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 C/sup 3/ 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 C/sup 3/ 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.<
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