The KGBR viewpoint-lighting ambiguity and its resolution by generic constraints

Abstract

We describe a novel viewpoint-lighting ambiguity which we call the KGBR. This ambiguity assumes orthographic projecting or an affine camera, and uses Lambertian reflectance functions including case/attached shadows and multiple light sources. A KGBR transform alters the geometry (by a three-dimensional affine transformation) and albedo properties of objects. If two objects are related by a KGBR transform then for any viewpoint and lighting of the first object there exists a corresponding viewpoint and lighting of the second object so that the images are identical up to an affine transformation. The Generalized Bas Relief (GBR) ambiguity is obtained as a special case of the KGBR. We describe generic viewpoint and lighting assumptions and show that either, or both, resolve this ambiguity by biasing towards objects with planar geometry.