Shading computations on the radiation manifold

How may the shape of a smooth surface be inferred from an image? Traditional methods in computer vision for inferring shape-from-shading assume that surface shading depends entirely on surface orientation. In many illumination scenarios, however, shading may occur independently of surface orientation. For example, when an extended light source such as the sky casts a continuous shadow on a flat ground, the resulting shading is due to illumination variations only.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.The scope of the thesis reaches beyond shape-from-shading, however. The radiation manifold is used to solve two other shading problems in which illumination varies across space, namely the radiosity equation in computer graphics and the shape-from-darkness problem in computer vision. The thesis thus provides a unifying framework in which a variety of shading problems may be understood and solved