Abstract
When an unknown object with Lambertian re
ectance is viewed orthographical ly, there is
an implicit ambiguity in determining its 3-d structure: we show that the object's visible
surface f (x; y) is indistinguishable from a generalized bas-relief " transformation of the
object,
f (x; y) = f (x; y) + x + y: For each image of the object il luminated by an arbitrary
number of distant light sources, there exists an identical image of the transformed
object il luminated by similarly transformed light sources. This result holds both for the
il luminated regions of the object as wel l as those in cast and attached shadows. Furthermore,
neither smal l motion of the object, nor of the viewer wil l resolve the ambiguity
in determining the
attening (or scaling) of the object's surface. Implications of this
ambiguity on structure recovery and shape representation are discussed.