A Weighted Pseudo-Zernike Feature Extractor for Face Recognition Shahpour Alirezaee Electrical Engineering Department AmirKabir University of Technology Tehran, Iran
[email protected]
University of Windsor Windsor, Ontario, Canada
[email protected]
Hassan Aghaeinia Electrical Engineering Department AmirKabir University of Technology Tehran, Iran
Karim Faez Electrical Engineering Department AmirKabir University of Technology Tehran, Iran
[email protected] Abstract - Pseudo-Zernike polynomials are well known and widely used in the analysis of optical systems. In this paper, a weighted Pseudo-Zernike feature is introduced for face recognition. We define a weight function based on the face local entropy. By this weight function, the role of high information region, i.e. eyes, noses and lips, will be intensified on the extracted features. For classification, a single hidden layer feedforward neural network has been trained. To evaluate the performance of the proposed technique, experimental studies are carried out on the ORL database images of Cambridge University. The numerical results show 98.5% recognition rate on the ORL database with the order 8 of weighted Pseudo-Zernike feature and 44, 98, 40 neurons for the input, hidden, and output layers while this amount is 96% for the original Pseudo-Zernike. Keywords: Face recognition, Feature extraction, PseudoZernike moment.
1
Majid Ahmadi Electrical & Computer Engineering Department
Introduction
Face recognition has been a very popular research topic in recent years. A complete face recognition system should include three stages, face localization, feature extraction and classification [1], [2], [3]. The first stage requires detection of the location of the face, which is difficult, because of the unknown position, orientation and scaling of the face in an arbitrary image. The second stage involves extraction of pertinent features from the localized facial image obtained in the first stage. Finally, the third stage requires classification of facial images based on the derived feature vector obtained in the previous stage. This paper has been focused on the feature extraction. In order to design a high recognition rate system, the choice of feature extractor is very crucial and extraction of pertinent features from two-dimensional images of human face plays an important role in any face recognition system. There are various techniques reported in the literature that
[email protected] deal with this problem. This study has been focused on the Pseudo-Zernike moment [4], [5]. In this paper we have proposed a weighted PseudoZernike feature for face recognition. The weight function is proportional to the local stripe entropy. This weight is capable to intensify the role of high information areas such as eyes, lips and nose regions. This paper is organized as follows. The second section describes the Pseudo-Zernike moments. The weight function and the weighted Pseudo-Zernike feature will be defined in the third section. The numerical results are presented in the fourth section. Finally, the conclusions will be discussed.
2
Pseudo-Zernike Moment Invariants
Statistical-based approaches for feature extraction are very important in pattern recognition for their computational efficiency and their use of global information in an image for extracting features[6]. The advantages of considering orthogonal moments are, that they are shift, rotation and scale invariant and very robust in the presence of noise. The invariant properties of moments are utilized as pattern sensitive features in classification and recognition applications. Pseudo Zernike polynomials are well known and widely used in the analysis of optical systems. Pseudo-Zernike polynomials are orthogonal sets of complex-valued polynomials defined as:
Vn,m(x, y) = Rn,m(x, y) ⋅ exp(j ⋅ m⋅ tan−1(y )) x
(1)
x2 + y2 ≤ 1 Where m ≤ n , n ≥ 0 and Radial polynomials are defined as:
{R } n ,m
Rn , m ( x , y ) =
n− m
∑D
⋅(x2 + y2 ) n , m ,s
s =0
n−s 2
(2)
Where,
Dn, m ,s = (−1) s .
(2.n + 1 − s)! s!.(n − m − s)!.(n + m + 1 − s)!
(3)
The Pseudo-Zernike of order “n” and repetition “m” can be computed using the scale invariant central moments GM pq and the radial geometric moments RM pq as follows:
An ,m =
n− m
n +1
π
+
n +1
π
The proposed weight function, i.e. γ (x ) , is proportional to the stripes entropy in the vertical stripe scanning. We have defined γ (x ) as the normalized value of alternation on the stripe entropy as follows:
2
∑D
n , m ,s ( n − s − m ) even , s =0
k m ⎛ k ⎞ ⎛m⎞ × ∑∑ ( − j ) b ⋅ ⎜⎜ ⎟⎟ ⋅ ⎜⎜ ⎟⎟ ⋅ GM 2 k + m −2 a −b, 2 a +b a =0 b = 0 ⎝a⎠ ⎝b⎠ n− m
Our experimental results show that the entropy measure is a robust feature in presence of noise. For proof the robustness of the entropy measure, the white gaussian noise up to 40 dbw have been added to the database image and the entropy measure has been computed. Figure 1 presents the effects of noise on the face image as well as on the horizontal and vertical stripe entropies. As can be seen (Figure 1), noise has distorted faces considerably. But in the entropy space, not only the shape of entropy function has been preserved but also the important points are unchanged in vertical and horizontal functions. Therefore, the entropy function can be a robust function in the face images.
(4)
γ ( x) =
2
∑D
n , m ,s ( n − s − m ) odd , s = 0 d
m
m
m
H ( x ) = ∑ pi log i =1
Where
k = (n − s − m) / 2 , d = ( n − s − m + 1) / 2 , and RM pq
is as follows:
∑∑f (x, y)(x − x ) (y − y ) p
0
GMpq =
X
( p+q+2)
α
3
x
2 1/ 2
(x − x0)p ( y − y0)q
y
( p+q+2)
α
and x is the center of stripe, and H min , H max are
Based on this weight function we have defined the weighted geometrical and radial moments as:
∑∑f (x, y)((x − x ) +(y − y ) ) 0
(8)
(5)
2
2
m 1 = − ∑ pi log pi pi i =1
minimum and maximum entropy. Figure 2 shows the weight function for two samples of the ORL faces.
q
0
y
0
RMpq =
(7)
Where H (x ) is the Shannon entropy [7]:
⎛ ⎞ ⎛ ⎞ × ∑∑ ( − j ) b ⋅ ⎜⎜ ⎟⎟ ⋅ ⎜⎜ ⎟⎟ ⋅ RM 2 d + m −2 a −b,2 a +b a =0 b = 0 ⎝a⎠ ⎝b⎠ d
H ( x ) − H min H max − H min
∑γ (x)∑f (x, y)(x − x ) (y − y ) p
GM_ newpq =
2
The Weighted Pseudo-Zernike
In face detection and recognition we are interested in high information areas such as eyes, nose, mouth etc. These areas convey fundamental information needed for face recognition. In this study, we are aiming to intensify the role of the high information area in feature extraction. For this reason we have used the local stripe entropy. Based on this idea, each L × W faces is vertically scanned with stripes of height H and width W. The amount of overlap between successive frames is P. In this study, H and P are respectively set to 5 and 2. Calculating the entropy for each stripe yields a value, which is related to the amount of information in that region.
q
0
(6)
X
0
y
( p+q+2)
α
(9)
2
and,
∑γ(x)∑f (x, y)((x−x )
2
0
RM_newpq =
x
1/ 2
+(y − y0 )2 ) (x − x0 ) p (y − y0 )q
y
( p+q+2)
α
2
(10) These moments will be used in the equation (4) for computing the Pseudo-Zernike moments. We have changed the order of Pseudo-Zernike moments from 6 to 10.
Figure 1. Effect of noise on the proposed feature,(a) ORL face sample corrupted with white gaussian noise with power 0, 5, 10, 15, 20, 25, 30, 35, 40 dbw respectively(b) entropy feature for horizontal frame scan (c) entropy feature for vertical frame scan
each person has also changed his/her facial expression in each of 10 samples (open/close eye, smiling/not smiling). The changes in scale have been achieved by changing the distance between the person and the video camera. For some individuals, the images were taken at different times, varying facial details (glasses/no glasses). Each image was digitizedand presented by a 112× 92 pixel array whose gray levels ranged between 0 and 255. In this study, absolute value of the Pseudo-Zernike moments from order 6 to 10 has been selected as a feature (normalized with A00 ). These features are extracted from
Figure 2. Face samples of the ORL database and extracted weight function
4
Neumerical Results
To check the performance of the proposed algorithm, experimental studies are carried out on the ORL database images of Cambridge University. The ORL database contains 400 face images from 40 individuals in different states. The total number of images for each person is 10. None of the 10 samples is identical to any other sample and they vary in position, rotation, scale and expression. The changes in orientation have been accomplished by rotating the person a maximum of 20 degree. For the same subject;
the localized face region [8], [9]. In this paper we have used the method of ref. [9] for face localization. For classification, a three-layer feedforward neural network has been trained [10]. The inputs to the neural network are feature vectors derived from the proposed feature extraction technique. We have set the number of input nodes in the input layer of the neural network equal to the number of feature vector elements. The number of nodes in the output layer is then set to the number of image classes. The number of the hidden layer neurons will be obtained experimentally. In this way, the hidden layer neurons have been increased to yield the best classification rate. The best network specification and related classification rate has been presented in table.1. The proposed method yield the best result of 98.5% recognition rate for the order 8 of the weighted pseudo-Zernike moment as the feature and feedforward neural network (with 44, 98, and 40 neurons for the input, hidden, and output layers) as the classifier.
Table.1. The feedforward network characteristics (PZ; Pseudo-Zernike and WPZ; Weighted pseudo-Zernike) Neural network specification
5
PZ
WPZ
PZ
WPZ
PZ
WPZ
PZ
WPZ
PZ
WPZ
Pseudo-Zernike order
6
6
7
7
8
8
9
9
10
10
Number of features
27
27
35
35
44
44
54
54
65
65
Input layer neurons
27
27
35
35
44
44
54
54
65
65
Hidden layer neurons
54
63
79
77
96
98
114
107
121
118
Output layer neurons
40
40
40
40
40
40
40
40
40
40
Classification rate%
90.25
89.75
91
92.5
96
98.5
95
94.25
94.75
95.5
Conclusion
In this paper a weighted Pseudo-Zernike feature was presented. The weight function is proportional to the local entropy, which can intensify the effects of the high information regions on the facial feature extraction. The Pseudo-Zernike moments from order 6 to 10 was selected as features and one hidden layer feedforward neural network was trained as the classifier. The results indicate 98.5% recognition rate for the 8 order weighted PseudoZernike moments while this amount is 96% for the original Pseudo-Zernike moment.
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[3] Y. Amit, D. Geman, and B. Jedynak, “Efficient Focusing and Face Detection,” vol. 163, pp. 124-156, 1998. [4] R. R. Baily and M. Srinath, “Orthogonal moment features for use with parametric and non-parametric classifiers,” IEEE Trans. Patt. Anal. Mach. Intell. 18, 4, pp.389-398, 1996. [5] S. O. Belkasim, M. Shridhar and M. Ahmadi, “Pattern recognition with moment invariants: a comparative study and new results,” Patt. Recogn. 24, 12, pp.1117-1138, 1991. [6] J.Haddadnia, M.Ahmadi, and K. Faez, “ An efficient feature extraction method with pseudo-zernike moment in RBF neural network-based human face recognition system,” , EURASIP journal on applied signal processing, 2003:9, pp.890-901. [7] E.Loutas, I.Pitas, and C.Nikou, “ Probabilistic Multiple Face Detection and Tracking Using Entropy Measures,” IEEE Trans. on Circuits and Systems for Video Technology, VOL. 14, NO. 1, Jan. 2004 [8] M.Yang, D.J. Kriegman, and N.Ahuja, “ Detecting Faces in Images: A Survey,”, IEEE Trans. on Pattern Analysis and Machine Intelligence, VOL. 24, NO. 1, Jan. 2002. [9]. J. Haddadnia and K. Faez, “Human face recognition based on shape information and pseudo Zernike moment,” 5th Int. Fall Workshop Vision, Modeling and Visualization, Saarbrucken, Germany, 22-24 November, pp. 113-118, 2000. [10]. A.k.Jain, J.Mao, K.M.Mohiuddin, “Artificial neural networks; A tutorial”, Computer, Volume: 29, Issue: 3, March 1996, pp: 31 - 44
