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Efficient Computation of a Hierarchy of Discrete 3D Gradient Vector Fields
New York University, U.S.A..ORCID iD: 0000-0002-1498-9062
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2012 (English)In: Topological Methods in Data Analysis and Visualization II / [ed] Peikert, R.; Hauser, H.; Carr, H.; Fuchs, R., Springer, 2012, 15-30 p.Chapter in book (Other academic)
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Text
Abstract [en]

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 for 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.

Place, publisher, year, edition, pages
Springer, 2012. 15-30 p.
Series
Mathematics and Visualization
National Category
Computer Science
Research subject
Computer Science; SRA - E-Science (SeRC)
Identifiers
URN: urn:nbn:se:kth:diva-184775OAI: oai:DiVA.org:kth-184775DiVA: diva2:916786
Note

QC 20160418

Available from: 2016-04-04 Created: 2016-04-04 Last updated: 2016-04-18Bibliographically approved

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http://www.csc.kth.se/~weinkauf/publications/absguenther12a.html

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