Abstract

Photometric stereo algorithms use a Lambertian reflectance model with a varying albedo field and involve the appearances of only one ob ject. This paper extends photometric stereo algorithms to handle all the appearances of all the ob jects in a class, in particular the class of human faces. Similarity among all facial appearances motivates a rank constraint on the albedos and surface normals in the class. This leads to a factorization of an observation matrix that consists of exemplar im- ages of difierent ob jects under difierent illuminations, which is beyond what can be analyzed using bilinear analysis. Bilinear analysis requires exemplar images of difierent ob jects under same illuminations. To fully recover the class-specific albedos and surface normals, integrability and face symmetry constraints are employed. The proposed linear algorithm takes into account the efiects of the varying albedo field by approxi- mating the integrability terms using only the surface normals. As an application, face recognition under illumination variation is presented. The rank constraint enables an algorithm to separate the illumination source from the observed appearance and keep the illuminant-invariant information that is appropriate for recognition. Good recognition results have been obtained using the PIE dataset.