Characterization of human faces under illumination variations using rank, integrability, and symmetry constraints

Photometric stereo algorithms use a Lambertian reflectance model with a varying albedo field and involve the appearances of only one object. This paper extends photometric stereo algorithms to handle all the appearances of all the objects 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 images of different objects under different illuminations, which is beyond what can be analyzed using bilinear analysis. Bilinear analysis requires exemplar images of different objects 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 effects of the varying albedo field by approximating 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.