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.


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    Title :

    Lambertian reflectance and linear subspaces


    Contributors:
    Basri, R. (author) / Jacobs, D. (author)


    Publication date :

    2001-01-01


    Size :

    913638 byte




    Type of media :

    Conference paper


    Type of material :

    Electronic Resource


    Language :

    English



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