Extended Waltz Operators for Collinear Edges

While the original Waltz filter only handles adjacent line segments meeting in a single point, we show it is relevant to handle the case of relations between disjoint but collinear segments in positions suggesting hidden continuity. Waltz filtering is a seminal work being the first well known example of polynomial time artificial intelligence reasoning for improving the consistency ofa set of constraints. Here we propose and prove the usefulness of one such constraint, opening the way for more involved logical solutions to image understanding. The utility of the new operators is shown using case studies illustrating stronger conclusions when reasoning with the new constraints is enabled. Keywords: Waltz Filtering Algorithm, ConstraintSatisfaction Problem