Shape from Shading: An Assessment

Previous efforts to recover surface shape from image irradiance are reviewed in order to assess what can and cannot be accomplished. The informational requirements and restrictions of these approaches are considered. In dealing with the question of what surface parameters can be recovered locally from image shading, it is shown that, at most, shading determines relative surface curvature, i.e., the ratio of surface curvature measured in orthogonal image directions. The relationship between relative surface curvature and the second derivatives of image irradiance is independent of other scene parameters, but insufficient to determine surface shape. This result places in perspective the difficulty encountered in previous attempts to recover surface orientation from image shading.