Three-Dimensional Shape From Line Drawings

Abstract

The problem of interpreting the shape of a three-dimen5ional space curve from its two-dimensional perspective image contour is considered. Observation of human perception indicates that a good strategy is to segment the image contour in such a way as to obtain approximately planar segments. The orientation of the osculating plane (the plane In which the space curve lies) can then be est.imated for these segment.s, and the three-dimensional shape recovered. The assumption of spatial isotropy is used to derive the theoretical results needed to formulate such an estimation strategy. The resulting estimation strategy allows a single three-dimensional structure (up to a single Necker reversal) to be assigned to any smooth image contour. An implementation is dPscrihed and shown to produce an interpretation that is quite similar to the analytically correct one in the case of a helix, even though a helix has substant.ial torsion. The general applicability of the algorit. hm is discussed.