Datensatz

Zusammenfassung

This thesis presents a novel computational framework that allows for a robust
extraction and quantification of the Morse-Smale complex of a scalar field
given on a 2- or 3-dimensional manifold. The proposed framework is based on
Forman's discrete Morse theory, which guarantees the topological consistency of
the computed complex. Using a graph theoretical formulation of this theory, we
present an algorithmic library that computes the Morse-Smale complex
combinatorially with an optimal complexity of
O(n^2) and efficiently creates a multi-level representation of it. We explore
the discrete nature of this complex, and relate it to the smooth counterpart.
It is often necessary to estimate the feature strength of the individual
components of the Morse-Smale complex -- the critical points and separatrices.
To do so, we propose a novel output-sensitive strategy to compute the
persistence of the critical points. We also extend this wellfounded concept to
separatrices by introducing a novel measure of feature strength called
separatrix persistence. We evaluate the applicability of our methods in a wide
variety of application areas ranging from computer graphics to planetary
science to computer and electron tomography.