From a 2D Shape to a String Structure Using the Symmetry Set

Arjan Kuijper, Ole Fogh Olsen, Peter J. Giblin, Philip Bille, Mads Nielsen

Abstract: Many attempts have been made to represent families of 2D shapes in a simpler way. These approaches lead to so-called structures as the Symmetry Set ( $\mathcal{SS}$ ) and a subset of it, the Medial Axis ( $\mathcal{MA}$ ). In this paper a novel method to represent the $\mathcal{SS}$ as a string is presented. This structure is related to so-called arc-annotated sequences, and allows faster and simpler query algorithms for comparison and database applications than graph structures, used to represent the $\mathcal{MA}$ . Example shapes are shown and their data structures derived. They show the stability and robustness of the $\mathcal{SS}$ and its string representation.