International Journal of Advanced Computer Engineering and Communication Technology (IJACECT)
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Multidirectional 2DPCA Based Face Recognition System
Shilpi Soni1, Raj Kumar Sahu2
1
M.E. Scholar, Department of E&Tc Engg, CSIT, Durg
Associate Professor, Department of E&Tc Engg, CSIT, Durg
Email: 1er.shilpi.soni@gmail.com, 2 rajkumarsao@gmail.com
2
two dimensional representations is built-in in 2DPCA,
which was proposed by Yang et al [2]. 2DPCA is more
efficient than PCA. 2DPCA extract the feature from the
matrix by projecting the image matrix along the
projection axes that are the eigen vectors of the image
scatter matrix. Recognition rate was further improved by
Directional 2DPCA (Di2DPCA), which was proposed
by Qi Zhu et al [3]. Di2DPCA can extract features from
the matrices in any direction where as 2DPCA reflects
the information in each row.
Abstract— In this paper, Multidirectional 2DPCA is
employed for face recognition of two different databases.
All face images are rotated and their two dimensional
principal components are calculated as features as features
of facial images. These features in various directions are
fused to form features of an individual’s facial image. The
results of this technique is compared over FERET database
and an inhouse self made database. For FERET database,
MDi2DPCA is giving 82.3% result and for self made
database it is giving 91.67% result.
Keywords— PCA,
Euclidean distance
2DPCA,
D2DPCA,
MD2DPCA,
In this paper we are adopting face recognition technique
by Di2DPCA technique. This paper is organized as
follows: Section I was a brief introduction of this paper.
Section II is giving an overview of face recognition
related works performed by before this work. Section III
is describing Methodology. Section IV is the
experimental results section where results obtained from
Di2DPCA and finally Section V is the conclusion of this
work.
I. INTRODUCTION
Face recognition technique deals with recognition of an
individual personality on the basis geometric or
statistical features of facial image. It includes face
tracking n a video sequence, face detection, face
verification, and finally face recognition. In all
applications of FR technology, after extraction of facial
images are converted into gray scale and normalized for
testing. This paper is based on the work for improving
recognition rate of various facial databases [1]. A face
recognition system has to perform Face tracking,
detection, verification and recognition. Face tracking
expects proposition of faces based on their preceding
trail and hence approximates the next position of those
faces. Face detection collects information of the
geometric replica of the face and non face images, and
then accepts a two-class classification method to
discriminate between them. Face verification deals with
verification of a claimed person and face recognition
concerns with distinguishing the identity of a person
from a record of identified persons. In this work,
principal component analysis is used for face
recognition. PCA is also known as eigenvector method
as it utilizes eigen values to represent linear variation in
high-dimensional data. PCA is one dimensional method
of data representation, but to increase recognition rate,
II. RELATED WORK AND BACKGROUND
A Principal component analysis is the most popular
dimensionality reduction technique used for image
based feature collection. Turk et. al [4]. developed eigen
face techniques for face recognition. Eigen vector and
eigen values project the eigen faces which represent
primary components of the faces. Weights derived from
these eigen vectors are used to represent the facial
features which are used for identification of individual
faces from a database.
Binary PCA (B-PCA) [5]has been proposed to replace
floating-point multiplications with integer additions, so
the time complexity of the testing procedure can be
significantly reduced. It was reported that B-PCA is 50
times faster than classical PCA.
Since PCA is an image-as-vector method, due to the
vectorization effect of PCA, the spatial redundancy
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ISSN (Print): 2319-2526, Volume -2, Issue -3, 2013
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International Journal of Advanced Computer Engineering and Communication Technology (IJACECT)
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within each image matrix is not taken into account, and
some information on local spatial relationships is lost. In
order to retain these information, 2DPCA is adopted
which is an image-as-matrix method. For image-asmatrix methods, an image is treated as a matrix and thus
does not destroy the spatial relationship of image pixels.
2DPCA
takes
a
2
dimensional-matrix-based
representation model and image covariance matrix is
constructed directly from the 2D image matrices.
2DPCA can evaluate the matrix accurately and
computationally more efficiently than PCA [6,7].
(1)
This 2D matrix is the arithmetic average of the training
images at each pixel point. Training images in each
rotated image database are subtracted from their
respective mean image to form variance.
Φ=Γ–Ψ
(2)
All of these mean subtracted rotated images, i.e.
variance of each image, are appended to form an array.
Then covariance matrix is calculated from each variance
matrix which is product of variance matrix with its
transpose.
Xu et al [8]. compared 2DPCA and PCA. A problem
pertains with 2DPCA, that it needs more coefficients
than PCA, so it needs more memory and more time in
classification. To overcome these problems, Zhou et al
[9,10]. proposed the bidirectional PCA (BDPCA) and
Zhang et. al[11].
proposed the 2directional
2dimensional PCA ((2D)2PCA). BDPCA and (2D)2PCA
reduces the dimension in both column and row
directions, for feature extraction.
Χ = ΑT Α =
(3)
Face Acquisition
To maintain correlations between variations of rows and
column diagonal principal component analysis (DiaPCA)
is proposed by Zhang et al[11]. They performed this task
by seeking the optimal projective vectors from the so
called diagonal face images which are used to extract
information in diagonal direction.
Face Database Formation
The features extracted from one or two directions are in
sufficient for achieving high accuracy. Since vectors of
the image matrix in different directions have different
effects during correct classification. To extract features
from the matrices in any direction, Qi Zhu et. al [12].
proposed directional 2DPCA (Di2DPCA). Their results
are further improved by Xiao Hu et. al [13]. which
proposed multi-oriented 2DPCA, where facial images
are rotated by θ degrees using bilinear interpolation.
Facial features were extracted from origin face image
and rotated images. Since the Di2DPCA can extract
features from matrix in different directions, in this work,
Multi-directional 2DPCA (MDi2DPCA) is incorporated
to improve accuracy. Here matching score level fusion is
used to integrate several Di2DPCA performed in
different directions for face recognition.
Training Dataset
Testing Dataset
Histogram Equalization
Histogram Equalization
Rotate by xo
Rotate by yo
Mean Image
Calculation
Mean Image
Calculation
Variance
Calculation
Variance
Calculation
Covariance
Calculation
Covariance
Calculation
Eigen Vector
Calculation
Eigen Vector
Calculation
Weight Matrix
Weight Matrix
Projection
Matrix
Projection
Matrix
Rotate by xo
Rotate by yo
Variance
Calculation
Variance
Calculation
Projection
Matrix
Projection
Matrix
Euclidean Calculation of xo
rotated image
Euclidean Calculation of yo
rotated image
Score Normalization
(Sigmoid Function)
Score Normalization
(Sigmoid Function)
Normalized Score Fusion (Weighted Summation)
III.
METHODOLOGY
Resultant Image (Minimum Fused
Value)
A In this paper, Multidirectional 2DPCA is used for
feature extraction. Face image is taken as two
dimensional matrixes and rotated in six different
directions. Rotated images are appended to form array.
Recognition rate is compared for four different facial
databases viz. FERET and an in house database. Feature
Extraction process is described as below-
Fig. 1 Flow chart of Directional 2DPCA Algorithm
Then covariance matrices of all facial images are added.
Eigen values & Eigen vectors are calculated as
X ⋅νi = μi ⋅νi
ΑT .Α. νi = μi ⋅νi
Training Phase- All training facial images which are
under training database are cropped. These images are
then rotated and appended as page wise arrays. Then
mean of each array is calculated
(4)
(5)
ΑT .Α ⋅ Α ⋅ νi = μi ⋅ Α ⋅ νi
(6)
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International Journal of Advanced Computer Engineering and Communication Technology (IJACECT)
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Χ ⋅ Α ⋅ νi = μi ⋅ Α ⋅ νi
(7)
Hence υi = Α ⋅ νi is one of the eigen vector of X.
Eigen vectors corresponding to highest eigen values are
selected. Eigenface Matrix is calculated which is
product of variance of each face image with d numbers
of highest eigen vectors.
Φ = A. Υ
(8)
Now projected train matrix calculation which is also
termed as eigen face matrix and is calculated as
ωk= φT. Ai
(9)
Fig. 2. In house Face image rotated by 0 o, 10o, 20o, 30o,
40o, 50o
where i= 1, 2, 3……number of training images
where values of weights are selected such that, w1 + w2
=1.
Testing Phase- Facial images under test is then cropped
and then rotated. The cropped and rotated test face
image is subtracted from mean image of database,
Φ t = Γt – Ψ
Recognition- At this stage, test image is recognized with
training image. To carry out this task, simply minimum
value of fused score s is found.
(10)
Projected Test image of each of rotated image is then
calculated from their respective eigen face matrix.
ωt
=φ
T
. Φt
Output = min (
(16)
)
Its location reflects the facial image under test. Principal
component
(11)
IV.
Classification- Euclidean Distance is used to calculate
the distance. It is given by
EXPERIMENTAL RESULTS
In this paper, database used are In house & FERET face
database base is used. Database used is In house self
made Face database.This database contains images of 12
individuals with 9 image each. Rotated images and final
output images by Directional 2DPCA are shown in fig 2
&fig. 3 . On the basis of results, Table I is drawn,
comparing results face recognition by 1DPCA and
Directional 2DPCA. And Table II is comparison of
recognition rates by varying eigen values.
(12)
Normalization- By normalization, distance scores of
each of left and right half face image are mapped
between 0 and 1. Sigmoid function is used for
normalization in this technique.
Face Image Under Test
Resultant Facial Image
(13)
Where
(14)
is normalized score,
is raw distance score, µk is
mean and σk is standard deviation of kth half face image
Fig .3.Test Image and Output Image
Fusion- Fusion is combining of different feature vectors.
Here fusion is being performed by weighted summation
method. It is given by
(15)
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International Journal of Advanced Computer Engineering and Communication Technology (IJACECT)
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TABLE I
COMPARISON OF RECOGNITION RATE ON INHOUSE
FACE DATABASE HAVING 12 INDIVIDUALS
Testing
Training
S.
images
Recognition
images
No.
per
Rate (%)
per class
class
1
8
1
91.67
2
2
75
6 7
3
6
3
69.44
4
8
1
91.67
7
2
75
6
3
69.44
5
4
6
TABLE III
COMPARISON OF RECOGNITION RATE ON FERET FACE
DATABASE
S.
No.
1
2
3
4
No. of
Rotations
No. of
Eigen
Features
20
30
20
30
6
4
Correct
Outputs
(out of
300
tests)
245
242
247
242
Recognition
Rate (%)
81.67
80.67
82.33
80.67
90
80
On the basis of these results comparison plot is drawn
Recognition Rate (%)
70
100
90
Recognition Rate (%)
80
70
60
60
50
40
30
20
50
40
10
30
0
20 Eigen Features
30 Eigen Features
6
4
Number of Rotating Directions
20
10
0
8
7
6
V. CONCLUSIONS
Number of Training Images per Class
In FERET Database contains 1200 images, 300
persons with 4 images each. Rotated image and output
image of FERET database are shown in fig. 4 and fig. 5
The paper presents a face recognition approach using
Multidirectional 2DPCA. In the first database which is
FERET database, 4 training images are taken for 300
individuals and one image for testing. Recognition rate
is calculated for varying direction of rotation. For 4
numbers of rotations and 20 numbers of eigen features
recognition rate is maximum i.e 82.33%. In another
database, which is In house database having 12
individuals, recognition rate is achieved maximum
which is 91.67%, for both 6 and 4 directions of rotations
in case of 8 images for training and one for testing
image. Here also 20 numbers of eigen features are
selected.
REFERENCES
Fig.4. In FERET Face image rotated by 0o, 10o, 20o, 30o,
40°,50o
Face Image Under Test
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Turk, M. And Pentland, A. 1991,‘‘ Eigenfaces
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26(1): 131–137.
[4].
Qi Zhu, Yong Xu , ‘‘Multi-directional twodimensional PCA with matching score level
Resultant Facial Image
Fig.5. Test Image and Output Image
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International Journal of Advanced Computer Engineering and Communication Technology (IJACECT)
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