Abstract

Given the human ability to recognize familiar objects from simple line drawings or silhouettes, the study of occluding contours promises insights into the way the human visual system represents objects and their shape. Hoffman and Richards¹ argued that the human visual system partitions complex surfaces into parts or primitives and represents the 3-D shape of objects in terms of spatial relationships between these parts. In the present study an outline of a theory of parts is given which is based on the notion of primitive, featureless compact surfaces, which can be combined to form surfaces with bulges, or removed to leave holes. Rules based on surface curvature have been derived to decompose an arbitrary smooth surface into its constituent parts. Koenderink² showed that the sign of curvature of the occluding contour equals the sign of Gaussian curvature along the fold locus. Knowledge of surface curvature along folds can then be extended to regions in between folds, resulting in a so-called curvature interpretation. Expressions for the number of curvature interpretations as a function of the shape of the contour have been derived and possible constraints such as genericity and locality are discussed.

© 1985 Optical Society of America