Modeling a three-dimensional shape from a silhouette by detecting symmetry

A human being, observing a silhouette outline of an object, can estimate its three-dimensional (3-D) shape. This process has implications for the problem of recognizing and understanding 3-D shapes, since a similar process is needed in 3-D shape modeling of computer graphics. One idea for such 3-D shape modeling is to generate generalized cylinders on the basis of symmetry of the silhouette. This means finding symmetrically related pairs of points on the outline and estimating cross sections of the object from line segments connecting respective pairs of points. A generalized cylinder for the object can be constructed from the set of such cross sections. However, the symmetric point pairs previously were extracted by heuristic methods, and some instability was involved. This paper applies a recently proposed method of computing symmetric point pairs based on geometric division of the plane to 3-D shape modeling. Two ways to develop it are proposed: (1) prune it if the symmetric axis has branches, thereby generating a generalized cylinder for the trunk; and (2) generate generalized cylinders for the trunk and for respective branches, thereby modeling a complex shape as a self-intersecting object composed of multiple segments. The segment decomposition is implemented by natural reasoning.