A Possible Neural Mechanism for Computing Shape From Shading

Shading is the variation in image intensity due to changes in surface shape, and has long been recognized as one of the most important visual cues to surface shape. Leonard0 Da Vinci, for instance, wrote in his notebooks: “Shading appears to me to be of supreme importance in perspective, because, without it opaque and solid bodies will be ill-defined.” Despite its importance, however, relatively little is known about how people extract shape from shading. Perhaps the major obstacle to understanding is the lack of a good theoretical model. For although the physics is well understood, the mathematical problem is so underconstrained that no solution is possible without the use of simplifying assumptions (Horn 1975; Pentland 1984). Examination of the physics shows that there are three types of simplifications that might be useful. These are assumptions about the surface shape (e.g., smoothness), the distribution of illumination (e.g., a single light source direction), or about the reflectance function (e.g., Lambertian reflectance). Of these three categories, assumptions about illumination are the least controversial: almost all research has accepted the hypothesis that people assume a single, distant illuminant within ”fairly large” image regions. Assumptions about surface shape have received the most attention in recent research. There have been two types of simplifying assumptions that have been found useful: (1) smoothness assumptions, first employed by Horn (1975), and (2) assumptions about local surface curvature, first employed by Pentland (1984). The resulting shape-from-shading techniques have estimated surface orientation, so that integration is required