Mapping Image Properties into Shape Constraints: Skewed Symmetry and Affine-Tramsfornable Patterns, and the Shape-from-Texture Paradigm

In this paper we demonstrate two new approaches to deriving three-dimensional surface orientation information (“shape”) from two-dimensional image cues. The two approaches are the method of affine-transformable patterns and the shape-from-texture paradigm. They are introduced by a specific application common to both: the concept of skewed symmetry. Skewed symmetry is shown to constrain the relationship of observed distortions in a known object regularity to a small subset of possible underlying surface orientations. Besides this constraint, valuable in its own right, the two methods are shown to generate other surface constraints as well. Some applications are presented of skewed symmetry to line drawing analysis, to the use of gravity in shape understanding, and to global shape recovery.