Face Recognition Based on Wavelet Transform and Image Principle Component Analysis

Yang Jun College of Computer

Science, Sichuan Normal University, Chengdu, 610066,

China Institute of Image & Graphic, College of Computer, Sichuan

University, Chengdu 610064, China

yangjun204@yahoo.com.cn

Yuan Hong-zhao Institute of Image & Graphic, College of Computer, Sichuan

University, Chengdu 610064, China

Zhang Xiu-qiong Institute of Image & Graphic, College of Computer, Sichuan

University, Chengdu 610064, China

Gao Zhi-sheng Institute of Image & Graphic, College of Computer, Sichuan

University, Chengdu 610064, China

Abstract

Image principle component analysis (IMPCA) is a

rapid direct feature extract approach from matrix. We present the basic theory of IMPCA from the view of minimizing the mean reconstruction error. We analyze the feature generated from IMPCA and find they present row characters. Wavelet transform can be used in reducing noise of images and the wavelet image should be more suitable for recognition. Our proposed method firstly transforms face image with wavelet and gets coefficients of different frequency, then horizontal detail coefficient is enhanced. The image generated by wavelet inverse transform is as new object and is recognized using IMPCA. The experiment result on ORL face database presents the proposed method is efficient and the recognition accuracy rate is better than IMPCA only. Keywords: image principle component analysis

(IMPCA); wavelet transform; face recognition;

1. Introduction

Feature extract is key point for face recognition. Principle component analysis (PCA) is a classic method for feature extract and reducing feature dimensions based on minimizing the mean reconstruction error. Sirovich and Kirby [1] applied PCA for efficient representation of a face image for the first time. They represented a face image as an addition

of a small number of weight values defined as a facial basis vector and mean vector. Since Turk and Pentland [2] proposed the Eigenfaces method for face recognition in 1991, the classic method based on appearance, many modified methods [3,4,5] were proposed. These methods based PCA regard a face image as a vector by concatenating its columns. Because resolving eigenvectors of covariance matrix of these high-dimensional vectors is needed for getting transforming axes, the implementation of PCA is time consuming and it is difficult to get accurate eigenvectors [6]. Yang et al. [6,7] proposed a novel image representation and recognition technique, called image PCA (IMPCA) which directly extracted feather from image matrix. The dimension of covariance matrix used in IMPCA is far lower than PCA. So IMPCA not only requires much less time for training and feature extract, but also can get more accurate eigenvectors. Wang et al. [8] considered that IMPCA can be regarded as a PCA with rows of image. Zhang and Zhou [9] proposed a (2D)2PCA method which used row characters and column characters of images. Xu et al [10] presented that IMPCA is the best approach for directly extract features from matrices for minimizing the mean reconstruction error. Wavelet is powerful mathematic tool, often used in weakening noise and compressing of image. Since the feature extracted by IMPCA strengthen the row characters, we think that the image generated by wavelet inverse transform which horizontal detail coefficient is

2008 International Conference on Computer and Electrical Engineering

978-0-7695-3504-3/08 $25.00 © 2008 IEEE

DOI 10.1109/ICCEE.2008.34

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enhanced in wave field would be more suited for recognition based on IMPCA. 2. IMPCA based on image reconstruction

We get a feature vector y by projecting a image X(m,n) to a vector u as a coordinate axis using (1) by IMPCA:

Xuy = (1) If the number of axes is n, then we can get vectors,

y1=Xu1, y2=Xu2,…,yn=Xun. In case the axes satisfy ui

Tuj=1 where i=j and uiTuj=0 on other, 1<i,j<n, then

∑ == n

iT

ii uyX1

. Where the number of axes is lower

than n, the reconstructed image ∑ =

∧= d

iT

ii uyX1

and

the deviation of X and ∧X is:

∑∑ +=+=

∧==− n

diT

iin

diT

ii uXuuyXX11

(2)

If we use the square of the Frobenius norm of a matrix as the scale of error, the mean square error of training images will be:

⎥⎦⎤

⎢⎣⎡ −−=−

∧∧∧)))((()||(|| 2 T

F XXXXtrEXXE (3)

According to (2), we have TXXXX ))((

∧∧−− ＝∑ +=

n

diTT

ii XuXu1

(4)

iXu is a m×1dimension vector and TTi Xu ,1×m

here, so we have

iTT

iTT

ii XuXuXuXutr =)( (5) According to (3),(4),(5), it is certain that

∑ +=

∧=− n

di iTT

iF uXXEuXXE1

2 )()||(|| (6)

Resolving the minimum of (6) means minimizing the mean error of reconstruction images. (6) is a function of variable ui and Langragian multiplier method can be implemented for the problem. So we get (7) when (6) reach its extreme.

iiiT uuXXE λ=)( (7)

(7) presents ui is the eigenvector of correlation matrix. of X and the error is:

∑ +=

∧=− n

di iFXXE1

2 )||(|| λ (8)

So when the coordinate axes are composed of n eigenvectors associated n largest eigenvalues of

)( XXE T , the mean reconstruction error reaches minimum value.

Coordinate axes are got by (9) in classic IMPCA [7] which has the meaning of maximize the total scatter of

train samples in extracted feature. Here X is mean value of training samples. If images are centered in advance, they will be equal.

iiiT uuXXXXE λ=−− ))()(( (9)

Fig.1 shows some reconstruction images of a face image by IMPCA. It presents the row characters are primary feature of IMPCA.

2 4 6 10 20 Figure 1: Reconstruction images of IMPCA (number

means n largest eigenvectors were preserved)

3. Wavelet transform of image

The analysis and synthesis procedures lead to the pyramid-structured wavelet decomposition [11]. The 2-D wavelet analysis operation consists in filtering and down-sampling horizontally using the 1-D lowpass filter L and highpass filter H to each row in the image I(x, y), producing the coeIcient matrices IL(x, y) and IH (x, y).Vertically filtering and down-sampling follows, using the lowpass and highpass filters L and H to each column in IL(x, y) and IH (x, y) and produces four subimages ILL(x, y), ILH (x, y), IHL(x, y) and IHH (x, y) for one level of decomposition. ILL(x, y) is a smooth subimage corresponding to the low-frequency band of the multi scale decomposition (MSD) and can be considered as a smoothed and subsampled version of the original image I(x, y), i.e. it represents the coarse approximation of I(x, y). ILH (x, y), IHL(x, y) and IHH (x, y) are detail subimages, which represent the horizontal, vertical and diagonal directions of the image I(x, y).They can be expressed as follows:

),()2()2(),(,

mkIymlxklyxImkLL ∑ −−=

),()2()2(),(,

mkIymlxkhyxImkLH ∑ −−=

),()2()2(),(,

mkIymhxklyxImkHL ∑ −−=

),()2()2(),(,

mkIymhxkhyxImkHH ∑ −−= (10)

The 2-D pyramid algorithm can iterate on the smooth subimage ILL(x; y) to obtain four coefficient matrices in the next decomposition level and so on. Fig.2 shows a face image and its 2 level wavelet images.

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(a) origin image (b)2 level wavelet image

Figure 2: A face image and 2 level wavelet decomposition

4. Feature extract and recognition

Wavelet transform can be used in image denoise. We think the smooth image in some wavelet decomposition level can be a better recognition object for noising being weaken. On the other hand, the image generated by wavelet inverse transform which horizontal detail coefficient is enhanced in wave field would be more suited for recognition based on IMPCA. Our approach firstly decomposes an image with someone wavelet. Coarse approximation ILH (x, y) is enhanced by ILH (x, y)=eILH(x, y), where e>1.The restore image generated by inverse wavelet transform is used as the new recognition object based on IMPCA. Nearest neighborhood classifier is utilized in recognition phase and the distance of probe image and template is defined with Frobenius norm of deviation matrix of probe and template. If number of template is N, the distances of a probe face with each template are expressed D={d1,d2,…dN}. So class associated with minimum value of D is decided as the class of probe face. 5. Experiment

This experiment was performed on the ORL database. All the face images of the ORL face database were obtained against a dark homogeneous background. These images contain various facial expressions (smiling/no smiling, open/closed eyes) and facial detail. The subjects were in up-right, frontal position with tolerance for some tilting and rotation of up to about 20 degree. For each of the 40 subjects, 10 different images were created. Db4 was selected as wavelet base in our experiments.

Table 1 shows the accuracy rates of origin images, 3 level wavelet approximate images and 3 level wavelet approximate images enhanced horizontal detail when the first 2, 3, 4 or 5 face images of all the subjects were, respectively, used as training and template samples, and the corresponding remaining images were regarded as probe samples. The number of coordinate axes is six and. the enhancing multiple e is 1.1. The

result presents that the wavelet image and enhanced wavelet image is more suitable for recognition no where number of training images.

Table 1: Recognition accuracy rates in various numbers of training samples

number of training images

2 3 4 5

origin images 82.19 84.64 89.17 91.50

3 level wavelet images 89.69 91.79 92.92 93.00

enhanced 3 level wavelet images 90.31 92.14 93.33 93.50

We selected first 5 images of every person were

regarded as training samples and others as probe images in the next experiments. Fig.3 shows accuracy rates vary with number of coordinate axes and the enhancing multiple e is 1.1.

2 3 4 5 6 7 8 9 100.88

0.89

0.9

0.91

0.92

0.93

0.94

number of eigenvector

accu

racy

rat

e (%

)

origin image3 level wavelet imageenhanced 3 level wavelet image

Figure 3: Accuracy rate curves on different coordinate

axes

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 20.925

0.93

0.935

0.94

0.945

0.95

accu

racy

rat

e (%

)

e

Figure 4: Accuracy rate variety with the magnified parameter e

Fig.4 shows accuracy rates vary with the magnified parameter e. It presents that only when the parameter e is some one value, the accuracy rate can reach maximum.

Table 2 shows the accuracy rates, training time and recognition time of proposed methods and PCA and the number of axes is 8. From the table, we can see recognition time of the methods based on wavelet is longer than PCA and only IMPCA because of wavelet

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images extract, but the training time is more less because the dimension of wavelet images is lower than origin image.

Table 2: Training and recognition time of different approaches

accuracy rate

recognition time

trainingtime

origin image 0.915 3.812 0.313 3 level wavelet

image 0.925 9.406 0.047

enhanced 3 level wavelet image 0.93 12.735 0.047

PCA(170 eigenvectors) 0.885 3.891 12

6. Conclusion

We proposed a face recognition method that combing wavelet and IMPCA. We extracted more suitable feature by enhancing the horizontal detail coefficient in wavelet field. The experiment result presents that the method based on wavelet decomposition has more accuracy rate than only IMPCA and PCA and appropriate magnifying the horizontal detail coefficient in wavelet is helpful to improve accuracy rate. Researching the impacts of subimages in wavelet field for recognition is the next work. References [1] M Kirby, L Sirovech, Application of the KL procedure for the characterization of human Faces. IEEE Trans. on Pattern Analysis and Machine Intelligence, 1990, 12(1): 103-108.

[2] M Turk, A Pentland,. Eigenfaces for recognition, Cognitive Neuroscience, 1991, 3(1): 71-86. [3] M H Yang, Kernel Eigenfaces vs. Kernel Fisherfaces: face recognition using Kernel methods. in: IEEE Conference Automatic Face and Gesture Recognition (AFGR), 2002, pp. 215–220 [4] R Gottumukkal, V K Asari, An improved face recognition technique based on modular PCA approach, Pattern Recognition Letter. 2004, 25 (4) 429–436 [5] C. Twining, C. Taylor, The use of kernel principal component analysis to model data distributions, Pattern Recognition, 2003,36 (1): 217–227. [6] J Yang, D Zhang, A F Frangi, et al. Two dimensional PCA: A new approach to appearance-based face representation and recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2004, 24(1):131-137. [7] J Yang, J Y Yang, From image vector to matrix: A straightforward image projection technique—IMPCA vs PCA. Pattern Recognition, 2002, 35(9): 1997-1999. [8] L W Wang, X Wang, X R ZHang, et al. The Equivalence of Two-dimensional PCA to Line-based PCA,. Pattern Recognition Letters, 2005, 26(1): 57-60. [9] D Q Zhang, Zh H Zhou, (2D)2PCA: Tow-directional Tow-dimensional PCA for Efficient Face Representation and Recognition, Neurocomputing, 2005, 69(1-3): 224-231 [10] Y Xu, J Yang, Y N Zhao, et al. An Approach to Image Dimension Reduction and Its Application to Face Images, Journal of Electronics & Information Technology, 2008, 30(1):180-185 [11] S.G. Mallat, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Trans. on Pattern Analysis and Machine Intelligence. 11 (1989) 674–6

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