Multiscale Representation and Matching of Curves Using Codons

Abstract A powerful representation of plane curves by curvature primitives called codons has been proposed by Hoffman and Richards ( Proceedings, AAAI, 1982 , pp. 5-8). Previously these were limited to representing only continuously varying, smooth, closed curves. Also, in practice their extraction from real data is complicated by the presence of noise and fine detail. In this paper we have extended the set of codons so that both open and closed curves containing straight lines and cusps can be completely represented. The problems of noise and obscuring fine detail have been solved by representing curves at all their natural scales. Codons at different scales are linked to form a hierarchical curve representation, called the codon-tree. To increase their power for model matching the qualitative codon descriptions are augmented by a set of shape features. These are used in combination with an extended set of rewrite rules from Leyton′s process grammar ( Artificial Intelligence 34, 1988, pp. 213-247), enabling one curve to be deformed until it matches another.