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March 1, Tuesday
13:00 – 15:00

Variations in lighting can have a significant impact on the appearance of an object. In this talk I will provide a novel characterization of this variability for the case of Lambertian objects. In particular, I will use harmonic analysis to show that the set of all reflectance functions (the mapping from surface normals to intensities) produced by Lambertian objects under distant lighting lies close to a 9D linear subspace.

This implies, in general, that 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. In addition, a simple analytic characterization of this linear space is derived. These results are obtained by representing lighting using spherical harmonics and describing the effects of Lambertian materials as the analog of a convolution.

We use these results to develop novel algorithms for object recognition and shape reconstruction that work under complex lighting that include unknown combination of point and extended light sources.