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  Efficient Computation of a Hierarchy of Discrete 3D Gradient Vector Fields

Günther, D., Reininghaus, J., Prohaska, S., Weinkauf, T., & Hege, H.-C. (2012). Efficient Computation of a Hierarchy of Discrete 3D Gradient Vector Fields. In R. Peikert, H. Hauser, H. Car, & R. Fuchs (Eds.), Topological Methods in Data Analysis and Visualization II (pp. 15-29). New York, NY: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0015-0DD8-0 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0024-5275-1
Genre: Book Chapter
Latex : Efficient Computation of a Hierarchy of Discrete {3D} Gradient Vector Fields

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 Creators:
Günther, David1, Author           
Reininghaus, Jan1, Author
Prohaska, Steffen1, Author
Weinkauf, Tino2, Author           
Hege, Hans-Christian1, Author
Affiliations:
1External Organizations, ou_persistent22              
2Computer Graphics, MPI for Informatics, Max Planck Society, ou_40047              

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 Abstract: This paper introduces a novel combinatorial algorithm to compute a hierarchy of discrete gradient vector fields for three-dimensional scalar fields. The hierarchy is defined by an importance measure and represents the combinatorial gradient flow at different levels of detail. The presented algorithm is based on Forman�s discrete Morse theory, which guarantees topological consistency and algorithmic robustness. In contrast to previous work, our algorithm combines memory and runtime efficiency. It thereby lends itself to the analysis of large data sets. A discrete gradient vector field is also a compact representation of the underlying extremal structures � the critical points, separation lines and surfaces. Given a certain level of detail, an explicit geometric representation of these structures can be extracted using simple and fast graph algorithms.

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Language(s): eng - English
 Dates: 2012
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: DOI: 10.1007/978-3-642-23175-9_2
BibTex Citekey: guenther12a
Other: Local-ID: 8B6701156B964471C1257AD90034C083-guenther12a
 Degree: -

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Title: Topological Methods in Data Analysis and Visualization II
  Subtitle : Theory, Algorithms, and Applications
Source Genre: Book
 Creator(s):
Peikert, Ronald1, Editor
Hauser, Helwig1, Editor
Car, Hamish1, Editor
Fuchs, Raphael1, Editor
Affiliations:
1 External Organizations, ou_persistent22            
Publ. Info: New York, NY : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 15 - 29 Identifier: ISBN: 978-3-642-23174-2

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Title: Mathematics and Visualization
Source Genre: Series
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Pages: - Volume / Issue: - Sequence Number: - Start / End Page: - Identifier: -