朗伯反射率与线性子空间

R. Basri, D. Jacobs
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引用次数: 1886

摘要

我们证明了朗伯物体在远距离各向同性光照下产生的所有反射率函数(从表面法线到强度的映射)的集合接近于9D线性子空间。这意味着在各种光照条件下获得的凸朗伯物体的图像可以用低维线性子空间精确地近似,解释了先前的经验结果。我们也给出了这个线性空间的一个简单解析表征。我们通过使用球面谐波来表示照明,并将朗伯材料的影响描述为卷积的模拟来获得这些结果。这些结果使我们能够构建基于线性方法的物体识别算法,以及使用凸优化来执行非负光照函数的算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Lambertian reflectance and linear subspaces
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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