Computing Symmetry Sets from 2D Shapes

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 (SS) and a subset of it, the Medial Axes (MA). While the latter is commonly used, the former is still in the mathematical research stage. One reason for this is that in contrast to the SS, the MA can be computed efficiently and fastly, and yields one connected component for a closed shape. A drawback of the MA representation is its graph-structure that makes comparison with the MA of another shape difficult and time-consuming.

In this paper a novel method to represent the SS as a string is presented. This structure allows faster and simpler query algorithms for comparison and database applications. Second, new ways to visualize these sets are presented. They use the distances from the shape to the set as extra dimension as well as the so-called pre-Symmetry Set (pre-SS). Information revealed by these representations can be used to calculate the novel representation structure that is based on the SS and the shape's evolute.

Example shapes are shown and their datastructures derived. They show the stability and robustness of the latter, compared to the MA.