@conference {12651,
	title = {Face recognition in the presence of multiple illumination sources},
	booktitle = {Computer Vision, 2005. ICCV 2005. Tenth IEEE International Conference on},
	volume = {2},
	year = {2005},
	month = {2005/10//},
	pages = {1169 -1176 Vol. 2 - 1169 -1176 Vol. 2},
	abstract = {Most existing face recognition algorithms work well for controlled images but are quite susceptible to changes in illumination and pose. This has led to the rise of analysis-by-synthesis approaches due to their inherent potential to handle these external factors. Though these approaches work quite well, most of them assume that the face is illuminated by a single light source which is usually not true in realistic conditions. In this paper, we propose an algorithm to recognize faces illuminated by arbitrarily placed, multiple light sources. The algorithm does not need to know the number of light sources and works extremely well even while recognizing faces illuminated by different number of light sources. Results using this algorithm are reported on multiple-illumination datasets generated from PIE by T. Sim, et al. (2003) and Yale Face Database B by W. Zhao, et al. (2003). We also highlight the importance of the hard non-linearity in the Lambert{\textquoteright}s law which is often ignored, probably to linearize the estimation process},
	keywords = {approach;estimation, illumination, Lambert, law;analysis-by-synthesis, nonlinearity;multiple, process;face, recognition;hard, recognition;light, source;face, sources;},
	doi = {10.1109/ICCV.2005.92},
	author = {Aggarwal,G. and Chellapa, Rama}
}
@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.}
}
