Shape from shading as a partially well-constrained problem

For general objects, and for illumination from a general direction, the constraints on shape imposed by shading are studied. It is argued that, for a typical image, shading determines shape essentially up to a finite ambiguity. Thus regularization is often unnecessary and should be avoided. For some images, shape from shading is a partially well-constrained problem: the surface is uniquely determined over most of the image, but infinitely ambiguous in small regions bordering the image boundary, even though the image contains singular points. The main result is that, contrary to previous belief, the image of the occluding boundary does not strongly constrain the surface solution. It is shown that characteristic strips are curves of steepest ascent on the imaged surface. A theorem characterizing the properties of generic images is presented