An enhanced subspace method for face recognition

Abstract

In this paper we introduce a new face recognition approach based on the representation of each individual by several lower dimensional subspaces obtained by an unsupervised clustering of different poses: this provides a higher robustness to face variations than traditional subspace approaches. A set of subspaces is created for each individual, starting from a feature vector extracted through a bank of Gabor filters and non-linear Fisher transform. Extensive experiments carried out on the FERET database of faces, which is the most common benchmark in this area, prove the advantages of the proposed approach when compared with other well-known techniques. These results confirm the robustness of our approach against appearance variations due to expression, illumination and pose changes or to aging effects.

Introduction

Face images can be represented by feature vectors in a high dimensional vector space, obtained by a simple raster scanning of the face image or by means of some more sophisticated feature extraction techniques such as discrete cosine transform (DCT) (Manjunath et al., 1992), Gabor wavelet decomposition and local scale interaction (Pan et al., 2000), fractal image coding (Komleh et al., 2001) and many others. The processing of vectors in such a space is usually a difficult task due to some problems that characterize high dimensional spaces known as “dimensionality curse”. A general approach adopted to deal with this problem is to reduce the dimensionality of the feature vectors by means of dimensionality reduction transforms that allow to retain only the most significant dimensions to represent or discriminate the face images. In the last years, a variety of dimensionality reduction transforms have been applied in the context of face recognition (Franco et al., 2003): Karhunen-Loève (KL) transform (Turk and Pentland, 1991) (also known as Principal Component Analysis), which has obtained a renewed interest for the representation and recognition of faces, singular value decomposition (SVD) (Vasilescu and Terzopoulos, 2002), factor analysis (FA) (Baek and Draper, 2002) and discriminant analysis (LDA) (also called Fisher discriminant analysis) (Zhao, 1999). Some extensions of Principal Component Analysis have been studied and applied to face recognition: nonlinear principal component analysis (Krame, 1991), kernel principal component analysis (Yang et al., 2000) and independent component analysis (Li et al., 2001). Recently, several works proposed effective subspace-based approaches, where the retained dimensions are chosen according to class-specific features instead of taking into account the whole sample variability (Belhumeur et al., 1997). Some authors introduced a mixture of principal components (Cappelli et al., 2002) where the data distribution is represented using a mixture of eigenspaces. More sophisticated approaches have been proposed by Zhao (1999), with the aim of accounting for non-linear face variations. A comparative performance analysis carried out in (Belhumeur et al., 1997) among several subspace methods shows that the method based on Fisher transform performs significantly better than the others.

The approach here presented, called enhanced subspace method (ESM), is based on subspace-classification (Oja, 1983); in this work more subspaces for each individual are created using unsupervised clustering methods (we tested fuzzy C-means (Bezdek, 1981), EM (Duda et al., 2000) and K-means (Duda et al., 2000)). This allows to better represent the intra-class variability that characterizes face images. Moreover, observing that face recognition can be considered a complex non-linear problem, we adopt a non-linear approach to feature extraction, in order to achieve a more effective global class separability: the feature extraction process is based on Gabor filters, followed by a dimensionality reduction performed using non-linear Fisher transform (NLF) (Duin et al., 2000).

The experimental results obtained on the most common database in this field (FERET, Phillips et al., 2000) show that our approach outperforms other subspace methods reported in the literature. The system is evaluated not only on the basis of recognition accuracy, since the use of this unique indicator is insufficient for a significant evaluation of the approach; other parameters characterizing the security level of the system, such as EER and Zero-FAR are considered. In particular the system presented in this work not only gives good recognition performance (high accuracy), but also allows very low values of EER and Zero-FAR to be obtained. The results on FERET database are particularly interesting since they prove the effectiveness of our method in dealing with problems where only few poses are available for each individual (only one per person in FERET). This behavior is in contrast with that of other subspace methods which usually gain low performance in these conditions, due to their incapacity to learn the intra-class variability even in presence of derived poses.

The paper is organized as follows: in Section 2 a description of the system architecture is given and the single steps of the method are detailed, in Section 3 the experimental results are discussed and, finally, Section 4 draws the conclusions.