Lambertian Reflectance and Linear Subspaces

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Lambertian Reflectance and Linear Subspaces (2000)

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by Ronen Basri , David Jacobs

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526 - 20 self

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@ARTICLE{Basri00lambertianreflectance,
    author = {Ronen Basri and David Jacobs},
    title = {Lambertian Reflectance and Linear Subspaces},
    journal = {},
    year = {2000},
    volume = {25},
    pages = {383--390}
}

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Abstract

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, 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 non-negative lighting functions. Finally, we show a simple way to enforce non-negative lighting when the images of an object lie near a 4D linear space. Research conducted w...

Keyphrases

linear subspace lambertian reflectance linear space object recognition convex lambertian object surface normal wide variety object lie use convex optimization spherical harmonic simple analytic characterization non-negative lighting linear method non-negative lighting function lambertian material lambertian object low-dimensional linear subspace simple way reflectance function prior empirical result

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