Journal
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
Volume 25, Issue 2, Pages 218-233Publisher
IEEE COMPUTER SOC
DOI: 10.1109/TPAMI.2003.1177153
Keywords
face recognition; illumination; Lambertian; linear subspaces; object recognition; specular; spherical harmonics
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We prove that the set of all Lambertian reflectance functions (the mapping from surface normals to intensities) obtained with arbitrary distant right 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 fighting 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 fighting 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 fighting functions. We also show a simple way to enforce nonnegative Fighting 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.
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