Interpreting line drawings of curved objects

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Abstract

In this paper, we study the problem of interpreting line drawings of scenes composed of opaque regular solid objects bounded by piecewise smooth surfaces with no markings or texture on them. It is assumed that the line drawing has been formed by orthographic projection of such a scene under general viewpoint, that the line drawing is error free, and that there are no lines due to shadows or specularities. Our definition implicitly excludes laminae, wires, and the apices of cones.

A major component of the interpretation of line drawings is line labelling. By line labelling we mean (a) classification of each image curve as corresponding to either a depth or orientation discontinuity in the scene, and (b) further subclassification of each kind of discontinuity. For a depth discontinuity we determine whether it is a limb—a locus of points on the surface where the line of sight is tangent to the surface—or an occluding edge—a tangent plane discontinuity of the surface. For an orientation discontinuity, we determine whether it corresponds to a convex or concave edge. This paper presents the first mathematically rigorous scheme for labelling line drawings of the class of scenes described. Previous schemes for labelling line drawings of scenes containing curved objects were heuristic, incomplete, and lacked proper mathematical justification.

By analyzing the projection of the neighborhoods of different kinds of points on a piecewise smooth surface, we are able to catalog all local labelling possibilities for the different types of junctions in a line drawing. An algorithm is developed which utilizes this catalog to determine all legal labellings of the line drawing. A local minimum complexity rule—at each vertex select those labellings which correspond to the minimum number of faces meeting at the vertex—is used in order to prune highly counter-intuitive interpretations. The labelling scheme was implemented and tested on a number of line drawings. The labellings obtained are few and by and large in accordance with human interpretations.