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Traditional photometric stereo algorithms employ a Lambertian reflectance model with a varying albedo field and involve the appearance of only one object. In this paper, we generalize photometric stereo algorithms to handle all appearances of all objects in a class, in particular the human face class, by making use of the linear Lambertian property. A linear Lambertian object is one which is linearly spanned by a set of basis objects and has a Lambertian surface. The linear property leads to a rank constraint and, consequently, a factorization of an observation matrix that consists of exemplar images of different objects (e.g., faces of different subjects) under different, unknown illuminations. Integrability and symmetry constraints are used to fully recover the subspace bases using a novel linearized algorithm that takes the varying albedo field into account. The effectiveness of the linear Lambertian property is further investigated by using it for the problem of illumination-invariant face recognition using just one image. Attached shadows are incorporated in the model by a careful treatment of the inherent nonlinearity in Lambert's law. This enables us to extend our algorithm to perform face recognition in the presence of multiple illumination sources. Experimental results using standard data sets are presented.
Linear Lambertian object, generalized photometric stereo, illumination-invariant face recognition, multiple illumination sources, rank constraint, bilinear analysis, integrability, face symmetry.

S. K. Zhou, D. W. Jacobs, G. Aggarwal and R. Chellappa, "Appearance Characterization of Linear Lambertian Objects, Generalized Photometric Stereo, and Illumination-Invariant Face Recognition," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 29, no. , pp. 230-245, 2007.
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