Abstract

All plane curves can be described at an abstract level by a sequence of five primitive elemental shapes, called codons, which simply capture the relations between the extrema of curvature. The codon description provides a basis for enumerating all smooth 2-D curves. Let each of these smooth plane curves be considered as the silhouette of an opaque 3-D object. Clearly an infinity of 3-D objects can generate any one of our codon silhouettes. How then can we predict which 3-D object corresponds to a given 2-D silhouette? To restrict the infinity of choices, we impose two mathematical properties of smooth surfaces plus one simple viewing constraint. The constraint is an extension of the notion of general position and seems to drive our preferred inferences of 3-D shapes, given only the 2-D contour.

© 1985 Optical Society of America