Canonical Stiefel Quotient and its application to generic face recognition in illumination spaces

This paper presents a new paradigm for face recognition in illumination spaces when the identities of training subjects and test subjects do not overlap. Previous methods employ illumination models to create a projector from an illumination basis and perform single image classification. In contrast, we apply an illumination model to an image and create a set of illumination variants. For a gallery image, these variants are expressed as a point on a Stiefel manifold with an associated tangent plane. Two projections of the probe image illumination variants onto this tangent plane are defined and the ratio between these two projections, called the Canonical Stiefel Quotient (CSQ), is a measure of distance between images. We show that the proposed CSQ paradigm not only outperforms the traditional single image matching approach but also other variants of image set matching including a geodesic method. Furthermore, the proposed CSQ method is robust to the choice of training sets. Finally, our analyses reveal the benefits of using image set classification over single image matching.