facial verification using a modular kernel eigen spaces

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Proceedings of the International Conference , “
Computational Systems and Communication Technology”



8
th

, MAY 2010
-

by Cape Institute of Technology,

Tirunelveli Dt
-
Tamil Nadu,PIN
-
627 114,INDIA

FACIAL
VERIFICATION

USING A MODULAR
KERNEL EIGEN SPACES

1
Golda Jude P
,



2
Dr. K. Muneeswaran

1
PG student

2
Professor &

Head

Department
of Computer science and Engineering




Mepco schlenk engineering college






Sivakasi, virudhun
agar
-
6
26005










goldjude
@
gmail
.com


Abstract
-

In this
paper face

recognition accuracy i
s
improved by developing a new

kernel
Eigen

space and
implemented on the phase congruency ima
ge extracted
from the

visual image
.

Smaller

sub
-
regions in
a
predefined neighborhood within the phase congruency
images of the training samples are merged to obtain a
large set of features. These features are then projected
into higher

dimensional spaces u
sing kernel methods.

The proposed method

helps to overcome the
illumination,

expression

variations.

ORL database is
used for the experiment.




Keywords
-
kernel,
phase
congruency,
Feature

extraction



1.

INTRODUCTION


Face Recognition is a biometric identificati
on by
scanning a person's face and matching it against a library
of known faces. A healthy human can detect a face
easily and identify that face, whereas for a computer to
recognize faces, the face area should be detected and
recognition comes next. Hence
for a computer to
recognize faces the photographs should be taken in a
controlled environment
. The prime application of face
recognition is to identify the individuals for the purpose
of security.



Even though face recognition technology [
2
] has
moved fro
m

linear subspace methods [2]

such as
Eigen
and Fisher faces [4], [5
]

to nonlinear methods
namely

kernel principal component analysis (KPCA) and kernel
Fischer
discriminate

analysis (KFDA) [6]

[7
], many of
the problems are yet to be addressed
.

The feature

selection process presented in this paper is derived from
the concept of modular spaces [10
]. The face images that
affected due to variations such as non

uniform
illumination, expressions and partial occlusions are
confined mostly to local regions. Modula
rizing the
images would help to localize these variations, provided

the modules created are

sufficiently

small.

Linear subspace approaches such as PCA does not
capture the relationship among more than two variables.
In order to capture the relationships
among more than
two pixels, the dat
a


is projected into nonlinear higher
dimensional spaces using the kernel method.


The paper
is
organized as follows
.
A step to
obtain the phase congruency image is

explained in
s
ection

2
. M
odularization is explained i
n section
3
. The
process of obtaining modular kernel
Eigen

features is
explained in

Section

4
.

Architectural

d
esign is explained
in section
5
.

Experimental result in section 6 followed
by conclusion in 6
.


2.

PHASE CONGRUENCY



Phase congruency i
s a method of edge detection
that is particularly robust against changes in illumination
and contrast.

The concept is similar to coherence except
that it applies to functions of different wavelength.

For
example, the
Fourier decomposition

of a
square wave

consists of
sine

functions,
whose frequencies are odd
multiples of the fundamental frequency. At the rising
edges of the square wave, each sinusoidal component
has a rising phase; the phases have maximal congruency
at the edges. This corresponds to the human
-
perceived
edges in an ima
ge where there are sharp changes
between light and dark.


A . Steps for calculating phase congruency image



Convolve the face image I(x,y) with a bank of 2
-
D log
Gabor filter with different orientations and scales. The
2
-
D log Gabor is constructed using

a Gaussian function
in the angular direction which is given b
y




(1)


6
orientations

and 3
scales

are
chosen
.
0

is the
orientation of the filt
er and


is the standard deviation
of the Gaussian function.


The log Gabor has a transfer function of the form





(2)


)
2
/(
)
)
(
(
2
0
2
0
)
(







e
G
))
)
/
(log(
2
/(
)
)
/
log(
(
2
2
)
(
o
o
w
k
w
w
e
w
G


Proceedings of the International Conference , “
Computational Systems and Communication Technology”



8
th

, MAY 2010
-

by Cape Institute of Technology,

Tirunelveli Dt
-
Tamil Nadu,PIN
-
627 114,INDIA

The amplitude of the response at a given sca
le and
orientation is computed by




(3)




The phase congruency of the image calculated over
various scales and orientation is calculated by








(4)


Where represents

the even and odd components at a
scale
n

and orientation
o









Fig. 1. Original image


fig. 2. Phase congruency image obtained







from

the original image




3.

MODULARIZATION


Several experimental results
show

that with

module
sizes of 4 X4, 8X 8, and 16X 16 on face images of size
64
X
64. It has been observed in
[9] that, maximum
recognition accuracy is obtained when the images were
divided into sub
-
regions of size 8X8.Larger module size
(16X16) leads to lesser localization of the facial
variations and smaller module size (4 X4) misses the
sub
-
region information c
ontent. This leads to the
conclusion that the sub
-
regions in the modular approach
needs to occupy specific facial feature information.
Hence, in the proposed neighborhood defined modular
space approach, several 8X8 modules are created by
combining 4X 8 mod
ules in a neighborhood region of
size 16X 16 for a 64X64 face image
. As a result 448
modules are created
[1]

and then each module is
projected to the
Eigen

spaces and then it is classified
according to the minimum distance measure.

A.
General steps for propo
sed

modularization for
NXN image siz
e



1
.

Each image is divided into
)
/
(
)
/
(
n
N
n
N


to get
n
n



to get number of large modules
.

2.
Each module

of size
)
/
(
)
/
(
n
N
n
N


is then divided

into modules of size
)
/
(
)
/
(
j
n
N
i
n
N



, where

j
i

is the number of small modules within a
modules
.

3

.
P modules can then be created by merging
j
i

number of

small modules in a neighborhood according to the
relation
)
)!
(
!
/
)
)!
((
k
j
i
k
j
i
P




, where k i
s the
number of
small modules to merge
.



4.

OBTAINING MODULAR KERNEL EIGEN
FEATURES


Kernel PCA has been applied to face
recognition applications and is observed to be able to
extract nonlinear features. The process of obtaining the
weights for the input pat
terns in the kernel principal
component analysis transformed space is described
below.


Let
i
x

be the

vectors belonging to the training
sample set
}
....
,
,
{
3
2
n
i
x
x
x
x
X

where
n
i
R
x

and
‘c’ be the number of clas
ses in the training set. Mean of
the data
o
m

is given by






m
k
k
o
x
m
m
1
0
1

(5)


Let Φ be the mapping between the input
space

X

and the
feature space


Φ:

X
-
>
H,

H can be assumed to be a Hilbert space

Covariance matrix

C
is calculated as








V
V
C





(6)

The re
lationship between the eigenvector and the sample

training vector

in feature space is





m
i
i
i
x
V
1
)
(






(7)

The projection of the sample vector onto the
Eigen

vector is given by

2
2
)
,
(
)
,
(
y
x
o
y
x
e
A
no
no
no











)
,
(
))
,
(
(
))
,
(
(
)
,
(
2
2
y
x
A
y
x
o
y
x
e
y
x
PC
no
n
o
no
n
no
n
o
Proceedings of the International Conference , “
Computational Systems and Communication Technology”



8
th

, MAY 2010
-

by Cape Institute of Technology,

Tirunelveli Dt
-
Tamil Nadu,PIN
-
627 114,INDIA


)
,
(
)
(
.
1
k
m
i
i
i
k
x
x
k
x
V











(8)

5. ARCHITECTURAL

DESIGN



A. Steps in training image

1. Obtain the phase congruency maps for each
image

of the training set .

2. Modulariz
e each of the training images.

3. Create and process each set of
modules

separately
.

4. Generate the kernel matrix for each
vectorized module set after an appropriate
kernel is
selected
.

5. Apply KPCA for each module set and obtain
the weights for al
l the individual modules.



B. steps in test image


1. Extract the phase congruency features of the test
image.

2. Create the modular regions.

3. Obtain the weights for each individual module using
the vectorized modules and the Kernel matrix

4. C
lassify each module by using a minimum distance
classifier on the generated weights from the training and
the testing phase.



































Fig.3
.

Face recognition technique for training image



6.
RE
SULTS


For experiment purpose ORL database is used.
There are 40
individuals. T
here are 10 images per
individual in the ORL
database

with 40 images
.
Diff
erent tests are conducted,

s
uch

as changing the
training and test images used for each individual and
using less or more number of training and test images in
order to test the systems reaction to these changes.

A .Neighborhood Defined Modular phase
congr
uency Based Kernel PCA

(NMPKPCA)


The
modules created are projected
to higher
dimensional spaces using ke
rnel spaces. Table 1 shows
the
recognition rate obtained for the different test and
train images.

The train and test images are disjoint.

Table

1

shows 80,160,180 train images with 2,4,6
images per individual are trained respectively.
ORL
database is used for the experiment to test and train the
different images.
Similarly 40,80,120 test images with
1,2,3 images per individual are tested respective
ly.



TABLE 1

RECOGNITION RATE FOR DIFFERENT TEST AND TRAIN IMAGES




No of test
images

No of
tra
in
images

Recognized
image

Not
Recognized
image

Recognition
Rate

in %

40

80

35

5

87.5

80

160

75

5

93.6

120

180

112

8

95

Result

Phase congruency feature extraction

Extraction of modules and projection into Eigen
subspaces

Nearest neighbor classification of modules

Voting

Proceedings of the International Conference , “
Computational Systems and Communication Technology”



8
th

, MAY 2010
-

by Cape Institute of Technology,

Tirunelveli Dt
-
Tamil Nadu,PIN
-
627 114,INDIA



7. CONCLUSION

AND FUTURE WORK




This paper presents

a face recognition technique
using visua
l

f
ace

images
. The feature selection is robust
to the variations that occu
r in the face images
captured
in visual
. The novel modular kernel
Eigen

spaces
approach has been able to provide high recognition
accuracy in images affected due to partial occlusions,
expressions and nonlinear lighting variations.
Steps are
by taken to te
st various combination of
training and
testing image.


REFERENCES

[1] Satyanadh gundimada and Vijayan K. Asari,”Face Recognition using
multisensory images based on localized kernel eigen spaces” IEEE
transactions on image processing, vol.18,No.6

june 2009

[
2
] W. Zhao, R. Chellappa, and A. Rosenfeld, “Face recognition: A literature
survey,”
ACM Comput. Surv.
, vol. 35, pp. 399

458, 2003.

[
3
] P. N. Belhumeur, J. P. Hespanha, and D. J. Kriegman, “Eigenfaces
vs.Fisherfaces: Recognition using class specific line
ar projection,”
IEEE
Trans. Pattern Anal. Mach. Intell.
, vol. 19, pp. 711

720, 1997.

[
4
] M. Turk and A. Pentland, “Eigenfaces for recognition,”
J. Cogn.
Neurosci.
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86, 1991.

[5
] A. Pentland, B. Moghaddam, and T. Starner, “View
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based a
nd modular
eigenspaces for face recognition,” in
Proc. IEEE Conf. Computer Vision and
Pattern Recognition
, 1994, pp. 84

91.

[
6
] J. Huang, P. C. Yuen, W. S. Chen, and J. H. Lai, “Kernel subspace LDA
with optimized Kernel parameters on face recognition,” in
Proc. IEEE Int.
Conf. Automatic Face and Gesture Recognition
, 2004, pp. 327

332.

[7
] M. H. Yang, N. Ahuja, and D. Kriegman, “Face recognition using kernel
eigenfaces,”
Adv. NIPS
, vol. 14, pp. 215

220, 2002.

[8
] M. H.Yang, “Kernel eigenfaces vs. kernel fish
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Gesture Recognition, 2002.

[9
] J. Yang, Z. Jin, J. Y. Yang, D. Zhang, and A. F. Frangi, “Essence of
kernel fisher discriminant: KPCA plus LDA,”
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pp. 2097

2100, 2004.

[10
] R. Gottumukkal and K. V. Asari, “An improved face recognition
technique based on modular PCA approach,”
Pattern
Recognition
. Lett.
, vol.
25,pp.429

436,2004
Proceedings of the International Conference , “
Computational Systems and Communication Technology”



8
th

, MAY 2010
-

by Cape Institute of Technology,

Tirunelveli Dt
-
Tamil Nadu,PIN
-
627 114,INDIA