A signal-processing framework for reflection
A signal-processing framework for reflection
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DOI：
10.1145/1027411.1027416
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发表时间：
2004-10
期刊：
影响因子：
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通讯作者：
R. Ramamoorthi;P. Hanrahan
中科院分区：
文献类型：
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作者：
R. Ramamoorthi;P. Hanrahan
提出了一种用于分析均匀凸曲面在远距离照明下的反射光场的信号处理框架。这种分析在图形学和视觉学两方面都具有理论意义，并且在许多计算机图形学问题中也具有实际意义——例如，在确定光照分布和双向反射分布函数（brdf）、环境地图渲染和基于图像的渲染中。众所周知，在我们的假设下，反射算子的性质类似于卷积。在本文中，我们形式化了这些概念，表明反射光场可以用一种精确的定量方式来考虑，即通过将照明和BRDF卷积得到，即通过使用BRDF过滤入射照明。在数学上，我们可以将反射光场的频率空间系数表示为照明和BRDF的球谐系数的乘积。这些结果在确定逆绘制问题的适定性和条件反射方面具有实际意义——从真实照片中估计BRDF和照明参数。此外，我们能够推导出许多常见的BRDF和照明模型的球谐系数的解析公式。从这种形式分析中，我们能够确定精确的条件，在这些条件下，brdf和光照分布的估计是良好的。我们的数学分析对前向渲染也有影响——特别是在环境地图指定的复杂照明条件下物体的有效渲染。研究结果，特别是兰伯曲面的解析公式，在计算机视觉识别、光度立体和运动结构等领域也具有重要意义。
We present a signal-processing framework for analyzing the reflected light field from a homogeneous convex curved surface under distant illumination. This analysis is of theoretical interest in both graphics and vision and is also of practical importance in many computer graphics problems---for instance, in determining lighting distributions and bidirectional reflectance distribution functions (BRDFs), in rendering with environment maps, and in image-based rendering. It is well known that under our assumptions, the reflection operator behaves qualitatively like a convolution. In this paper, we formalize these notions, showing that the reflected light field can be thought of in a precise quantitative way as obtained by convolving the lighting and BRDF, i.e. by filtering the incident illumination using the BRDF. Mathematically, we are able to express the frequency-space coefficients of the reflected light field as a product of the spherical harmonic coefficients of the illumination and the BRDF. These results are of practical importance in determining the well-posedness and conditioning of problems in inverse rendering---estimation of BRDF and lighting parameters from real photographs. Furthermore, we are able to derive analytic formulae for the spherical harmonic coefficients of many common BRDF and lighting models. From this formal analysis, we are able to determine precise conditions under which estimation of BRDFs and lighting distributions are well posed and well-conditioned. Our mathematical analysis also has implications for forward rendering---especially the efficient rendering of objects under complex lighting conditions specified by environment maps. The results, especially the analytic formulae derived for Lambertian surfaces, are also relevant in computer vision in the areas of recognition, photometric stereo and structure from motion.