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Title: | Cancellation of critical points in 2D and 3D morse and morse-smale complexes | Authors: | Čomić, Lidija De Floriani L. |
Issue Date: | 12-May-2008 | Journal: | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Abstract: | Morse theory studies the relationship between the topology of a manifold M and the critical points of a scalar function f defined on M. The Morse-Smale complex associated with f induces a subdivision of M into regions of uniform gradient flow, and represents the topology of M in a compact way. Function f can be simplified by cancelling its critical points in pairs, thus simplifying the topological representation of M, provided by the Morse-Smale complex. Here, we investigate the effect of the cancellation of critical points of f in Morse-Smale complexes in two and three dimensions by showing how the change of connectivity of a Morse-Smale complex induced by a cancellation can be interpreted and understood in a more intuitive and straightforward way as a change of connectivity in the corresponding ascending and descending Morse complexes. We consider a discrete counterpart of the Morse-Smale complex, called a quasi-Morse complex, and we present a compact graph-based representation of such complex and of its associated discrete Morse complexes, showing also how such representation is affected by a cancellation. © 2008 Springer-Verlag Berlin Heidelberg. | URI: | https://open.uns.ac.rs/handle/123456789/15507 | ISBN: | 3540791256 | ISSN: | 3029743 | DOI: | 10.1007/978-3-540-79126-3_12 |
Appears in Collections: | FTN Publikacije/Publications |
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