Sparse Representation for View-Based Face Recognition

Introduction

With the ever-increasing security threats, the problem of invulnerable authentication systems is becoming more acute. Traditional means of securing a facility essentially depend on strategies corresponding to “what you have” or “what you know”, for example smart cards, keys and passwords. These systems however can easily be fooled. Passwords for example, are difficult to remember and therefore people tend to use the same password for multiple facilities making it more susceptible to hacking. Similarly, cards and keys can easily be stolen or forged. A more inalienable approach is therefore to go for strategies corresponding to “what you are” or “what you exhibit” i.e. biometrics. Although the issue of “liveliness” has recently been highlighted due to the advancement in digital media technology, biometrics arguably remain the best choice. Among the other available biometrics, such as speech, iris, fingerprints, hand geometry and gait, face seems to be the most natural choice (Li & Jain, 2005). It is nonintrusive, requires a minimum of user cooperation and is cheap to implement. The importance of face recognition is highlighted for widely used video surveillance systems where we typically have facial images of suspects.

It is long known that appearance-based face recognition systems critically depend on manifold learning methods. A gray-scale face image of order a×b can be represented as an ab dimensional vector in the original image space. However, any attempt of recognition in such a high dimensional space is vulnerable to a variety of issues often referred to as curse of dimensionality. Typically, in pattern recognition problems it is believed that high-dimensional data vectors are redundant measurements of an underlying source. The objective of manifold learning is therefore to uncover this “underlying source” by a suitable transformation of high-dimensional measurements to low-dimensional data vectors. View-based face recognition methods are no exception to this rule. Therefore, at the feature extraction stage, images are transformed to low dimensional vectors in face space. The main objective is to find a basis function for this transformation, which could distinguishably represent faces in the face space. Linear transformation from the image space to the feature space is perhaps the most traditional way of dimensionality-reduction, also called “Linear Subspace Analysis”.

A number of approaches have been reported in the literature including Principle Component Analysis (PCA) (Turk & Pentland, 1991), (Jolliffe, 1986), Linear Discriminant Analysis (LDA) (Belhumeur, Hespanha, & Kriegman, 1997) and Independent Component Analysis (ICA) (Yuen & Lai, 2002). These approaches have been classified in two categories namely reconstructive and discriminative methods. Reconstructive approaches (such as PCA and ICA) are reported to be robust for the problem related to contaminated pixels, whereas discriminative approaches (such as LDA) are known to yield better results in clean conditions (Duda, Hart, & Stork, 2000). Nevertheless, the choice of the manifold learning method for a given problem of face recognition has been a hot topic of research in the face recognition literature. These debates have recently been challenged by a new concept of “Sparse Representation Classification (SRC)” (Wright, Yang, Ganesh, Sastri, & Ma, 2009). It has been shown that unorthodox features such as down-sampled images and random projections can serve equally well. As a result, the choice of the feature space may no longer be so critical (Naseem, Togneri, & Bennamoun, 2009) (Wright, Yang, Ganesh, Sastri, & Ma, 2009). What really matters is the dimensionality of the feature space and the design of the classifier. The key factor to the success of sparse representation classification is the recent development of “Compressive Sensing” theory. In sparse representation classification, a down-sampled probe image vector is represented by a linear combination of down-sampled gallery images vectors. The ill-conditioned inverse problem is solved using the l₁-norm minimization. The sparse nature of the l₁-norm solution helps identifying the true class of a given probe.