Independent Component Analysis of Edge Information for Face Recognition

Kailash J.Karande & Sanjay N Talbar
International Journal of Image Processing (IJIP) Volume (3) : Issue (3) 120
Independent Component Analysis of Edge Information
for Face Recognition
Kailash J. Karande kailashkarande@yahoo.co.in
Department of Information Technology,
Sinhgad Institute of Technology, Lonavala,
Dist-Pune, Maharashtra State. (India) 410401.
Sanjay N. Talbar sntalbar@yahoo.com
Department of Electronics & Telecommunication
SGGS Institute of Engineering &Technology, Nanded,
Maharashtra State, India.
Abstract
In this paper we address the problem of face recognition using edge information
as independent components. The edge information is obtained by using
Laplacian of Gaussian (LoG) and Canny edge detection methods then
preprocessing is done by using Principle Component analysis (PCA) before
applying the Independent Component Analysis (ICA) algorithm for training of
images. The independent components obtained by ICA algorithm are used as
feature vectors for classification. The Euclidean distance and Mahalanobis
distance classifiers are used for testing of images. The algorithm is tested on two
different databases of face images for variation in illumination and facial poses
up to 1800rotation angle.
Keywords: Principle Component analysis (PCA), Independent Component Analysis (ICA), Laplacian of
Gaussian ( LoG) and Canny edge detection Euclidean distance classifier, Mahalanobis distance classifier.
1. INTRODUCTION
Face recognition is a task that humans perform routinely and effortlessly in their daily
lives. Wide availability of powerful and low-cost desktop and embedded computing
systems has created an enormous interest in automatic processing of digital images and
videos in a number of applications, including biometric authentication, surveillance,
human-computer interaction, and multimedia management. Research and development
in automatic face recognition follows naturally.
Research in face recognition is motivated not only by the fundamental challenges this
recognition problem poses but also by numerous practical applications where human
identification is needed. Face recognition, as one of the primary biometric technologies,
became more and more important owing to rapid advances in technologies such as
digital cameras, the Internet and mobile devices, and increased demands on security.
Face recognition has several advantages over other biometric technologies: It is natural,
non intrusive, and easy to use. Among the six biometric attributes considered by
Hietmeyer [1], facial features scored the highest compatibility in a Machine Readable
Travel Documents (MRTD) [2] system based on a number of evaluation factors, such as
enrollment, renewal, machine requirements, and public perception.

A face recognition system is expected to identify faces present in images and videos
automatically. It can operate in either or both of two modes: (1) face verification (or
authentication), and (2) face identification (or recognition). Face verification involves a
one-to-one match that compares a query face image against a template face image
whose identity is being claimed. Face identification involves one-to-many matches that
compare a query face image against all the template images in the database to
determine the identity of the query face.
There are two predominant approaches to the face recognition problem: geometric
(feature based) and photometric (view based). As a researcher interest in face
recognition continued and many different methods are proposed, like well studied
methods using Principle Component Analysis (PCA), Linear Discriminant Analysis (LDA)
and Elastic Bunch Graph Matching (EBGM). In order to organize the vast field of face
recognition, several approaches are conceivable. For instance, algorithms treating the
face and its environment as uncontrolled systems could be distinguished from systems
that control the lighting or background of the scene, or the orientation of the face. Or
systems that use one or more still images for the recognition task could be distinguished
from others that base their efforts on video sequences.
The comparison of face recognition using PCA and ICA on FERET database with
different classifiers [3] [4] are discussed and found that the ICA has better recognition
rate as compared with PCA with statistically independent basis images and also with
statistically independent coefficients. Their findings are based on the frontal face image
datasets are encouraging with few face expressions. Marian S Bartlett used version of
ICA [5] derived from the principle of optimal information transfer through sigmoidal
neurons on face images from FERET database has proved that ICA representation gave
the best performance on the frontal face images. Feature selection in the independent
component subspace [6] which gives the benefits for face recognition with changes in
illumination and facial expressions. Fusion of ICA features like Spatial, Temporal and
Localized features [7] [8] for Face Recognition are considered as optimization method.
An independent Gabor features (IGFs) method and its application to face recognition
using ICA [9] is discussed by Chengjun Liu; Wechsler, H. The novelty of the IGF method
comes from 1) the derivation of independent Gabor features in the feature extraction
stage and 2) the development of an IGF features-based probabilistic reasoning model
(PRM) classification method in the pattern recognition stage. In particular, the IGF
method first derives a Gabor feature vector from a set of down sampled Gabor wavelet
representations of face images, then reduces the dimensionality of the vector by means
of principal component analysis, and finally defines the independent Gabor features
based on the independent component analysis (ICA).
The illumination has great influence on how a face image looks. Researchers have
proved that for a face image, the difference caused by illumination changes has even
exceeded the difference caused by identity changes [10]. The big challenge of face
recognition lies in dealing with variations of pose, illumination, and expression. Also there
is need to address the problem of identity changes using structural components.
In this paper we propose the face recognition using Edge information and ICA with large
rotation angles with poses and variation in illumination conditions. Here we used the edge
information of face images using different standard edge detection function operators like
canny, Laplacian of Gaussian (log). The edge information is being used to calculate
independent components for face recognition. We used the database which has the large
rotation angles up to 180
0
change between the images of person while looking right and
or left. We considered the face images having various orientations of the face i.e.: looking
front, looking left, looking right, looking up, looking up towards left, looking up towards
right, looking down. In this study we considered the samples of individual person which

consist of sufficient number of images having expressions, changes in illumination and
large rotation angles. For illumination variation the effects of light on face image from left,
right, top and bottom sides are considered. The paper is organized as follows. In Section
2 we introduce the ICA and information about edge detection in section 3. The section 4
specifies the need of the preprocessing before applying the ICA algorithm. The modified
Fast ICA algorithm is presented in the Section 5 and classifiers are discussed in section
6. Experimental results are discussed in Section 7 and accordingly the conclusions are
drawn in Section 8.
2. Introduction to ICA
ICA will be rigorously defined as a statistical ‘latent variable’ model. Assume that we
observe n linear mixtures x1, ....., xn of n independent components
njnjjj sasasax +++= ......2211 For all j. (1)
we have now dropped the time index t; in the ICA model, we assume that each mixture xj
as well as each independent component sk is a random variable, instead of a proper time
signal. The observed values xj(t), e.g. the microphone signals in the cocktail party
problem, are then a sample of this random variable. Without loss of generality, we can
assume that both the mixture variables and the independent components have zero
mean. If this is not true, then the observable variables xi can always be centered by
subtracting the sample mean, which makes the model zero-mean.
It is convenient to use vector-matrix notation instead of the sums like in the previous
equation. Let us denote by x the random vector whose elements are the mixtures x1, ...,
xn. And likewise by s the random vector with elements s1, ..., sn. Let us denote by A the
matrix with elements aij. Generally, bold lower case letters indicate vectors and bold
upper-case letters denote matrices. All vectors are understood as column vectors; thus x
T
or the transpose of x, is a row vector. Using this vector-matrix notation, the above mixing
model is written as
x =As (2)
Sometimes we need the columns of matrix A; denoting them by aj the model can also be
written as,
x = ∑=
n
i 1
aisi (3)
The statistical model in equation.(2) is called independent component analysis or ICA
model[11]. The ICA model is a generative model which means that it describes how the
observed data are generated by a process of mixing the components si. The independent
components are latent variables, meaning that they cannot be directly observed. Also the
mixing matrix is assumed to be unknown. All we observe is the random vector x, and we
must estimate both A and s using it. This must be done under as general assumptions as
possible.
The starting point for ICA is the very simple assumption that the components si are
statistically independent. It will be seen that we also assume that the independent
component must have nongaussian distributions. However, in the basic model we do not
assume these distributions known (if they are known, the problem is considerably
simplified). For simplicity, we are also assuming that the unknown mixing matrix is
square, but this assumption can be sometimes relaxed. Then, after estimating the matrix
A, we can compute its inverse, say W, and obtain the independent component simply by:
s = Wx. (4)

ICA is very closely related to the method called blind source separation (BSS) or blind
signal separation. A “source” means here an original signal, i.e. independent component,
like the speaker in a cocktail party problem. “Blind” means that we know very little, if
anything, on the mixing matrix, and make little assumptions on the source signals. ICA is
one method perhaps the most widely used, for performing blind source separation.
3. Edge Detection
Edges are boundaries between different textures. Edge also can be defined as
discontinuities in image intensity from one pixel to another. The edges for an image are
always the important characteristics that offer an indication for a higher frequency.
Detection of edges for an image may help for image segmentation, data compression, and
also help for well matching, such as image reconstruction and so on.
Laplacian of a Gaussian (LoG) Detector: Consider the Gaussian function
2
2
2
)( σ
r
erh
−
−= (5)
where r
2
=x
2
+y
2
and σ is the standard deviation. This is smoothing function which, if
convolved with an image, will blur it. The degree of blurring is determined by the value of σ.
The Laplacian function [13] is
2
2
2
4
22
2
)( σ
σ
σ
r
e
r
rh
−





 −
−=∇ (6)
For obvious reason, this function is called the Laplacian of a Gaussian (LoG). Because of
the second derivative is a linear operation, convolving an image with )(2
rh∇ is the same
as convolving the image with the smoothing function first and then computing the Laplacian
of the result. This is the key concept underlying the LoG detector.
Canny Edge Detection:
Finds edge by looking for local maxima of the gradient of f(x, y). The gradient is calculated
using the derivative of a Gaussian filter. The method uses two thresholds to detect strong
and weak edges and includes the weak edges at the output only if they are connected to
strong edges. Therefore this method is more likely to detect true weak edges. The Canny
edge detector[13] is the most powerful edge detector provided by function edge. In this
method the image is smoothed using a Gaussian filter with a specified standard deviation,
σ, to reduce noise. The local gradient,
[ ] 2/122
),( yGxGyxg += (7)
and edge direction,
)/(tan),( 1
GxGyyx −
=α (8)
are computed at each point. Gx and Gy computed using sobel, prewitt or Roberts method
of edge detection. An edge point is defined to be a point whose strength is locally maximum
in the direction of the gradient.
4. Preprocessing by PCA
There are several approaches for the estimation of the independent component analysis
(ICA) model. In particular, several algorithms were proposed for the estimation of the basic
version of the ICA model, which has a square mixing matrix and no noise. Practically when
applying the ICA algorithms to real data, some practical considerations arise and need to
be taken into account. To overcome these practical considerations we implemented a
preprocessing technique in this algorithm that is dimension reduction by principal

component analysis. That may be useful and even necessary before the application of the
ICA algorithms in practice. Overall face recognition benefits from feature selection of PCA
and ICA combination [6].
A common preprocessing technique for multidimensional data is to reduce its dimension
by principal component analysis (PCA) [3]. Basically, the data is projected linearly onto a
subspace
xEX n=
~
(9)
so that the maximum amount of information (in the least-squares sense) is preserved.
Reducing dimension in this way has several benefits. First, let us consider the case
where the number of independent components (ICs) n is smaller than the number of
mixtures; say m. Performing ICA on the mixtures directly can cause big problems in such
a case, since the basic ICA model does not hold anymore. Using PCA we can reduce the
dimension of the data to n. After such a reduction, the number of mixtures and ICs are
equal, the mixing matrix is square, and the basic ICA model holds.
The question is whether PCA is able to find the subspace correctly, so that the n ICs can
be estimated from the reduced mixtures. This is not true in general, but in a special case
it turns out to be the case. If the data consists of n ICs only, with no noise added, the
whole data is contained in an n-dimensional subspace. Using PCA for dimension
reduction clearly finds this n-dimensional subspace, since the eigenvalues corresponding
to that subspace, and only those eigenvalues, are nonzero. Thus reducing dimension
with PCA works correctly. In practice, the data is usually not exactly contained in the
subspace, due to noise and other factors, but if the noise level is low, PCA still finds
approximately the right subspace. In the general case, some weak ICs may be lost in the
dimension reduction process, but PCA may still be a good idea for optimal estimation of
the strong ICs.
5. ICA Algorithm
Here we used the modified FastICA algorithm [11] for computing of independent
components. Before computing the independent components we use to calculate the
principle components and then whitened those components to reduce the size of matrix. In
the previous section we have seen the need to use PCA before applying ICA. After finding
principle components we whiten the eigenvector matrix to reduce the size of matrix and
make it square. To estimate several independent components, we need to run the ICA
algorithm several times with weight vectors w1, ...,wn. To prevent different vectors from
converging to the same maxima we must decorrelates the outputs w
T
1x, ...,w
T
n x after
every iteration.
A simple way of achieving decorrelation is a deflation scheme based on a Gram-Schmidt-
like decorrelation[13]. This means that we estimate the independent components one by
one. When we have estimated p independent components, or p vectors w1, ...,wp, we run
the one-unit fixed-point algorithm for wp+1, and after every iteration step subtract from wp+1
the projections w
T
p+1 wj wj , j = 1, ..., p of the previously estimated p vectors, and then
renormalize wp+1:
∑=
+++ −=
p
j
jjp
T
pp WWWWW
1
111 (10)
1111 / ++++ = pp
T
pp WWWW (11)

In certain applications, however, it may be desired to use a symmetric decorrelation, in
which no vectors are privileged over others. This can be accomplished, e.g., by the
classical method involving matrix square roots,
WWWW T 2/1
)( −
= (12)
where W is the matrix (w1, ...,wn)
T
of the vectors, and the inverse square root (WW
T
)
−1/2
is obtained from the eigenvalues decomposition of WW
T
= FDF
T
as (WW
T
)
−1/2
= FD
−1/2
F
T
. A simpler alternative is the following iterative algorithm,
||||/ T
WWWW = (13)
As we are using the ICA algorithm the training time required is more as compared to
other methods. For the algorithm developed in this paper required around few seconds time
as training time.
6. Similarity Metrics using Classifiers
As we are using the ICA algorithm the feature extraction time required is more as
compared to other methods. For the algorithm developed in this paper required around few
seconds time as extraction time. The query image will be more similar to the database
images if the distance is smaller. For similarity measurement we used the Euclidean
distance classifier and Mahalanobis distance classifier [12][14], for calculating the minimum
distance between the query image and images to be matched from the database. If x
and y are the two d-dimensional feature vectors of the database image and query image
respectively, then these distance metrics are defined as follows. Euclidean distance to
determine closeness reduces the problem to computing the distance measures:
∑=
−=
d
i
iiE yxyxd
1
2
)(),( (14)
If the distance is small, we say the images are similar and we can decide which the most
similar images in the database are. Another distance metrics for comparison of the
retrieval of images used is Mahalanobis metric:
)()()(),( 12
yxxCovyxyxdMah −−= −
(15)
The results of these classifiers are very much close to each other. In Mahalanobis
metrics the time required for similarity measure is more due to involvement of the
covariance matrix.
7. Experimental Results
The experimental results presented in this paper are divided in to two parts. Both parts
evaluate the face representation using Laplacian of Gaussian ( LoG) and Canny edge
detection for feature extraction methods. In first part the face images having variation in
illumination conditions are used. In second part face images are used with large rotation
angles. There are four stages of the algorithm developed in MATLAB environment. In the first
stage we calculate the edge information using LoG or Canny edge detection method. The

second stage is used for preprocessing of image matrix using PCA for dimension reduction.
Third stage is used to find out independent components as feature vectors using ICA
algorithm. In last stage we used different two classifiers for testing of input image to be
recognized.
Figure 1: Various view of face images with different illumination conditions in Asian face database
Two standard databases are used for evaluation of these results. The first database is
published by IIT Kanpur [16] widely used for research purpose known as Indian face
database. In this database images of 60 persons with 10 sample images with different
orientations and views are available. The second database known as Asian face image
database [15] is from Intelligent Multimedia research laboratories having face images of 56
male persons with 10 samples each; which consist of variation in illumination conditions and
different views. The resolution of all images we used in the algorithm is 128 x128 for
computational purpose. Few face images are shown in Figure 1 and Figure 4 from both the
databases with various views.
In this study we have explored feature selection techniques using Edge information and ICA
for face recognition. Feature selection techniques are warranted especially for ICA features,
since these are devoid of any importance ranking based on energy content. The study is
carried out on the face database that contains both facial expression with pose variation and
illumination variations. We implemented the algorithms for face recognition using Edge
information and ICA on the different conditions of face images with different set of images.
These set of images we used are by selecting the first 50, 100, 150 or 200 independent
components.

Figure 2: Edge information of few face images
The edge detected images are shown in Figure 2 and are then preprocessed by PCA.
The independent components are obtained by ICA algorithm and few are shown in Figure
3. These are the independent components obtained for face images with variation in
illumination. The light condition on the face images are from left and right sides as well as
from top and down directions. Under different illumination conditions the results are
encouraging as shown in table 1.The images used in this part are from Asian face
database with different illumination conditions as shown above in Figure 1. For training
we used different sets of independent components varying from 50 to 200. The edge
information for the images with large rotation angles are shown in Figure 5 and
corresponding few independent components are shown in Figure 6. For this part we used
images from Indian face database with large rotation angle up to 180
0
.
Figure 3: Independent Components of few face images

Figure 4: Various view of face images with different face orientations in Indian face database
Figure 5: Edge information of few face images
Figure 6: Independent Components of few face images

Table 1: Results of the face recognition algorithm
8. Conclusion
In this paper an independent component analysis of Edge information of face images has
been discussed and used for face recognition. Two standard databases are used, which
contains the face images with different orientations, expressions and change in illumination.
The performance of the algorithm suggested produces very good recognition rate varying
from 74% to 95%. Applying ICA on face images for recognition; selection of ICs are
required in order to give better performance. We used two different approaches for edge
detection where Canny edge detector has given better results as compared to LoG edge
detector. We adopted modified FastICA algorithm for computing the independent
components. If we observe the results of face recognition using ICA under variation of
illumination conditions the results are very good and encouraging. The results of the first
part with ICA method are also close to the results of second part. This implies that ICA for
edge information of face images is less sensitive to illumination change as compared to
face orientations as shown in results.
9. REFERENCES
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Conditionsof
imagesused
foralgorithm
Database
used
Noof
Components
used(PCs&
ICs)
Recognition
rateusing
LoGEdge
detectorand
ICA(%)
Recognition
rateusing
CannyEdge
detectorand
ICA(%)
Classifier
used
Euclidean
distance
Mahalanobis
metric
Euclidean
distance
Mahalanobis
metric
200 74 76.5 80.5 83.5
150 79.33 82 84.67 86.66
100 79 83 85 87
Part I- Pose
variation with large
rotation angles
Indian face
database.
50 82 86 88 91.5
200 74 78 86 92.33
150 81 83 90 93.33
100 82 88.67 90 94
Part II- Variation of
illumination
conditions.
Asian face
database.
50 84.5 87.5 91.5 95

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