A Signal-Processing Framework for Reflection

Ravi Ramamoorthi and Pat Hanrahan

Submitted to the ACM Transactions on Graphics, August 2002


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 first part of the 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. Our mathematical analysis also has implications for forward rendering---especially the efficient rendering of objects under complex lighting conditions specified by environment maps.

Part 1: Reflection as Convolution PDF or gzipped PS

Part 2: Analytic Formulae for Common Lighting and BRDF Models PDF or gzipped PS

Ravi Ramamoorthi
Last modified: Sat Aug 10 23:55:58 PDT 2002