The use of gradient and dual space in line-drawing interpretation

Abstract

This paper reviews the application of gradient space and dual space in programs that interpret line-drawings and examines whether they can provide a basis for a fully adequate program. Mackworth's program Poly is analyzed at length. Counterexamples show first that the procedure must be generalized from gradient to dual space, and then that constraints in the form of inequalities as well as equations must be handled which necessitates a radical re-design. A proof that Poly itself is valid under perspective as well as orthographic projection although its derivation in terms of gradient space is not, further indicates that gradient (or dual) space is not the important element in Mackworth's approach. Other ways of using dual space by Kanade and Huffman are discussed but they do not convincingly rebut the conclusion that dual space is peripheral to the design of a competent program. Finally the conclusion that the plane equation approach derived from the developments described, while theoretically adequate, is awkward to use because it fails to offer intuitive clarity, is supported by contrasting it with the alternative method of sidedness reasoning.