@article {14886,
	title = {Lambertian reflectance and linear subspaces},
	journal = {Pattern Analysis and Machine Intelligence, IEEE Transactions on},
	volume = {25},
	year = {2003},
	month = {2003/02//},
	pages = {218 - 233},
	abstract = {We prove that the set of all Lambertian reflectance functions (the mapping from surface normals to intensities) obtained with arbitrary distant light sources lies close to a 9D linear subspace. This implies that, in general, the set of images of a convex Lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a low-dimensional linear subspace, explaining prior empirical results. We also provide a simple analytic characterization of this linear space. We obtain these results by representing lighting using spherical harmonics and describing the effects of Lambertian materials as the analog of a convolution. These results allow us to construct algorithms for object recognition based on linear methods as well as algorithms that use convex optimization to enforce nonnegative lighting functions. We also show a simple way to enforce nonnegative lighting when the images of an object lie near a 4D linear space. We apply these algorithms to perform face recognition by finding the 3D model that best matches a 2D query image.},
	keywords = {2D, 4D, 9D, analog;, analytic, characterization;, convex, convolution, distant, functions;, harmonics;, image, image;, intensities;, Lambertian, light, lighting, linear, methods;, nonnegative, normals;, object, optimization;, programming;, query, recognition;, reflectance;, reflectivity;, set;, sources;, space;, spherical, subspace;, subspaces;, surface},
	isbn = {0162-8828},
	doi = {10.1109/TPAMI.2003.1177153},
	author = {Basri,R. and Jacobs, David W.}
}
