsity in the Primal Parameters
Face Recognition Using Independent Component Analysis and Support Vector Machines
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Transcript of Face Recognition Using Independent Component Analysis and Support Vector Machines
Face Recognition using Independent Component
Analysis of GaborJet (GaborJet-ICA) Kishor S Kinage
1 and S. G. Bhirud
2
1D J Sanghvi College of Engineering /Electronics & Telecomm. Department, Mumbai, India
Email: [email protected] 2
VJTI/Computer Engineering Department, Mumbai, India
Email: [email protected]
Abstract—In this paper a new face recognition technique
based on Independent Component Analysis of GaborJet
(GaborJet-ICA) is proposed. Existing face recognition
systems using Gabor wavelets convolve a whole face image
with a set of 40 Gabor wavelets. We have derived Gabor
feature vector from facial landmarks (fiducial points)
known as GaborJets. We then transformed this GaborJet
feature vector into the basis space of PCA and ICA. A
series of experiments based on ORL database were then
performed to evaluate the performance. During our
experiments we varied number of subspace dimensions from
2 to 40 and numbers of independent components derived
were in the range 1 to 200. As literature on PCA and ICA
subject is contradictory, we compared the performance for
GaborJet-PCA and GaborJet-ICA. The results show
maximum accuracy of 82.25% and 84.5% for GaborJet-
PCA and GaborJet-ICA respectively. This proves that the
difference in performance between ICA and PCA is of
2.25%, which is insignificant.
Index Terms—PCA, ICA, Gabor, GaborJet, wavelet, face
recognition
I. INTRODUCTION
Face recognition is a challenging problem in pattern
recognition research. 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, subspace analysis
techniques and feature based.
Subspace analysis approach attempts to capture and
define the face as a whole. The face is treated as a two-
dimensional 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
classification is usually performed according to a simple
distance measure in the multidimensional space. PCA[2-
5], ICA[6], and LDA[7] are well-known approaches to
face recognition that use feature subspaces.
PCA is probably the most widely used subspace
projection technique for face recognition. A major
disadvantage of appearance based approaches is that they
are sensitive to lighting variation and expression changes
since they require alignment of uniform-lighted image to
take advantage of the correlation among different images.
An elastic bunch graph matching (EBGM) method
developed by Wiskott et al.[8] alleviate these problems.
The EBGM method utilizes an attributed relational graph
to characterize a face, with facial landmarks (fiducial
points) as graph nodes. Gabor wavelet around each
fiducial point as node attributes and distances between
nodes as edge attributes. Compared to image intensity,
Gabor wavelet is less sensitive to illumination changes.
However, since Gabor wavelet is a general image
processing tool, which is not specifically designed for
face recognition, Gabor features do not contain face
specific information learned from face training data.
Therefore, directly using Gabor features may not be the
best approach.
It is reasonable to use statistical techniques for better
selection of Gabor features in order to integrate the
advantages of Gabor wavelet and the statistical
techniques. A similar approach has been used in [9],
where Gabor feature vector was derived from a set of
downsampled Gabor wavelet representations of face
images. Dimensionality of the vector was reduced by
means of principal component analysis (PCA) and
independent component analysis(ICA).
This paper proposes new face recognition technique
based on Independent Component Analysis of GaborJets
(GaborJet-ICA). Instead of deriving Gabor feature from
a whole face image as used in [9], we have derived Gabor
feature vector from facial landmarks (fiducial points)
known as GaborJets. GaborJets are a collection of
complex Gabor coefficients from the same location in an
image. The coefficients are generated using Gabor
wavelets of a variety of different sizes, orientations, and
frequencies. GaborJets act as feature vectors that
describe the landmark from which the jet was taken. We
then transform this GaborJet feature vector into the basis
space of PCA and ICA. Trained face images are
represented as points in this space. In order to identify,
GaborJet feature vector of test images are also projected
into the basis space of PCA and ICA. Euclidean distance
was used to estimate the similarity. We then compared
the performance in both PCA and ICA. PCA decorrelates
the input data using second-order statistics and thereby
generates compressed data with minimum mean-squared
reprojection error. ICA minimizes both second order and
higher order dependencies in the input. ICA can be
viewed as a generalization of PCA.
The reason for comparing PCA and ICA is that the
literature on the subject is contradictory. For example,
Liu and Wechsler [10], and Bartlett et al. [11,12] claim
that ICA outperforms PCA, while Baek et al. [13] claim
that PCA is better, Moghaddam [14] claims that there is
no statistical difference in the performance between the
2010 6th International Colloquium on Signal Processing & Its Applications (CSPA)
978-1-4244-7120-1/10/$26.00 ©2010 IEEEThis is pre-proceedings only. The final proceedings copy is as listed in IEEExplore.
two. The relative performance of the two is therefore an
open question.
The remainder of the paper is organized as follows:
next section describes feature vectors extraction. Section
III describes the concept subspace projection. 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. FEATURE VECTORS EXTRACTION
A. Gabor Wavelet
Bidimensional Gabor Filters[8], correspond to a
family of bidimensional Gaussian functions modulated by
a cosine function (real part) and a sine function
(imaginary part). These filters are given by a family of
Gabor kernel,
���, �� = ��� ������� ��� ����
� ���
(1)
�� = ����� + ��!"� �� = −��!"� + �����
(2)
Where the arguments, x and y specify the position of a
image.
There are five parameters that control the wavelet
1. θ specifies the orientation of the wavelet. This
parameter rotates the wavelet about its center. This
particular set uses eight different orientations over the
interval 0 to π. Orientations from π to 2π would be
redundant due to the even/odd symmetry of the wavelets
i.e. θϵ &0, �( , ��
( , )�( , *�
( , +�( , ,�
( , -�( .
2. λ specifies wavelength of the cosine wave, or
inversely the frequency of the wavelet. Wavelets with a
large wavelength will respond to gradual changes in
intensity in the image. Wavelets with short wavelengths
will respond to sharp edges and bars.
/014,4√2, 8,8√2, 168
3. ϕ specifies phase of the sine wave. Typically Gabor
wavelets are either even or odd. Convolution with both
phases produces a complex coefficient, i.e. 90 :0, ��;
4. σ specifies radius of the Gaussian. This parameter
is usually proportional to the wavelength, such that
wavelets of different size and frequency are scaled
versions of each other, i.e. σ =_λ
5. γ specifies the aspect ratio of the Gaussian. This
parameter was included such that the wavelets could also
approximate some biological models. The wavelets used
here have circular Gaussian, i.e. γ=1 .
This yields 8 orientations, 5 frequencies, and 2 phases
for a total of 80 different wavelets. Figure 1 shows
family of all 80 Gabor wavelet kernals. This is known as
a wavelet transform because the family of kernels is self-
similar, all kernels being generated from one mother
wavelet by dilation and rotation.
The Gabor wavelet representation captures salient
visual properties such as spatial localization, orientation
selectivity, and spatial frequency. The Gabor wavelets
have been found to be particularly suitable for image
decomposition and representation when the goal is the
derivation of local and discriminating features.
B. GaborJet
Landmarks (fiducial points) are parts of the face that
are easily located and have similar structure across all
faces. In our approach we manually choose 5 landmarks
namely, left eyeball centre, right eyeball center, nose tip
and two mouth corners as shown in figure 5.
A GaborJet representation <��, �, �, /, 9, =, >� at the
chosen landmark is the convolution of image with the
family of Gabor kernals ���, �� obtained around a given
pixel �̅ = (x,y). We have used Gabor kernals of 5 sizes
i.e. (16x16), (22x22), (32x32), (45x45) and (64x64).
During convolution, the size of image around pixel �̅ =
(x,y) i.e. landmark was chosen same as that of Gabor
kernel. In that way, each face image is finally represented
by a large GaborJet feature vector of size 400 combining
5 local vectors @ABC of size 80 each,
DEFGHIJKLC = M@ANC , @A�
C , @AOC , @AP
C , @AQC R. (3)
GaborJet describes the behavior of image around the
chosen landmark. Therefore, the GaborJet will contain a
good description of the local frequency information
around the landmark.
Figure 1. Family of 80 Gabor wavelet kernals with 8 orientations, 5
frequencies, and 2 phases
2010 6th International Colloquium on Signal Processing & Its Applications (CSPA)
978-1-4244-7120-1/10/$26.00 ©2010 IEEEThis is pre-proceedings only. The final proceedings copy is as listed in IEEExplore.
Figure 2. Feature extraction in proposed face recognition system.
Figure 3. Matching phase of proposed face recognition system.
Figure 4. Sample face images from ORL face database.
Figure 5. Location of fiducial points
III. SUBSPACE PROJECTION
A. Principal Component Analysis (PCA)
Principal Component Analysis (PCA) has been proven
to be an effective face-based approach. Sirovich and
Kirby[3] first proposed using Karhunen-Loeve(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, PCA-based methods suffer from two
limitations, namely, poor discriminatory power and large
computational load.
The eigenfaces method of face representation is based
on PCA [4]. It regards each face image as a feature vector
by concatenating the rows or columns of the image
together, using the intensity of each pixel as a single
feature. Thus each image can be represented as an "-
dimensional vector, where " is the number of pixels in
each image. Let 1�S, ��,…, �U8 be a set of V training
images taking values in an "-dimensional image space.
Define the total scatter matrix WC as follows
WC = X��Y − �̅���Y − �̅�CU
YZS
(4)
where V is the number of training images and �̅ is the
mean image of all training images. Consider a linear
transformation mapping the original "-dimensional image
space into an [-dimensional feature space, where
[ << " .
The new m-dimensional feature vectors �] are defined
by
�] = ^C��] − �̅�, (5)
the linear transformation , where ^ = M_S,_�,…,_`R is
the set of "-dimensional eigenvectors of WC corresponding to the [ largest eigenvalues. The _Y are
usually called eigenfaces in face recognition. The
extracted m-dimensional feature vectors, i.e. �] , instead
of the original "-dimensional ones are used in the
subsequent recognition process. We can see that the
dimension of the reduced feature vector m is much less
than the dimension of the input faces vector n. The axis
of large variance probably corresponds to signal, while
axes of small variance are probably noise. Eliminating
these axes therefore improves the accuracy of matching.
C. Independent Component Analysis (ICA)
Independent Component Analysis (ICA)[15] is a
recently developed statistical technique that can be
viewed as an extension of standard PCA. Using ICA, one
tries to model the underlying data so that in the linear
expansion of the data vectors the coefficients are as
independent as possible. ICA bases of the expansion must
be mutually independent while the PCA bases are merely
uncorrelated. ICA has been widely used for blind source
separation and blind convolution. Blind source separation
tries to separate a few independent but unknown source
signals from their linear mixtures without knowing the
mixture coefficients. Let � be the vector of unknown
source signals and � be the vector of observed mixtures.
2010 6th International Colloquium on Signal Processing & Its Applications (CSPA)
978-1-4244-7120-1/10/$26.00 ©2010 IEEEThis is pre-proceedings only. The final proceedings copy is as listed in IEEExplore.
If a is the unknown mixing matrix, then the mixing
model is written as
� = a� (6)
It is assumed that the source signals are independent of
each other and the mixing matrix is invertible. Based on
these assumptions and the observed samples, ICA tries to
find the mixing matrix a or the separating matrix b such
that
_ = b� = ba�, (7)
is an estimation of the independent sources.
Unfortunately, there may not be any matrix b that fully
satisfies the independence condition, and there is no
closed form expression to find b. Instead, there are
several algorithms that iteratively approximate b so as to
indirectly maximize independence. Since FastICA [16]
algorithm claims to yield the highest performance for
identifying faces we considered this algorithm in this
work.
C. Preprocessing for ICA (Centering and Whitening)
Before the application of the ICA algorithm we
transform the observed vector � linearly so that we obtain
a new vector �c which has unit variance:
de�c�cCf = I (8)
The whitening transformation is always possible. One
popular method is to use the eigen-value decomposition
of the covariance matrix de��Cf = dgdC, where d is
the orthogonal matrix of eigenvectors of de��Cf and g is
the diagonal matrix of its eighenvalues, g =h!i��hS, … , hj�. Note that de��Cf can be estimated in a
standard way from the available sample k�1�, . . . , k�m�.
Whitening can now be done by
�c = dgN�dC� = an�,
(9)
The utility of whitening resides in the fact that the new
mixing matrix an is orthogonal.
This can be seen from
de�c�cCf = ande��CfanC = ananC = o (10)
Here we see that whitening reduces the number of
parameters to be estimated from "� to j�jS�
� .
D. The FastICA Algorithm[15]
FastICA is based on a fixed-point iteration scheme for
finding a maximum of the nongaussianity of pC�.
Denote by � the derivative of the nonquadratic function
q; for example the derivatives of the functions G in are:
�S�_� = ri"ℎ�iS_�
�S��_� = _��t�−_�/2�
(11)
The basic form of FastICA algorithm is as follows:
1. Choose an initial (e.g. random) weight vector p.
2. Let p� = de���pC��f − de���pC��fp .
3. Let = vw ||vw|| .
4. If not converged, go back to 2.
Note that converge means that the old and new values
of w point in the same direction.
To estimate several independent components, we need
to run the one-unit FastICA algorithm using several units
with unit vectors pS, … , pj.
To prevent different vectors from converging to the
same maxima we must decorrelate the outputs
pSC�, … , pjC� after every iteration. A simple way of
doing this is a Gram-Schmidt like decorrelation. This
means we estimate the independent components one by
one. When we have estimated t independent components,
or t vectors pS, … , pA, we run the one unit fixed point
algorithm for pA�S, and subtract pA�S from the
“projections” pA�SC pypy, < = 1, . . . , t of the previously
estimated t vectors, and then renormalize pA�S:
1. Let pA�S = pA�S − ∑ pCA�SpyAyZS py
2. Let pA�S = v{wN|v}{wNv{wN
(12)
IV. THE PROPOSED METHOD
Independent Component Analysis (ICA) uses face
image as input data, then it should be aligned well and
should not include some in-plane and in-depth rotation.
The face region should be extracted from the original
image and the brightness and contrast should be stable.
This makes ICA difficult to use in real application. We
tried to overcome these shortcomings by keeping the
basic concept that the most distinctive features act as a
basis axis in the space. The GaborJet feature vector has
useful characteristics. It provides robustness against
varying brightness and contrast in the image. Since the
characteristics of the local face area can be represented, it
is more effective than using the original face image
directly. To overcome the shortcomings mentioned
above, we used GaborJet feature vector as input of ICA.
Let the number of fiducial points that can get the
GaborJet are V, with 80 Gabor kernals we construct the
V × 80 dimensional array. If we use � gallery images, a
� = V × 80 by � matrix could be constructed. Basis
vectors could be calculated from matrix ��C .We then
transform this GaborJet feature vector into the basis space
of PCA and ICA. Dimensionality of GaborJet feature
vector is first reduced by PCA and then Independent
GaborJet features are derived. Trained face images are
represented as points in this space. In order to identify,
GaborJet feature vector of test images are also projected
onto the basis space of PCA and ICA. Euclidean distance
was used to estimate the similarity.
V. EXPERIMENTAL RESULTS
The experiment is performed using ORL face database
from AT&T (Olivetti) Research Laboratories [17],
Cambridge. The database contains 40 individuals with
each person having ten frontal images. Figure 4 shows
some of the sample face images from this database. There
are variations in facial expressions such as open or closed
eyes, smiling or non-smiling, and glasses or no glasses.
All images are 8-bits grayscale of size 112x92 pixels. We
select 200 samples ( 5 for each individual ) for training.
The remaining 200 samples are used as the test set.
We first manually located 5 fiducial points namely, left
eyeball centre, right eyeball center, nose tip and two
mouth corners as shown in figure 5. Geometric
normalization [18,19] was performed on these images.
2010 6th International Colloquium on Signal Processing & Its Applications (CSPA)
978-1-4244-7120-1/10/$26.00 ©2010 IEEEThis is pre-proceedings only. The final proceedings copy is as listed in IEEExplore.
With 5 fiducial points for each face image we made a 400
dimensional GaborJet feature vector using 80 Gabor
wavelet kernals. As the total number of individuals in
database was 40, a large GaborJet feature vector of 40 by
400 matrix was constructed.
We then transform this GaborJet feature vector into the
basis space of PCA and ICA. Trained face images are
represented as points in this space. In order to identify,
GaborJet feature vector of test images are also projected
into the basis space of PCA and ICA. Euclidean distance
was used to estimate the similarity. We compared the
performance with GaborJet-PCA and GaborJet-ICA.
In face recognition experiments of GaborJet-PCA we
evaluated the performance of the system by varying
principal components from 2 to 100. Table I depicts some
of sample results for GaborJet-PCA. Figure 6 shows plot
of number of principal components vs recognition
accuracy. Beyond principal component 40, consistent
accuracy of 82.25% was obtained in case of GaborJet-
PCA.
We experimented then with the GaborJet-ICA.
Dimensionality of GaborJet feature vector was first
reduced using PCA and then Independent GaborJet
features were derived. During our experiments we varied
number of subspace dimensions from 2 to 40 and number
of independent components derived, were in the range 1
to 200. Table 2 depicts some of the sample results and
figure 7 shows plot of number of independent
components vs recognition rate for various values of
subspace dimensions. Corresponding to subspace
dimension of 40 and independent component of beyond
40 a maximum accuracy of 84.5% was obtained for
GaborJet-ICA.
TABLE II. RECOGNITION ACCURACY FOR GABORJET-PCA
Number of
principal
components
Accuracy
in %
5 53.5
10 69
15 75
20 80
25 80.75
30 81
35 81.75
40 82.25
45 to 100 82.25
VI. CONCLUSION
We propose a face recognition scheme that combined
GaborJet features and ICA. Gabor wavelet representation
captures salient visual properties such as spatial
localization, orientation selectivity, and spatial frequency.
PCA/ICA reduces redundancy and represent
decorrelated/independent features explicitly. We
compared the recognition performances of GaborJet-PCA
and GaborJet-ICA for various values of PCA dimensions
and independent components. We found maximum
accuracy of 82.25% and 84.5% for GaborJet-PCA and
GaborJet-ICA respectively. This proves that difference in
performance of 2.25% between ICA and PCA is
insignificant.
In our future work, we plan to carry out further
experiments with curvelets, which is better at handling
curve discontinuities.
TABLE I. RECOGNITION ACCURACY FOR GABORJET-ICA
Recognition accuracy
independent
component
dimension
10
dimension
20
dimension
30
dimension
40
1 10.75 12.25 9.00 11.00
11 69.50 65.00 60.00 58.75
21 69.00 80.50 78.00 77.50
31 69.50 82.50 83.75 82.25
41 68.50 80.50 82.75 84.00
51 68.50 81.00 82.25 83.75
61 68.50 81.00 83.50 83.75
71 67.50 80.50 83.25 84.00
81 68.50 80.50 82.75 83.75
91 66.75 80.00 83.50 83.00
121 68.50 80.00 82.75 83.00
151 68.75 80.25 83.25 84.50
181 67.75 81.25 83.00 84.00
Figure 6: Plot number of principal components vs recognition
accuracy.
Figure 7: Number of independent components vs recognition rate for
various values of subspace dimensions.
2010 6th International Colloquium on Signal Processing & Its Applications (CSPA)
978-1-4244-7120-1/10/$26.00 ©2010 IEEEThis is pre-proceedings only. The final proceedings copy is as listed in IEEExplore.
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2010 6th International Colloquium on Signal Processing & Its Applications (CSPA)
978-1-4244-7120-1/10/$26.00 ©2010 IEEEThis is pre-proceedings only. The final proceedings copy is as listed in IEEExplore.