Face recognition using Gabor-based complete Kernel Fisher Discriminant analysis with fractional power polynomial models

O R I G I N A L A R T I C L E

Face recognition using Gabor-based complete Kernel Fisher

Discriminant analysis with fractional power polynomial models

Received: 20 December 2006 / Accepted: 6 April 2009 / Published online: 28 April 2009
Springer-Verlag London Limited 2009

Abstract This paper presents a novel face recognition method by integrating the Gabor wavelet representation of face images and the enhanced powerful discriminator, complete Kernel Fisher Discriminant (CKFD) with frac-tional power polynomial (FPP) models. The novelty of this paper comes from (1) Gabor wavelet, is employed to extract desirable facial features characterized by spatial frequency, spatial locality and orientation selectivity to cope with the variations in illumination and facial expressions, which improves the recognition performance; (2) a recently proposed powerful discriminator, namely CKFD, which enhances its discriminating ability using two kinds of discriminant information (i.e., regular and irreg-ular information), is employed to classify the Gabor fea-tures; (3) the FPP models, are employed to CKFD analysis to enhance the discriminating ability. Comparing with existing principal component analysis, linear discriminant analysis, kernel principal component analysis, KFD and CKFD methods, the proposed method gives the superior results with the ORL, Yale and UMIST face databases.

Keywords Face recognition
Gabor wavelet
Kernel-based method
Complete Kernel Fisher Discriminant (CKFD)
Fractional Power Polynomial (FPP) models

1 Introduction

Face recognition has become an active research area in recent years due to its wide applications, and many approaches have been developed in the last years. Authors consider how to enhance the recognition performance from extracting what features to represent a face image and classifying a new face image with what classifier based on this representation. On the feature extraction, the current methods are classified into two parts, one is based on signal processing method, and other is based on machine learning methods. For the first one, Gabor wavelets are widely used to extracting the facial features for recognition. Gabor wavelets can capture the properties of spatial localization, orientation selectivity and spatial frequency selectivity to cope with the variations in illumination and facial expressions because its kernels are similar to the 2D receptive field profiles of the mammalian cortical simple cells. The Gabor feature vector is therefore derived from the Gabor wavelet representation of face images for face recognition. Gabor methods were reported to perform excellently on feature extraction for face recognition in the previous works [1–5]. On the feature extraction based on machine learning, dimensionality reduction is a popular method and widely used in face recognition. Among them, the most popular methods are principal component analysis (PCA) [6–8], independent component analysis [9,10] and linear discriminant analysis (LDA) [6]. Moreover, in recent years, kernel-based nonlinear feature extraction techniques

J.-B. Li (&)

Department of Automatic Test and Control, Harbin Institute of Technology, 339, 150001 Harbin, People’s Republic of China e-mail: [email protected]

J.-S. Pan

Department of Electronic Engineering, National Kaohsiung University of Applied Sciences, D415 Chien-Kung Road, Kaohsiung 807, Taiwan

Z.-M. Lu

Visual Information Analysis and Processing Research Center, Harbin Institute of Technology Shenzhen Graduate School, Room 202L, Building No. 4, HIT Campus Shenzhen University Town, 518055 Xili, Shenzhen, People’s Republic of China

123

have attracted much attention in the areas of pattern rec-ognition and machine learning [11–13]. Some algorithms using the kernel trick are developed in recent years, such as kernel principal component analysis (KPCA) [14], kernel discriminant analysis (KDA) [15] and support vector machine [16]. KPCA was originally developed by Scho¨lkopf et al. [17], while KDA was first proposed by Mika et al. [15]. KDA has been applied in many real-world applications owing to its excellent performance on feature extraction. Researchers have developed a series of KDA algorithms [12,18–21]. Recently, a novel improved KDA algorithm, complete Kernel Fisher Discriminant (CKFD), is proposed for face recognition [22].

In this paper, we propose a novel face recognition method using Gabor-based CKFD with FPP models. The proposed method, which is robust to variations in illumi-nation and facial expression, utilizes the enhance discrim-inator, CKFD [4], to classify Gabor features derived from the Gabor wavelet representation of face images. To make full use of all the features produced by the different Gabor kernels, we adopt the CKFD with FPP models classifier, which applies the fractional power polynomial (FPP) models [1] to enhance discriminant power, to derive a low-dimensional feature representation with enhanced dis-crimination power by reducing the dimensionality of the Gabor vector space. The feasibility of the novel Gabor-based CKFD with FPP models method is successfully tested with the ORL, Yale and UMIST face databases, the variations of whose images are across pose, time and facial expression. The effectiveness of the proposed method is shown in terms of both absolute performance indices and comparative performance against some popular face rec-ognition schemes such as PCA, LDA, KPCA, KFD and CKFD methods.

The remainder of this paper is organized as follows. A review of Gabor wavelets and the CKFD with FPP models classifier is presented in Sect.2. The proposed method, namely Gabor-based CKFD with FPP Models, is intro-duced in Sect.3. In Sect.4, simulations with two face databases are presented to demonstrate the effectiveness of Gabor-based CKFD with FPP models method for face recognition. Conclusions are summarized in Sect.5.

2 Background

Among various face recognition techniques, the dimen-sionality reduction technique is exciting since the low-dimensional feature representation with high discriminatory power is very important for face recognition (FR) systems, and PCA and LDA are classic methods for dimensionality reduction and feature extraction. As the linear methods,

although successful in many cases [3], PCA and LDA cannot provide reliable and robust solutions to those FR problems with complex face variations since the distribu-tion of face images under a perceivable variadistribu-tion in view-point, illumination or facial expression is highly nonlinear and complex. Recently, researchers applied kernel machine techniques to solve the nonlinear problem successfully [11, 13, 14]. Especially, KPCA and Kernel Fisher Dis-criminant (KFD) have been developed and widely used in face recognition [12, 15–20]. Many researchers have developed the KFD method [4–6]. Especially, Zhang [4] proposed the CKFD by improving the KFD method using two kinds of discriminant information, i.e., the regular and irregular information. In the kernel machine, three kinds of kernels, i.e., polynomial kernels, Gaussian kernels, and sigmoid kernels are widely used. Wu [21] proposed the FPP models to enhance the performance of kernel machine. A FPP is not necessarily a kernel, as it might not define a positive semi-definite Gram matrix, thus the FPPs are called models rather kernels.

The Gabor wavelets can capture the properties of spatial localization, orientation selectivity and spatial frequency selectivity to cope with the variations in illumination and facial expressions. Wu [21] proposed a method by com-bining KPCA and Gabor wavelet for face recognition. Donato et al. [23] have recently shown through simulations that the Gabor wavelet representation gives better perfor-mance than other techniques for classifying facial actions.

2.1 Gabor wavelets and feature representation

The Gabor wavelets, whose kernels are similar to the 2D receptive field profiles of the mammalian cortical simple cells, exhibit desirable characteristics of spatial locality and orientation selectivity, and are optimally localized in the space and frequency domains [21]. A 2D Gabor function g(x, y) can be defined by:

gðx; yÞ ¼ 1 2prxry
 exp 1 2 x2 r2 x þy 2 r2 y ! þ 2pjWx " # ð1Þ

Its Fourier transform G(u, v) can be written by:

Gðu; vÞ ¼ exp 1 2 ðu  WÞ2 r2 u þv 2 r2 v " # ( ) ð2Þ

where W denotes the center frequency of G(u, v) along the u axis, ru¼r_2px and rv¼r_2py. rx and ry characterize the

spatial extent along x and y axis, respectively, while ruand

rv characterize the band width along u and v axis,

respectively. A self-similar filter dictionary can be obtained by proper dilations and rotations of g(x, y) through the generation function:

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In the first part of simulations, Gabor-based CKFD with FPP models method performs better than with Gaussian kernels and polynomial kernels. Although a FPP model might not define a positive semi-definite Gram matrix, it has been successfully used in practice. As results shown in our simulations, FPP models enhance the face recognition performance.

The advantage of Gabor feature characterized by spatial frequency, spatial locality and orientation selectivity to cope with the variations due to illumination and facial expression changes, is approved in the second part of simulations. As the results shown in the simulations, Gabor wavelets improve the face recognition performance. What attracts our attention is that Gabor wavelets with low number of scales perform better than ones with high number of scales, while the choice of the number of ori-entations affects not so much the recognition performance. For the face images, the distribution of feature information mostly converges in the low frequency phase, so overfull high frequency information will influence representation of the discriminant features.

Selection of kernel functions and kernel parameters will influence the recognition performance straightly and the parameters are selected through cross-validation method. It is worth to study further that kernel parameters are auto-matically optimized.

We implement the simulation with ORL face database, Yale face database and UMIST face database. The face images of the three face databases are taken under different lighting conditions and different facial expressions and poses. In all simulations, our approach consistently per-forms better than the PCA, LDA, KPCA, KFD and CKFD approaches. Our method also provides a new idea to do with PIE problem of face recognition.

6 Conclusion

A novel face recognition method based on a novel Gabor-based CKFD with FPP models is proposed in this paper. In the proposed method, we apply the enhanced powerful discriminator, CKFD with FPP models, to classify Gabor features derived from the Gabor wavelet representation of face images. Simulation results show that enhancing performance using Gabor wavelets and FPP models is feasible. On the other hand, the proposed method performs better than other popular face recog-nition methods, i.e., PCA, LDA, KPCA, KFD and CKFD. Results also show that the proposed method is robust to the changes in pose, illumination and expres-sions. Besides the superiority of our approach, some issues should be studied in the feature work. Selection of kernel functions, kernel parameters and the fusion

coefficient of CKFD are through the simulations, so how to choose them is our research topic in the future work.

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