Showing papers on "Illumination problem published in 2001"
TL;DR: A generative appearance-based method for recognizing human faces under variation in lighting and viewpoint that exploits the fact that the set of images of an object in fixed pose but under all possible illumination conditions, is a convex cone in the space of images.
Abstract: We present a generative appearance-based method for recognizing human faces under variation in lighting and viewpoint. Our method exploits the fact that the set of images of an object in fixed pose, but under all possible illumination conditions, is a convex cone in the space of images. Using a small number of training images of each face taken with different lighting directions, the shape and albedo of the face can be reconstructed. In turn, this reconstruction serves as a generative model that can be used to render (or synthesize) images of the face under novel poses and illumination conditions. The pose space is then sampled and, for each pose, the corresponding illumination cone is approximated by a low-dimensional linear subspace whose basis vectors are estimated using the generative model. Our recognition algorithm assigns to a test image the identity of the closest approximated illumination cone. Test results show that the method performs almost without error, except on the most extreme lighting directions.
5,027 citations
TL;DR: The Gohberg—Markus—Hadwiger Covering Problem for compact, convex bodies M\subset Rn with md M=2 is solved and an idea for a complete solution is outlined.
Abstract: We solve here the Gohberg--Markus--Hadwiger Covering Problem (or, what is the same, the illumination problem ) for compact, convex bodies M\subset R n with md M=2 . Moreover, we outline an idea for a complete solution, using md M .
10 citations
19 Nov 2001
TL;DR: In this paper, the authors consider the illumination and the strong illumination properties for closed bounded regions of Euclidean spaces, and they show how the regions with different illumination properties should be designed.
Abstract: We consider the illumination and the strong illumination properties for closed bounded regions of Euclidean spaces. These properties are intimately connected with a problem of chaoticity of the corresponding billiards. It is shown that there are only two mechanisms of chaoticity in billiard systems, which are called the mechanism of dispersing and the mechanism of defocusing. Our results show how the regions with different illumination properties should be designed. Especially each focusing mirror in the boundary of a region must be an absolutely focusing one. The notion of absolutely focusing mirrors is a new one in the geometric optic and it plays a key role for the illumination problem.