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: 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 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

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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

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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.

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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.

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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.

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