Pentland, A. P. (1984). Local shading analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, (2), 170-187.
Local analysis of image shading, in the absence of prior knowledge about the viewed scene, may be used to provide information about the scene. The following has been proved. Every image point has the same image intensity and first and second derivatives as the image of an umbilical point (a point with equal principal curvatures) on a Lambertian surface; there is exactly one combination of surface orientation, curvature, (overhead) illumination direction and albedo times illumination intensity that will produce a particular set of image intensity and first and second derivatives. A solution for the unique combination of surface orientation, etc., at umbilical points is presented. This solution has been extended by using general position and regional constraints to obtain estimates of the following:
- Surface orientation at each image point
- Whether the surface is planar, singly or doubly curved at each point The mean illuminant direction within a region
- Whether a region is convex, concave, or is a saddle surface.
Algorithms to recover illuminant direction, identify discontinuities, and estimate surface orientation have been evaluated on both natural and synthesized images, and have been found to produce useful information about the scene.