Shadows and shading flow fields

Many presume that parsing the shadows out of an image is a high-level task, because of the global nature of the shadow formation process. But shape-from-shading algorithms are low-level, in the sense that they seek solutions (surface normals or depth values) directly from image intensities. A dilemma arises: since shape-from-shading involves an illumination term, shadows must first be identified. We show that a structure intermediate between intensities and surfaces-the shading flow field-provides a solution to this dilemma. Our analysis is based on the observation that the geometric information that can be derived from images supports different inferences than the photometric information, and our specific goal will be to articulate this geometric structure and to show how shading flow fields can be reliably computed