Lambertian reflectance and linear subspaces

TitleLambertian reflectance and linear subspaces
Publication TypeConference Papers
Year of Publication2001
AuthorsBasri R, Jacobs DW
Conference NameComputer Vision, 2001. ICCV 2001. Proceedings. Eighth IEEE International Conference on
Date Published2001///
Keywordsfunctions;spherical, harmonics;convex, Lambertian, lighting;object, object;convex, objects;convex, optimization;isotropic, programming;object, recognition;, recognition;reflectance

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