Three Approaches in Computational Geometry and Topology: Persistent Homology, Discrete Differential Geometry and Discrete Morse Theory
Master thesis
Permanent lenke
http://hdl.handle.net/11250/258947Utgivelsesdato
2011Metadata
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Sammendrag
We study persistent homology, methods in discrete differential geometry and discrete Morse theory. Persistent homology is applied to computational biology and range image analysis. Theory from differential geometry is used to define curvature estimates of triangulated hypersurfaces. In particular, a well-known method for triangulated surfacesis generalised to hypersurfaces of any dimension. The thesis concludesby discussing a discrete analogue of Morse theory.