Shape from Shading in the Light of Mutual Illumination

Shape from shading schemes are based on the assumption that image radiance is a function of surface normal alone. Unfortunately, because surfaces illuminate one another, radiance is a complicated global property of surface shape. We review briefly the equations governing mutual illumination effects, and demonstrate that mutual illumination forms a major component of image radiance. We then discuss the consequences of mutual illumination effects for different theories of recovering shape from radiance. We show that discontinuities in image radiance originate solely in surface discontinuities, from shadows and from changes in surface reflectance. We argue that for a large class of shapes the response of edge detectors will also remain unchanged. Our proof involves a bookkeeping method that applies with minor modifications to discontinuities in derivatives of the radiance.