Abstract
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
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