In this thesis, a new approach to shape-from-shading is taken in which shading variations are attributed entirely to spatially varying illumination. This leads to a new analysis of the shape-from-shading problem, and to a new algorithm for solving it. In particular, a model of spatially varying illumination is developed which is in terms of the set of light rays in free space. This set is shown to be a four dimensional smooth manifold, called the radiation manifold. Local transformations between coordinate systems on this manifold are derived, and provide the basic mechanism of a new, parallel algorithm for inferring shape-from-shading.