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.
This work is part of the DSSCV project supported by the IST Programme of the European Union (IST-2001-35443). WWW home page: http://www.itu.dk/Internet/ sw1953.asp.
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Kuijper, A., Olsen, O.F. (2005). The Structure of Shapes Scale Space Aspects of the (pre-) Symmetry Set. In: Kimmel, R., Sochen, N.A., Weickert, J. (eds) Scale Space and PDE Methods in Computer Vision. Scale-Space 2005. Lecture Notes in Computer Science, vol 3459. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11408031_25
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DOI: https://doi.org/10.1007/11408031_25
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