Inferring three-dimensional shapes from two-dimensional silhouettes

Although an infinity of three-dimensional (3-D) objects could generate any given silhouette, we usually infer only one 3-D object from its two-dimensional (2-D) projection. What are the constraints that restrict this infinity of choices? We identify three mathematical properties of smooth surfaces plus one simple viewing constraint that seem to drive our preferred interpretation of 3-D shape from 2-D contour. The constraint is an extension of the notion of general position. Taken together, our interpretation rules predict that "dents" in a 3-D surface should never be inferred from a smooth 2-D silhouette.