Alternative 2D shape representations using the symmetry set
Among the many attempts made to represent families of 2D shapes in a simpler way, the Medial Axis (MA) takes a prominent place. Its graphical representation is intuitively appealing and can be computed efficiently. Small perturbations of the shape can have large impact on the MA and are regarded as instabilities, although these changes are mathematically known from the investigations on a super set, the Symmetry Set (SS). This set has mainly been in a mathematical research stage, partially due to computational aspects, and partially due to its unattractive representation in the plane. In this paper novel methods are introduced to overcome both aspects. As a result, it is possible to represent the SS as a string is presented. The advantage of such a structure is that it allows fast and simple query algorithms for comparisons. Second, alternative ways to visualize the SS are presented. They use the distances from the shape to the set as extra dimension as well as the so-called pre-Symmetry Set and anti-Symmetry Set. Information revealed by these representations can be used to calculate the linear string representation structure. Example shapes from a data base are shown and their data structures derived.
shapes symmetry set medial axis pre-symmetry set anti-symmetry set geometry skeletons