Casting Light on Illumination: A Computational Model and Dimensional Analysis of Sources

Abstract

We attempt to cast light on illumination by introducing a computational model of light sources and illumination. Spatially varying illumination is computed using coordinate transformations on the manifold of rays in space, and the ray manifold is shown to be 4 dimensional. The illumination model can be used to recover shape from shading in situations when direct illumination varies across space and provides the basis for relating different types of light sources (e.g., an overcast sky, the sun, a panel light, and a spotlight). A formal definition for light sources emerges that generalizes the standard definition of a source as an emitter and leads to a 4-D light source hypercube in which the different types of sources may be embedded.