Ramamoorthi R, Hanrahan P
Department of Computer Science, Stanford University, California 94305, USA.
J Opt Soc Am A Opt Image Sci Vis. 2001 Oct;18(10):2448-59. doi: 10.1364/josaa.18.002448.
We present a theoretical analysis of the relationship between incoming radiance and irradiance. Specifically, we address the question of whether it is possible to compute the incident radiance from knowledge of the irradiance at all surface orientations. This is a fundamental question in computer vision and inverse radiative transfer. We show that the irradiance can be viewed as a simple convolution of the incident illumination, i.e., radiance and a clamped cosine transfer function. Estimating the radiance can then be seen as a deconvolution operation. We derive a simple closed-form formula for the irradiance in terms of spherical harmonic coefficients of the incident illumination and demonstrate that the odd-order modes of the lighting with order greater than 1 are completely annihilated. Therefore these components cannot be estimated from the irradiance, contradicting a theorem that is due to Preisendorfer. A practical realization of the radiance-from-irradiance problem is the estimation of the lighting from images of a homogeneous convex curved Lambertian surface of known geometry under distant illumination, since a Lambertian object reflects light equally in all directions proportional to the irradiance. We briefly discuss practical and physical considerations and describe a simple experimental test to verify our theoretical results.
我们对入射辐射率与辐照度之间的关系进行了理论分析。具体而言，我们探讨了是否能够根据所有表面方向上的辐照度信息来计算入射辐射率这一问题。这是计算机视觉和逆辐射传输中的一个基本问题。我们表明，辐照度可被视为入射光照（即辐射率）与一个截断余弦传递函数的简单卷积。那么，估计辐射率就可被视为一种反卷积操作。我们根据入射光照的球谐系数推导出了一个简单的辐照度闭式公式，并证明了阶数大于1的奇数阶光照模式会完全消失。因此，这些分量无法从辐照度中估计出来，这与普赖森多费尔提出的一个定理相矛盾。从辐照度估计辐射率问题的一个实际应用是，在远距离光照条件下，根据已知几何形状的均匀凸曲面朗伯体表面的图像来估计光照，因为朗伯体物体在所有方向上均匀反射光，且反射光与辐照度成正比。我们简要讨论了实际和物理方面的考虑因素，并描述了一个简单的实验测试来验证我们的理论结果。
