Introduction
Face recognition research is important for both psychology and information science. How do we humans recognize faces and how faces are represented or encoded in our brain, are both long debated issues. Some of the theories of face recognition characteristics have been implemented in computer-based face recognition system. Following is a brief summary of the common approaches to face recognition.
An appearance based holistic approach to face recognition was introduced by Kirby & Sirovich (1990), and Turk & Pentland (1991) by representing facial images as eigenfaces. Subsequently, the concept of Fisher-Faces was introduced (Belhumeur et al., 1997; Etemad & Chellappa, 1997; Zhao et al., 1998). Liu & Wechsler (2001) introduced an enhanced Fisher classifier method for face coding and recognition. It relied on an enhanced Fisher Linear Discriminant model that used integrated shape and texture features (Liu & Wechsler, 2001). In a recent work, Vasilescu & Terzopoulos (2002) proposed a different type of facial representation named Tensor-Face.
In the actual practice of face detection, the image size can be quite small and Zhao et al. (1999) demonstrated that the image size could be very small for holistic face recognition. For example, a Linear Discriminant Analysis (LDA) system used 12×11 image for face recognition. Lin et al.’s (1997) Probabilistic Decision-Based Neural Network (PDBNN) system used 14×10, while neuropsychological research has shown that for human perception a minimum image of 18×24 is acceptable. Moreover, Zhao et al. (1999) insisted that there exists a universal face subspace of fixed dimension. For holistic recognition this means that the image size does not matter as long as it is larger than the subspace dimension. Zhao et al. also showed that smaller images perform slightly better perhaps due to the improvement of signal-to-noise ratio with the decrease in image size. More studies on the size of image and filter size were discussed in a recent paper by Zhang et al. (2006).
Lin et al. (1997) used a PDBNN method to create fully automatic face detection and recognition system. Shan et al. (2003) presented a method for lighting, expression and viewpoint independent face recognition by improving the eigenfaces method (Turk & Pentland, 1991). Bartlett et al. (2002) presented an in-depth analysis of the Independent Component Analysis (ICA) and its strength over the eigenface approach for face recognition. A comparative study on the effect of image compression techniques on the PCA, LDA and ICA was performed by Delac et al. (2007). Different ICA (Cao et al., 2004), two-dimensional (2D) PCA (Pang et al., 2008), and marginal fisher analysis-based face recognition approaches are also available in recently published works (Xu et al., 2005). Yan & Zhang (2008a, 2008b) proposed a method for face recognition based on correlation filter based class-dependence feature analysis.
Lades et al. (1993) applied Gabor wavelet for face recognition, using the Dynamic Link Architecture (DLA) framework. At first the DLA computes the Gabor jets and then it performs a flexible template comparison between the resulting image decompositions, applying graph-matching methods. In a later work Wiskott et al. (1997) expanded the DLA and developed a Gabor wavelet-based elastic bunch graph matching method that was used to recognize human faces. Lyons et al. (1999, 2000) proposed a two-class categorization of gender, race, and facial expression from facial image based on the 2D Gabor wavelet representation and the labeled elastic graph matching. Donato et al. (1999) have compared a method based on Gabor representation with other techniques, finding that the former provided better performance. In a series of work, Liu combined Gabor features with enhanced Fisher linear discriminant methods (Liu, 2002), kernel PCA with fractional power polynomial models on the Gabor features (Liu, 2004) and, Liu & Wechsler (2003) applied Gabor+PCA+ICA method for face recognition. Gabor representation of face (Liu, 2002; Liu, 2004; Liu & Wechsler, 2003; Lyons et al., 1999; Lyons et al., 2000; Wiskott, 1997), facial expression (Amin et al., 2005; Dailey et al. 2002), and gait (Tao et at., 2007) have shown good performance in classification and identification. Among other feature extraction and subspace projection method includes local binary pattern (LBP) texture features (Ahonen at al., 2006), effective part-based local representation method named locally salient ICA (LS-ICA) (Kim et al., 2005), and appearance based face recognition method called the Laplacianface approach (He et al., 2005).
There are two implementations of Gabor wavelet in vision science that are adopted from Gabor’s theory of communication (Gabor, 1946). One was proposed by Daugman (1985) in 1985, and the other one is Log-Gabor implementation proposed by Field (1987) in 1987. In this paper the results for applying Gabor and Log-Gabor filter to extract the initial features for face recognition are investigated. This experiment constructs 24 different filters for each of the Gabor and Log-Gabor wavelet. For both the wavelets, filters are created at eight orientations {0,π/8,π/4,3π/8,π/2,5π/8,3π/4,7π/8} for three scales (frequencies). Two major observations are (1) the recognition accuracy for the Gabor filter is maximum at orientation zero (
) and for Log-Gabor filter at orientation three (
) for a given frequency, if the orientation is considered with respect to the aligned face, (2) lower the frequency of a filter at a given orientation, higher the recognition accuracy.
The system is built based on the following hypothesis: If a set of subjects are represented as, s={s1,s2,…} then the set of images portrayed by the ith subject at the jth pose (or expression) is represented as, ei,j={ei,j,1,ei,j,2,…} in the image space. In this context, after applying Gabor or Log-Gabor filters on each of the images of ei,j, will produce Gi,j={Gi,j,1,Gi,j,2,…} as
Application of PCA on each of the Gabor or Log-Gabor feature vectors of Gi,j will produce 
as
Then classifiers (PNN) can be trained with a sub-set of 
to learn the class information. This means that after applying Gabor-PCA or Log-Gabor-PCA transformation of an image (ei,j,k), classifiers can still be used on the lower dimensional representation (Pi,j,k) of the image (ei,j,k) to identify the person (i) in that image. More precisely, it is possible for a classifier to associate the facial image (ei,j,k) in a lower dimensional (Gabor-PCA or, Log-Gabor-PCA) representation (Pi,j,k) with the person (i) in the image.