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Department of Electrical Engineering, Southern Taiwan University
Design of PCA and SVM based face
recognition system for intelligent
robots
Department of Electrical Engineering, Southern Taiwan University, Tainan
County, Taiwan, R.O.C.
Ming-Yuan Shieh, Kuo-Yang Wang, Juing-Shian Chiou,
Yu-Chia Hu, Chung-Chieh Lien and Shih-Wen Cheng
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Department of Electrical Engineering, Southern Taiwan University
Outline
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Abstract
Introduction
Face recognition system
Principal Component Analysis
SVM for recognition
Experimental results
Conclusion
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Department of Electrical Engineering, Southern Taiwan University
Abstract

This paper proposed the image recognition system that
integrates principal component analysis (PCA) and support
vector machine (SVM) for intelligent robots.

The integrated scheme aims to apply the SVM method to
improve the validity of PCA based image recognition
system on dynamic robotic visual perception. Experimental
results show that the proposed method simplifies features
effectively and obtains more accurate classification.
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Introduction

The proposed scheme is applied to the visual perception
system of the intelligent robot – Fairy robot for facial
recognition. From several experiments, the results show
the integrated scheme really benefits the human-robot
interaction.
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Face recognition system
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The procedures of the face detection and recognition
system are shown in Figure 1.
Fig. 1. The system flowchart of face detection and recognition.
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Principal Component Analysis(1/4)
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Suppose there are M samples of normalized facial images,
where each one is denoted by anN  N array. By rearranging
each array into a N 2 1 vector, the M samples can be as M
vectors, denoted as Γ1 ,Γ 2 ,...,Γ M . To average them, we get the
average vector as  .
Assume A  1 , 2 ,...,  M , the covariance matrix of all facial
samples C will be
1
C
M
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M
 
i 1
i
T
i
 AAT
(1)
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Department of Electrical Engineering, Southern Taiwan University
Principal Component Analysis(2/4)
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One can determine the eigenvalues and eigenvectors of C by
Cui  i ui i  1,2, L, N 2
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One can compute the eigenvalues and the eigenvectors of
the matrix , as shown in next equation, firstly because its
dimension is only M  M.
AT Avi   i vi i  1,2, L, N 2
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(2)
(3)
To multiply both sides of upper equation by the matrix A,
we have
AAT Avi   i Avi
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(4)
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Department of Electrical Engineering, Southern Taiwan University
Principal Component Analysis(3/4)
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In comparison with (2) and (4), while
ui  Avi

i   i

(5)
One can determine the eigenvalues and the eigenvectors of
C from (3). The eigenvector ui denotes the eigenface of ith
sample face as shown in (6).
M
ui    j vij
(6)
j 1
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Principal Component Analysis(4/4)
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If we sort the eigenvalues of all samples and then arrange
the relative eigenvectors into an eigenspace. Determine the
weighting matrix W of the eigenspace as (7)
i  uiT ( i  )  uiT  i

 W  1 , 2 ,...,  M 
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(7)
The vectors in the matrix W can be regarded as trained
image data of a sample. Each sample image has a relative
matrix W. While finish the computation of W for all
samples, it means the training of the face image database
has been accomplished.
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SVM for recognition(1/3)
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When we use the PCA to identify target feature weight will
be followed by the results using SVM recognition. First we
define the training sample:
(Wcp1 , y1 ),......,(Wcpq , yl ), Wcpq  R n q  1, 2,......, l , yq {0,Wi }
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(8)
In order to find the division of the hyperplane, we had to
resolve the question of quadratic optimization. The
constraints were
yq (w  Wcpq  b)  Wi q  1,2,......l
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(9)
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SVM for recognition(2/3)
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 w 
2
We also had to determine the minimum value of
.
So, we used the Lagrange multiplier to resolve the question
of quadratic optimization with linear constraints. We
obtained
1 2 1
L( w, b, a)  w   aq [ yq ( w  Wcpq  b)  Wi ],
2
q 1
aq  0

1
w
2
(10)
After performing the substitution, we were left with the
new equation
LD 

q

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1
2
 
q
j yq y jWcpqWcpj
(11)
qj
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Department of Electrical Engineering, Southern Taiwan University
SVM for recognition(3/3)
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After the optimal solution to the dual question had been
identified, each Lagrange modulus was expected to map
onto each trained data. The following equation is the final
function
 
f Wcp
 l

 sgn   q yq WcpqWcpj  b 
 q 1


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

(12)
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Experimental results
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Figure 2 shows the processed images which consist of the
ones after skin color segmentation, Sobel edge detection,
elliptic detection or face recognition.
Fig. 2. The screen of the proposed system interface
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Conclusion
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The PCA and SVM based image recognition system is
proposed for solving face detection and recognition
problems on human-robot interaction. The captured face
images are preprocessing by the PCA. Then, these data
will be analyzed by the SVM. It results in more accuracy
on distinguishing facial features for face recognition. The
experimental results demonstrate the feasibility of the
proposed method.
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Department of Electrical Engineering, Southern Taiwan University
Thanks for your attention!
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