%0 Conference Paper
%B Computer Vision, 2001. ICCV 2001. Proceedings. Eighth IEEE International Conference on
%D 2001
%T Lambertian reflectance and linear subspaces
%A Basri,R.
%A Jacobs, David W.
%K functions;spherical
%K harmonics;convex
%K Lambertian
%K lighting;object
%K object;convex
%K objects;convex
%K optimization;isotropic
%K programming;object
%K recognition;
%K recognition;reflectance
%X 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
%B Computer Vision, 2001. ICCV 2001. Proceedings. Eighth IEEE International Conference on
%V 2
%P 383 -390 vol.2 - 383 -390 vol.2
%8 2001///
%G eng
%R 10.1109/ICCV.2001.937651