Anzeige
Erschienen in:
2013 | OriginalPaper | Buchkapitel
Simplification Operators on a Dimension-Independent Graph-Based Representation of Morse Complexes
verfasst von : Lidija Čomić, Leila De Floriani, Federico Iuricich
Erschienen in: Mathematical Morphology and Its Applications to Signal and Image Processing
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Ascending and descending Morse complexes are defined by the critical points and integral lines of a scalar field
f
defined on a manifold
M
. They induce a subdivision of
M
into regions of uniform gradient flow, thus providing a compact description of the topology of
M
and of the behavior of
f
over
M
. We represent the ascending and descending Morse complexes of
f
as a graph, that we call the
Morse incidence graph (MIG)
. We have defined a simplification operator on the graph-based representation, which is atomic and dimension-independent, and we compare this operator with a previous approach to the simplification of 3D Morse complexes based on the cancellation operator. We have developed a simplification algorithm based on a simplification operator, which operates on the MIG, and we show results from this implementation as well as comparisons with the cancellation operator in 3D.