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. The equations governing mutual illumination effects are briefly reviewed, and it is demonstrated that mutual illumination can form a major component of image radiance. The consequences of mutual illumination effects for different theories of recovering shape from radiance are then discussed. It is shown that discontinuities in surface radiance originate only in surface discontinuities, in shadows, and in changes in surface reflectance. The proof involves a book-keeping method that applies with minor modifications to discontinuities in derivatives of the radiance. It is argued that discontinuities in radiance are an important shape cue, because they bear a tractable relationship to three dimensional shape. The actual value of the radiance of a surface cannot be of such importance, because it is intractably coupled to shape. Further it is suggested that, because discontinuities in the derivatives of radiance arise in a highly structured fashion, they may contain exploitable shape cues. Examples of these discontinuities occuring in real scenes are given.