Recognition of three-dimensional scenes using only line drawingshas been part of computer vision research for over 30 years. The linesin the image correspond to intersections between two planes, and theycan be described as convex, concave, or occluding. These line-labelingapproaches depend on descriptions of the junctions where surfacesintersect. Given constraints on the number of surfaces (usually three isthe limit) or the type of surfaces (planar or curved), it is possible tocreate complete catalogs of all possible types of junctions, then useconstraint satisfaction procedures to generate descriptions of theobjects. Earlier work with planar objects produced simple catalogs andsimple algorithms to generate line labelings for collections ofobjects.

This paper reports on results in cases where the objectshave curved surfaces. Unlike the planar case, a linearalgorithm can determine whether the object is physically possible. Thepaper derives algorithms and computational requirements for severalvariations on the problem, including knowing all vanishing points forall lines (which is unrealistic in practice), knowing no vanishingpoints, or knowing some (which is most likely).

This paper ties up most of the loose ends in the area of labelingline drawings of trihedral objects. Because it deals with curvedsurfaces, this technique is probably more useful than the early planarobject approaches.