Deterministic and Probabilistic Approaches to Labelling Line Drawings of Engineering Objects

Labelling line drawings is a useful technique in several applications, including that of automated interpretation of line drawings as polyhedral solid objects. Algorithms exist which can in practice label line drawings of trihedral polyhedra correctly in low-order polynomial time. However, the restriction to trihedral polyhedra is too limiting for practical applications. We are primarily interested in interpreting line drawings of engineering objects, and many of these objects contain non-trihedral (usually tetrahedral) vertices. We therefore investigate two alternative algorithms for labeliing drawings of such objects, one deterministic and the other probabilistic. We find that our deterministic solution achieves better results in terms of correctness but can be unacceptably slow, and that our probabilistic solution, while acceptably quick, is less successful in terms of correctness.