The structure of shapes scale space aspects of the (pre-) Symmetry Set

Abstract

Shapes simplify under to the intrinsic heat equation - the Mean Curvature Motion (MCM) - forming a shape scale space. The same holds for a representation of the shape, viz. the Symmetry Set (SS), a superset of the Medial Axis. Its singularities under the MCM are known, opening possibilities to investigate its deep structure. As data structure we use so-called Gauss diagrams, structures that depend on the pre-Symmetry Set, the SS in parameter space. Its properties, as well as its evolution and singularities under MCM, are presented. The set of all possible Gauss diagrams under MCM form a directed graph with one end point, in which the shape's scale space describes a specific path. These paths can be used for shape description and comparison. © Springer-Verlag Berlin Heidelberg 2005.