TY - CONF T1 - Lambertian reflectance and linear subspaces T2 - Computer Vision, 2001. ICCV 2001. Proceedings. Eighth IEEE International Conference on Y1 - 2001 A1 - Basri,R. A1 - Jacobs, David W. KW - functions;spherical KW - harmonics;convex KW - Lambertian KW - lighting;object KW - object;convex KW - objects;convex KW - optimization;isotropic KW - programming;object KW - recognition; KW - recognition;reflectance AB - We prove that the set of all reflectance functions (the mapping from surface normals to intensities) produced by Lambertian objects under distant, isotropic lighting lies close to a 9D linear subspace. This implies that the images of a convex Lambertian object obtained under a wide variety of lighting conditions can be approximated accurately with 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 non-negative lighting functions JA - Computer Vision, 2001. ICCV 2001. Proceedings. Eighth IEEE International Conference on VL - 2 M3 - 10.1109/ICCV.2001.937651 ER -