A linear complexity procedure for labelling line drawings of polyhedral scenes using vanishing points

The authors investigate the computational time complexity of the labeling problem for line drawings of polyhedral scenes. It is found that line drawings can be labeled in time proportional to the number of segments once the vanishing points associated to the possible directions for the edges are known. The vanishing points can be given a priori, otherwise they can in many cases be detected by standard techniques from the line drawing itself. The NP-completeness of the labeling problem for line drawings of trihedral scenes (Kirousis and Papadimitriou, 1988) is then due to the lack of knowledge about the vanishing points, which is equivalent to the knowledge of the possible directions for the edges. These results help draw a more accurate boundary between the problems in the interpretation of line drawings that are polynomially solvable and those that are NP-complete