Acquiring linear subspaces for face recognition under variable lighting

Previous work has demonstrated that the image variation of many objects (human faces in particular) under variable lighting can be effectively modeled by low-dimensional linear spaces, even when there are multiple light sources and shadowing. Basis images spanning this space are usually obtained in one of three ways: a large set of images of the object under different lighting conditions is acquired, and principal component analysis (PCA) is used to estimate a subspace. Alternatively, synthetic images are rendered from a 3D model (perhaps reconstructed from images) under point sources and, again, PCA is used to estimate a subspace. Finally, images rendered from a 3D model under diffuse lighting based on spherical harmonics are directly used as basis images. In this paper, we show how to arrange physical lighting so that the acquired images of each object can be directly used as the basis vectors of a low-dimensional linear space and that this subspace is close to those acquired by the other methods. More specifically, there exist configurations of k point light source directions, with k typically ranging from 5 to 9, such that, by taking k images of an object under these single sources, the resulting subspace is an effective representation for recognition under a wide range of lighting conditions. Since the subspace is generated directly from real images, potentially complex and/or brittle intermediate steps such as 3D reconstruction can be completely avoided; nor is it necessary to acquire large numbers of training images or to physically construct complex diffuse (harmonic) light fields. We validate the use of subspaces constructed in this fashion within the context of face recognition.

1 Introduction

To build a robust and efficient face recognition system, the problem of lighting variation is one of the main technical challenges facing system designers. In the past few years, many appearance-based methods have been proposed to handle this problem, and new theoretical insights, as well as good recognition results, have been reported [1], [2], [3], [5], [7], [9]. The main insight gained from these results is that there are both empirical and analytical justifications for using low-dimensional linear subspaces to model image variations of human faces under different lighting conditions. Early work showed that the variability of images of a Lambertian surface in fixed pose, but under variable lighting, where no surface point is shadowed, is a three-dimensional linear subspace [9], [12], [17], [22]. What has been perhaps more surprising is that, even with cast and attached shadows, the set of images is still well approximated by a relatively low-dimensional subspace, albeit with a bit higher dimension [5].