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.
Cited By
- Habel R and Wimmer M Efficient irradiance normal mapping Proceedings of the 2010 ACM SIGGRAPH symposium on Interactive 3D Graphics and Games, (189-195)
- Zhang T, Fang B, Yuan Y, Yan Tang Y, Shang Z, Li D and Lang F (2009). Multiscale facial structure representation for face recognition under varying illumination, Pattern Recognition, 42:2, (251-258), Online publication date: 1-Feb-2009.
- Ward G, Rubinstein F and Clear R A ray tracing solution for diffuse interreflection ACM SIGGRAPH 2007 courses, (11-es)
- Arikan O, Forsyth D and O'Brien J Fast and detailed approximate global illumination by irradiance decomposition ACM SIGGRAPH 2005 Papers, (1108-1114)
- Arikan O, Forsyth D and O'Brien J (2005). Fast and detailed approximate global illumination by irradiance decomposition, ACM Transactions on Graphics, 24:3, (1108-1114), Online publication date: 1-Jul-2005.
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