%0 Journal Article
%J Pattern Analysis and Machine Intelligence, IEEE Transactions on
%D 2003
%T Lambertian reflectance and linear subspaces
%A Basri,R.
%A Jacobs, David W.
%K 2D
%K 4D
%K 9D
%K analog;
%K analytic
%K characterization;
%K convex
%K convolution
%K distant
%K functions;
%K harmonics;
%K image
%K image;
%K intensities;
%K Lambertian
%K light
%K lighting
%K linear
%K methods;
%K nonnegative
%K normals;
%K object
%K optimization;
%K programming;
%K query
%K recognition;
%K reflectance;
%K reflectivity;
%K set;
%K sources;
%K space;
%K spherical
%K subspace;
%K subspaces;
%K surface
%X 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.
%B Pattern Analysis and Machine Intelligence, IEEE Transactions on
%V 25
%P 218 - 233
%8 2003/02//
%@ 0162-8828
%G eng
%N 2
%R 10.1109/TPAMI.2003.1177153