Line-drawing interpretation: a mathematical framework

The author reports on the progress toward a mathematical theory of line-drawing interpretation. A working framework is developed, and a variety of tools and techniques are demonstrated within it. He reviews related work and discusses his assumptions. He presents a projective mapping which he expects will find use in the extension of results derived for orthographic projection to perspective projection. H. Whitney´s definition (1955) of an excellent mapping is reviewed and it is shown that both orthographic and perspective projections of piecewise C³ surfaces are excellent under general viewpoint. It is thus demonstrated that there are only two types of local singularities, folds and cusps, associated with the projection of a C³ surface. The results render unnecessary the assumption of stability under perturbation of the viewed surface, which was required in previous work based on Whitney´s results. The modes of interaction between viewpoint-independent and viewpoint-dependent edges are dealt with and the continuity constraints imposed on the scene by its line drawing investigated