Essential loops and their relevance for skeletons and symmetry sets

Abstract

The Symmetry Set (SS) and its representation in parameter space, the pre-Symmetry Set, can be used to describe a shape with a linear data structure containing strings. As shape descriptor one specific string can be chosen. This string represents not only the major axis of the shape, but it also contains information of the complete shape. The string is augmented with information about the special points along the (pre-) Symmetry Set that it resembles. Changes in this simple line structure are directly related to so-called transitions (topological changes) of the SS and the Pre-SS. It also carries information about the skeleton, or Medial Axis. © Springer-Verlag Berlin Heidelberg 2005.