LETTERS

International Journal of Recent Trends in Engineering, Vol 2, No. 2, November 2009

51

Face Recognition based on Two-Dimensional

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 Two-Dimensional 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, 2D-PCA, 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 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 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 well-known 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 time-frequency 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. Wavelet-based methods prune away

these variable subbands, and focus on the subbands that

contain the most relevant information to better represent

the data[9].

1-D 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 2-D DWT on an image, (b) Three level 2-D

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 2-D 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 2-level 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

2-D

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. In PCA the 2-D image information

must be previously transformed into 1-D 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 non-negative

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 eigen-values, 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 2D-PCA 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) Multi-resolution Data

approximation and (3) Insensitive Feature extraction.

In view of the limitations in PCA and 2D-PCA 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 2-D wavelet at

appropriate LL subband. The reduced image data is then

sent to the 2D-PCA 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 2-D wavelet decomposition. The features are

extracted using 2D-PCA 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 2D-PCA

Figure 6. Subband LL3 face images projected in 2D-PCA

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 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 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 2-DPCA. We compared the

recognition performances of various wavelets at 8 levels,

1 to 8. Accuracy with only 2-DPCA is 85% where as the

average accuracy of 2-DPCA 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 mid-frequency 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

[1] W. Zhao, R. Chellappa, A. Rosenfeld, and P.J. Phillips,

“Face recognition: A literature survey,” CVL Technical

Report, University of Maryland, 2000.

[2] Matthew Turk and Alex Pentland, “Eigenfaces for

recognition”, in Journal of Cognitive Neuroscience, vol. 3,

No. 1, 1991, pp 71-86, A fundamental paper on the

eigenface approach.

[3] L. Sirovich and M. Kirby, “Low-Dimensional Procedure

for Characterization of Human Faces,” J. Optical Soc. Am.,

vol. 4, pp. 519-524, 1987.

[4] M. Kirby and L. Sirovich, “Application of the KL

Procedure for the Characterization of Human Faces,” IEEE

Trans. Pattern Analysis and Machine Intelligence, vol. 12,

no. 1, pp. 103-108, Jan. 1990.

[5] M. S. Bartlett, J. R. Movellan, and T. J. Sejnowski, “Face

recognition by independent component analysis,” IEEE

Trans. Neural Networks, vol. 13, pp. 1450–1464, Nov.

2002.

[6] P. N. Bellhumeur, J. Hespanha, D.J. Kriegman,

“Eigenfaces vs. Fisherfaces: recognition using class

specific linear projection”, IEEE Transactions on Pattern

Recognition Analysis and Machine Intelligence, vol. 19,

no. 7, 1997, pp. 711-720.

[7] J. Yang, D. Zhang, et al. “Two-dimensional PCA: a New

Approach to Appearance-Based Face Representation and

Recognition,” IEEE Trans. on Pattern Analysis and

Machine Intelligence, vol. 26, pp. 131-137, 2004.

[8] ORL face databases,

http://www.uk.research.att.com/pub/data/orl_faces.zip

[9] Dao-Qing Dai and Hong Yan,

“

Wavelets and Face

Recognition”, Face Recognition, Book edited by Kresimir

Delac and Mislav Girgic, I-Tech, Vienna, Aystria, June

2007, pp.558

[10] Bing Luo, Yun Zhang, Yun-Hong Pan, “Face Recognition

Based on Wavelet Transform and SVM”, International

Conference on Information Acquisition, Hong Kong,China.

373-377, 2005.

[11] Yuzuko Utsumi, Yoshio Iwai, Masahiko Yachida,

“Performance Evaluation of Face Recognition in the

Wavelet Domain”, International Conference on Intelligent

Robots and Systems, Beijing, China. 2006

© 2009 ACADEMY PUBLISHER

## Comments 0

Log in to post a comment