Shape from Shading: An Assessment

The authors review previous efforts to recover surface shape from image irradiance to assess what can and cannot be accomplished. They consider the informational requirements and restrictions of these approaches. In dealing with the question of what surface parameters can be recovered locally from image shading, they show 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. The various approaches reviewed in this paper have attempted to recover surface orientation from shading. To do so they have added extra information, such as known boundary conditions or constraints upon surface shape. The performance of these various models allows the authors to draw the following conclusions 1 Direct integration of differential models of scene properties requires much a priori information and has to contend with major computational problems 2 Local computation must play a major role in the recovery of scene parameters, but the models used have been overly restrictive in an effort to recover particular information and 3 A relaxation mechanism, based on a strong low-order differential model, seems a viable means of propagating spatial information and constraints. Shading provides a basis for an intrinsic image, specifying relative surface curvature and curvature change, but this intrinsic image alone is insufficient for surface shape recovery. Other models incorporating other image measurements are needed to complement shading. Such models should utilize the advantages of local computation.