Face Recognition using Improved FFT Based Radon by PSO and PCA Techniques

Hamid M. Hasan, Prof. Dr. Waleed A. AL.Jouhar & Dr. Majed A. Alwan
International Journal of Image Processing (IJIP), Volume (6) : Issue (1) : 2012 26
Face Recognition Using Improved FFT Based Radon by PSO and
PCA Techniques
Mr. Hamid M. Hasan Hamid2012net@gmail.com
Electrical Eng. Dept.
Basra University, college of Eng.
Basra , Iraq
Prof. Dr. Waleed A. AL.Jouhar Profwaleed54@yahoo.com
Electrical Eng. Dept.
Baghdad University, College of Eng.
Baghdad , Iraq
Dr. Majid A. Alwan Altimimee@yahoo.com
Electrical Eng. Dept
Basra University, college of Eng.
Basra , Iraq
Abstract
Face Recognition is one of the problems which can be handled very well using Hybrid techniques
or mixed transform rather than single technique. This paper deals with using of Radon Transform
followed by PCA and LDA techniques for Face Recognition. The data used are 2D Face Images
from ORL Database. The Radon Transform used is based on FFT slice theorem. The directions
along which the Radon transform is performed are selected using PSO in order to achieve a good
recognition rate. The best directions selected are less computation expensive as compared to the
full set of directions and achieve good recognition rate. The PCA is used to reduce the dimension
of the data produced by Radon Transform and the LDA is used to find a set of basis vectors
which maximizes the ratio between-class scatter and within–class scatter. In order to verify our
method many dataset partitioning scenarios into training set and testing set were conducted. And
the maximum recognition rate achieved was 97.5%.
Keywords: Face Recognition (FR), Radon Transform (RT), Fast Fourier Transform (FFT),
Principal Component Analysis (PCA), Linear Discrimenant Analysis(LDA) and Particle Swarm
Optimization (PSO).
1. INTRODUCTION
Face recognition is one of the most important biometrics which seems to be a good compromise
between actuality and social reception and balances security and privacy well. It has a variety of
potential applications in information security law enforcement and access controls. Face
recognition systems fall into two categories: verification and identification. Face verification is 1:1
match that compares a face images against a template face image. On the other hand face
identification is 1: N problem that compares a probe face image against all image templates in a
face database. Face recognition is a very difficult problem due to a substantial variations in light
direction (illumination) , different face poses , diversified facial expressions , Aging (changing the
face over time) and Occlusions (like glasses, hair, cosmetics). So the building of an automated
system that accomplishes such objectives is very challenging. In last decades many systems with
recognition rate greater than 90% has been done however a perfect system with 100%
recognition rate remains a challenge. Face recognition algorithms are divided by [1, 2] into three
categories as follows:

1. Holistic methods: These methods identify a face using the whole face images as input
and extract the overall features.
2. Feature based methods: these methods used the local facial features for recognition
(like eyes, mouths, fiducial points. etc.).
3. Hybrid methods: these methods used both feature based and holistic features to
recognize a face. These methods have the potential to offer better performance than
individuals.
2. A REVIEW OF THE RELATED 2-D FACE RECOGNITION TECHNIQUES
Thomas Heseltine [3] investigated three appearance based approaches for face recognition
which are the direct correlation method, the eignface method and fisherface method. the
recognition error rate reported is 18% , 20.4% , 17.8% respectively .
M. Chandra Mohan[4] they divide the face into four parts and evaluates the texture features in
each part separately the texture features are derived from parameters with different orientations,
this makes the face recognition easier and pose, illumination and rotation invariant.
P.Abouzar [5] using WT (Wavelet) and DCT ( Discrete Cosine Transform) followed by PCA the
proposed algorithm takes advantages of data reduction property of the three transforms. The
Support Vector Machine (SVM) was used to classify the images into different classes and the
error rate obtained is between 5%-7%.
Zhan Shi[6 ] they extract a number of features from facial images through taking Trace Transform
over different angular directions by using different trace functions then the features are projected
into a lower dimensional subspace. The recognition rate achieved is 95% in ORL database.
Laika Karsili [7 ] used a Radon Transform over the set of angles{0,60,120,180,240,300,360}, then
the produced data was reduced using PCA this achieves 70% recognition rate for rank 1 and
95% for rank 4.
Jamal A hmad [8] Investigated the effect of the step size for both the angle and the vector of the
radon transform on the performance of a face recognition system based on PCA it is founded
that step size of one for both produces recognition rate of 89%.
ZHANG et al, [9] proposed a feature extraction method based on finite Radon transform (FRAT)
then used soft threshold (ST) to select main FRAT coefficients. Finally 2DMMC was used to
extract features for classification from main FRAT coefficients. They achieved 89.02% recognition
rate on ORL database.
Ergun Gumus et al [10] they used Eigenfaces (PCA) and Support Vector Machine (VSM) on ORL
database they achieved recognition rate of 91,2% for PCA-AVM (RBF) Radial bases.
Zhang Lin et al [11] used Radon Transform with multiwavelet and PCA on Infrared imaged faces
and they achieved 95% classification accuracy with 70 element feature vector.
Yuehui Chen et al [12] proposed using DCT and Hybrid Flexible Neural Tree which was evolved
using PSO their experiment on ORL achieved 98.13% recognition rate .
Jian Zhang , Xianyun Fei[13] they used the PSO in order to select the optimum discrimination
eigenvectors of PCA and obtain the optimal recognition accuracy simultaneously they validate
their method with ORL database with recognition rate of 96%.
Dattatray V. Jadhao and Raghunath S. Holambe[14] they used Radon transform and Fourier
transform for face recognition on ORL database and achieved recognition rate of 97.33% the
images were classified on the nearest neighbor with 60 features .

Rabab M.Ramadan [15] used PSO to select the efficient features from DCT and DWT and apply
their method on ORL with recognition rate 94.7% and 96.8% respectively .
In this paper we used the Radon Transform which is improved by PSO to select the best
directions. Then a data reduction is performed using the PCA. A classification basis vectors are
derived using LDA which lead to a rank one recognition rate equal to 97.5% and the feature
vector size is 35 items per class (person).
3. THE METHOD AND MATERIALS
The method used in this paper for face recognition is depicted in figure (1). It consists the
enrollment phase and the testing phase. In the enrollment phase the training set of images are
transformed into Radon space using the Radon Transform. The set of directions (angles) along
which the transform is performed were calculated using the Particle Swarm Optimization (PSO).
Different sets of directions are shown in tables (1, 2, 3). The different sets are for different
classifier parameters which yield a good estimated recognition rate. The data generated by
Radon Transform are reduced using Principal Components Analysis (PCA). From those reduced
data set (i.e. the most effective components) a set of basis vectors which maximizes the ratio
between-class scatter and within–class scatter using Linear Discrimenant Analysis (LDA). One
basis vector for each class (i.e. Person) is derived and stored in the data base. So for ORL Image
database there are 40 basis vectors are stored regardless of the number of images used for each
person in the training set. The length of the basis vector depends on the number of components
selected by the PCA stage. In the testing phase the input image is transformed into the Radon
space using that set of directions which were used in the enrollment phase. The PCA reduction is
carried out as same as in the enrollment phase. The resultant vector is projected into the basis
vectors stored in the data base that is by inner product method. The highest product value which
must be higher than a predetermine threshold measures the similarity between the input image
and the specified class. The method which is stated in this paper was evaluated using the ORL
data base which contains photographs of faces taken at the Olivetti Research Laboratory in
Cambridge between April 1992 and April 1994.There are 10 different images of 40 distinct
subjects so there are 400 images in the data base. The images are grayscale with a resolution of
92 x 112. For some of the subjects, the images were taken at different times. There are variations
in facial expression and pose variation about 20 degrees and there is some variation in scale of
up to about 10%. There are some faces with glasses. Some images are shown in figure (2). In
the following sections the discussion of each main part of the method of process is presented.

FIGURE 1: Block diagram for the recognition system.
3.1 Radon Transform
There were many applications of Radon transform like Pose Estimation [17],Texture Analysis
[18], X-ray crystallography and Nuclear Magnetic Resonance(NMR)[19], Image Matching for
translation, rotation and uniform scaling Using Radon Transform[21]. Several definitions of the
radon transform existed. A very popular form expresses lines is:-
t ൌ x ‫כ‬ cosሺθሻ ൅ y ‫כ‬ sinሺθሻ ሺ1ሻ
Where θ is the angle and t is the smallest distance to the origin of the coordinate system. The
Radon transform for a set of parameters (t, θ) is the line integral through the image f(x, y), where
the line is positioned corresponding to the value of (θ and t) in Equation (2).
gሺt,θሻ ൌ ඵ fሺx, yሻδ൫t െ x cosሺθሻ െ y sinሺθሻ൯dx dy ሺ2ሻ
ାஶ
ିஶ
In the above equation g(t,θ) is the Radon Transform of the f(x,y) function at a specified value of t
and θ . The Radon transform can be calculated using FFT by applying the central-slice theorem
[13] which is stated that the 1-D Fourier transform of the integral projection at angle θ is equal to
the slice of the 2-D Fourier transform at the same angle. With the central-slice theorem the Radon
transform can be computed equivalently with 2-D FFT, a Cartesian-to-polar mapping, and a 1-D
FFT. The range of the θ is [0...179] and the range of the variable ( t ) depends on the dimension
of the underling image. In our case the t is in the range [1...112] and θ range is [0...179] that is for
full range directions. So each image is represented in Radon space as a vector of dimensions
equal to (180 x112) = 20160. In our work a subset of θ is selected from the full range using
Particle Swarm Optimization (PSO). The subset of θ values is selected according to the goodness
of the recognition rate achieved as the objective function. Using different values of parameters
used by the classifier a different subset are selected using PSO. Figure (3) shows a full range of θ
Radon transform and figure (4) shows a subset of θ Radon transform.
3.2 Particle Swarm Optimization (PSO)
PSO, first introduced by Kenny and Eberhart in 1995 [22], is one of the evolutionary computation
technology based on swarm intelligence. In a PSO system each solution called a "particle",
particles fly around in the search space of the problem to look for the optimal solution. Each
particle adjusts its position according to the flying experience of its own and the experience of
neighboring particles. Each particle updates its velocity and position using the following equation
[23]:-
Vi(k+1)=Vi(k)+c1* rand1( pbest(k) - Xi(k)) + c2* rand2( gbest(k) - Xi(k)) (3)
Xi (k+1)=Xi(k) + Vi(k+1) (4)
Where ,
Vi is called the velocity for particle i;
Xi is represent the position of particle i ;
Pbest is the best position of ith particle
gbest is the global best position ;
rand is random variable in [0,1];
c1 and c2 are the learning factors;
w is called the inertia weight
To search for optimal solution, each particle changes its velocity according to equation 3. The
value of Vi is clamped to the range [Vmin, Vmax] to avoid excessive roaming of particle outside
the search space. Then each particle moves to a new potential solution using equation 4. This
process is repeated until a stopping criterion is reached. The above equations (4,5) are the basic

equations and not guarantee the global solution. Using those equations PSO may be trapped in
local minima to avoid the local minima there are many variations and improvements to the basic
equations have been suggested [24-37]. In this work we used the PSO in order to select the best
set of directions (the values of θ) to be used in Radon transform. These set is selected from the
full set of θ from 0ᵒ to 179ᵒ in step of 1 degree. There are 24 particles in the swarm are used
with randomly selected values of θ. These particles moved and evolved towards the best
positions that yield a good Recognition rate. The objective function was constructed in order to
optimize both the recognition rate and the number of directions (θ) selected as well. Three sets
are depicted by tables( 1 ,2,3) for three values of N which is the length of the features vector used
by the classifier associated with objective function used. In our experiments, the set with N=60
was used. One thing that be mentioned about PSO is its convergence to a steady state of
accepted recognition rate very quickly and in stable manner.
3.3 Feature Reduction Using (PCA)
The PCA is a statistical method for reducing data dimensions [37,38]. In PCA the training data is
used in obtaining the Eigen basis vectors. Then the training set R and testing set T are projected
into those vectors. The PCA can be summarized by the following steps:-
a. Calculate the mean M of the training set and subtract it from the training set:
M ൌ
ଵ
୬
∑ R୧
୬
୧ୀଵ (5)
For all training set perform R୧ ൌ R୧ െ M
b. Calculate the Eigenvectors and Eigenvalues of the training set covariance matrix ܵ௧
S୲ ൌ R . RT
(6)
and pick the Eigen vectors corresponding to the N largest Eigen values of ܵ௧. These
construct the N principal components matrix ( V).
c. The Basis vectors matrix (U) is constructed as:
U ൌ V . RT
(7)
d. The reduced feature vector is calculated for training and testing data as:
WR ൌ R . U (8)
WT ൌ T . U (9)
The mean M must be subtracted from the testing data T also. Many experiments were
conducted using different numbers of Eigenvectors (N ) between (10-60) and the performance
are reported in figure(5,7 ).
3.4 Linear Discrimenant Analysis (LDA)
The LDA finds a set of basis vectors which maximizes the ratio between-class scatter and within
–class scatter [37]. Given N samples of C classes, let Ni be the number of samples in the ith class
Ci , let Mt be the mean of the whole data set, mi be the mean of the ith class Ci, the between-
class scatter matrix is defined by:
SB=∑ N୧
ୡ
୧ୀଵ ሺmi െ Mtሻ ሺmi െ MtሻT
(10)
And the within-class scatter matrix is defined by

Sw=∑ ∑୫୩‫א‬ୡ୧
ୡ
୧ୀଵ ሺmk െ miሻ ሺmk െ miሻT
(11)
Then the basis vectors is
W= arg max ቀ
|WTSB W|
|WTS౭ W|
ቁ (12)
Solving Equation(9) produces a matrix W whose columns are the eigenvectors corresponding to
the largest eigenvalues of SW
ିଵ
SB. These columns are the linear discriminant functions associated
with classes as a one function for each class. These functions are stored in the database in order
to perform the classification as following:
Each input vector ( T) to be classified is multiplied with W matrix as ( V ൌ Tିଵ
W ) the resulting
vector is the linear scores of the testing data T. The class probabilities are calculated using the
softmax transform as:
P ൌ
ୣ୶୮ ሺVሺ୧ሻ
∑ ୣ୶୮ ሺVሺ୧ሻ౟‫א‬C
(13)
Where C is the set of classes. Each class represents a person in the data base. The value of P
show how much the testing data T is near to a specified class, the higher value is the nearest
class so the classification is done. A threshold value P can be designated with in order to reject
the unknown or to do misclassification.
4. THE EXPERIMENTS
The developed face recognition method was applied to the ORL database. Five experiments
were conducted. Each with different partitioning scenario to the data set and the performance
was evaluated against the number of eigenvectors used see figure (5). The set of eigenvectors is
{10,20,25,30,35,40,45,50,55,60}. The set of directions (angles) used for radon transform is shown
in table (2). The five scenarios are:
a. Scenario #1.
In this scenario the ten images for each person are divided as 5 images for training and 5 images
for testing. The images were randomly selected. The maximum recognition rate was 93% that is
when 25 eigenvectors are selected. See figure (5). The Boxplot is shown in figure (6). It is appear
that the median is 90.5%, and the 75
th
percentile is around 92.5%.
b. Scenario #2.
In this scenario the ten images for each person are divided as 9 images for training and one
image for testing. The images were randomly selected. The maximum recognition rate was
97.5% that is when 35 eigenvectors are selected. See figure (5). See Boxplot at figure (6). It
appears that the median is 95%, and 75
th
percentile around 97%.
c. Scenario #3.
for testing. The images were randomly selected. The maximum recognition rate was 97.5% that is
when 35 eigenvectors are selected. See figure (5). See Boxplot at figure (6). It appears that the
median is 95%, and 75
th
percentile around 97.2%.
d. Scenario #4.
for testing. The images were randomly selected. The maximum recognition rate was 97.5% that is
when 50 eigenvectors are selected. See figure (5). See Boxplot at figure (6). It appears that the
median is 96.7%, and 75th

e. Scenario #5.
for testing. The images were randomly selected. The maximum recognition rate was 95.63% that
is when 60 eigenvectors are selected. See figure (5). See Boxplot at figure (5). It appears that the
median is 94.4%, and 75
th
5. DISCUSSION
In this work the using of Radon transform improves the performance of PCA+LDA techniques in
face recognition. That is if compared with mentioned literature [3, 5, 7, 8, 10, and 13]. The using
of PSO for selecting the best directions ( angles) used by Radon transform give better
performance as compared to [ 7,9]. This means that the subset selected using PSO is better than
the one selected in [7]. From the different scenarios conducted it appears that the performance is
improved with the increased number of images per person in the training set this is clear by
scenario #2 ,#3,#4 . From Boxplot in figure (7), which shows the performance against the number
of eigenvectors used over all scenarios in our experiment, it is clear that the number of
eigenvectors between (30-40) gain the good performance. It is also clear that the (35)
eigenvectors is the best.
6. CONCLUSIONS
A Face Recognition method has been described in this work. The core of this work is to apply the
PCA+LDA in Radon space rather than directly to the images. The images are transformed using
Radon Transform with a specified angles (directions) set determined using PSO in order to
achieve good recognition rate with less computation expensive. The Radon transform used in this
method was FFT based. The full range Radon transform is computational expensive if it is
performed for angles from 0 degree to 180 degree and for a large number of offsets. To reduce
the computations required a subset of angles and offset must be selected. So the PSO was used
to select that subset and maintaining a good recognition rate. This method was verified on ROL
data base using five different scenarios for training set selection. The best recognition rate was
97.5% when only 35 eigenvectors are used. The number of eigenvectors determines the length of
the signature vector that be used for each person in the data base. The recognition rate and the
size of signature that represent each person as well as the computation of Radon transform that a
achieved in this method is better than the related works stated in the literature review in section 2.
2 : Samples from ORL Database

TABLE 1 : angles calculated using PSO N=60
TABLE 2: angles calculated using PSO N=10
TABLE 3: angles calculated using PSO N=32
77 angles calculated using PSO N=60
2 4 11 19 21 23 26 28
29 35 36 39 40 41 42 43
44 46 47 51 52 57 58 59
61 62 65 68 71 73 75 79
80 81 83 84 85 89 90 92
93 95 96 98 99 100 106 108
111 112 119 120 122 126 131 134
124 125 126 130 132 134 135 137
135 140 141 144 145 146 149 155
156 161 162 174 178
1 6 8 10 11 12 14 15
17 20 25 28 30 32 33 35
47 49 52 53 54 56 58 59
60 61 62 63 64 68 69 70
71 72 73 75 79 80 84 85
92 95 96 98 103 104 105 108
109 110 114 115 116 119 121 122
124 125 126 130 132 134 135 137
138 142 143 146 151 152 153 154
156 159 161 166 168 169 170 171
172 173 175 179
1 3 4 6 10 11 16 23
24 25 26 27 28 31 32 33
34 35 36 38 42 43 46 47
48 51 52 53 55 57 58 60
61 62 64 73 79 82 86 87
89 91 92 97 98 99 100 101
103 106 107 108 109 112 118 119
120 121 122 123 124 125 126 128
129 134 136 140 141 142 145 147
149 150 151 152 153 156 158 162
163 164 166 168 171 175 176 177

FIGURE 4 :FFT Based Radon Transform using 90 angles FIGURE 3: FFT Based Radon for an image
transform for an image calculated using PSO
FIGURE 5: Performance against #of eigenvectors for different scenarios.
FIGURE 6: Box Plot show the performance for each scenario.
10 15 20 25 30 35 40 45 50 55 60
80
82
84
86
88
90
92
94
96
98
100
Number of Eign Vectors
RecognitionRate%
Scenario#1
Scenario#2
Scenario#3
Scenario#4
Scenario#5
80
82
84
86
88
90
92
94
96
98
100
1 2 3 4 5
Data Partitioning
Scenario
RecognitionRate%
The 5 Scenarios performance Box Plot
θ (degrees)
x'
20 40 60 80
10
20
30
40
50
60
70
80
90
100
110
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
x 10
4
θ (degrees)
x'
0 20 40 60 80 100 120 140 160
20
40
60
80
100 2000
4000
6000
8000
10000
12000
14000
16000
18000

FIGURE 7: Box plot shows the performance against #of eigenvector cross the 5 scenarios.
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