Research in Shape Analysis by unknow

Author:unknow
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

Topological analysis of discrete fields can be approached in two ways. In the first approach, space is decomposed into simplicial cells, and continuous topological properties are embedded in discrete space. This is called combinatorial topology. The second approach, so-called digital topology, defines topological concepts such as adjacency and continuity on a digital grid based on set and graph theories. Other topological properties are then derived based on these definitions. Both approaches are relevant to the topological analysis of implicit surfaces such as level sets and phase fields. We will first discuss the combinatorial approach for Morse theory very briefly. Then we will give a more detailed review of digital topology since our method is based on this approach. However, it should be mentioned that discretization of topological properties is not a trivial matter; adaptation of continuous properties on discrete fields might cause information loss.

Discrete Morse theory is based on the combinatorial approach; discrete Morse functions are defined on simplicial complexes. Other methods based on Morse theory such as Reeb graphs and Morse-Smale complex use these discrete Morse functions as the basis of their computation. However, discrete Morse theory suffers from stability issues, and computation of Morse-Smale functions can be problematic due to the sensitivity to noise [7].

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.