Robustness-Based Simplification of 2D Steady and Unsteady Vector Fields

Handle URI:
http://hdl.handle.net/10754/599529
Title:
Robustness-Based Simplification of 2D Steady and Unsteady Vector Fields
Authors:
Skraba, Primoz; Wang, Bei; Chen, Guoning; Rosen, Paul
Abstract:
© 2015 IEEE. Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification techniques based on the topological skeleton successively remove pairs of critical points connected by separatrices, using distance or area-based relevance measures. These methods rely on the stable extraction of the topological skeleton, which can be difficult due to instability in numerical integration, especially when processing highly rotational flows. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness which enables the pruning of sets of critical points according to a quantitative measure of their stability, that is, the minimum amount of vector field perturbation required to remove them. This leads to a hierarchical simplification scheme that encodes flow magnitude in its perturbation metric. Our novel simplification algorithm is based on degree theory and has minimal boundary restrictions. Finally, we provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets. We show local and complete hierarchical simplifications for steady as well as unsteady vector fields.
Citation:
Skraba P, Wang B, Chen G, Rosen P (2015) Robustness-Based Simplification of 2D Steady and Unsteady Vector Fields. IEEE Transactions on Visualization and Computer Graphics 21: 930–944. Available: http://dx.doi.org/10.1109/tvcg.2015.2440250.
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
IEEE Transactions on Visualization and Computer Graphics
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
1-Aug-2015
DOI:
10.1109/tvcg.2015.2440250
PubMed ID:
26357256
Type:
Article
ISSN:
1077-2626
Sponsors:
The authors thank Jackie Chen for the combustion dataset and Mathew Maltude from LANL and the BER Office of Science UV-CDAT team for the ocean datasets. P. Rosen was supported by DOE NETL and KAUST award KUS-C1-016-04. P. Skraba was supported by TOPOSYS (FP7-ICT-318493). G. Chen was supported by US National Science Foundation (NSF) IIS-1352722. B. Wang was supported by INL 00115847 DE-AC0705ID14517 and DOE NETL.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorSkraba, Primozen
dc.contributor.authorWang, Beien
dc.contributor.authorChen, Guoningen
dc.contributor.authorRosen, Paulen
dc.date.accessioned2016-02-28T05:52:50Zen
dc.date.available2016-02-28T05:52:50Zen
dc.date.issued2015-08-01en
dc.identifier.citationSkraba P, Wang B, Chen G, Rosen P (2015) Robustness-Based Simplification of 2D Steady and Unsteady Vector Fields. IEEE Transactions on Visualization and Computer Graphics 21: 930–944. Available: http://dx.doi.org/10.1109/tvcg.2015.2440250.en
dc.identifier.issn1077-2626en
dc.identifier.pmid26357256en
dc.identifier.doi10.1109/tvcg.2015.2440250en
dc.identifier.urihttp://hdl.handle.net/10754/599529en
dc.description.abstract© 2015 IEEE. Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification techniques based on the topological skeleton successively remove pairs of critical points connected by separatrices, using distance or area-based relevance measures. These methods rely on the stable extraction of the topological skeleton, which can be difficult due to instability in numerical integration, especially when processing highly rotational flows. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness which enables the pruning of sets of critical points according to a quantitative measure of their stability, that is, the minimum amount of vector field perturbation required to remove them. This leads to a hierarchical simplification scheme that encodes flow magnitude in its perturbation metric. Our novel simplification algorithm is based on degree theory and has minimal boundary restrictions. Finally, we provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets. We show local and complete hierarchical simplifications for steady as well as unsteady vector fields.en
dc.description.sponsorshipThe authors thank Jackie Chen for the combustion dataset and Mathew Maltude from LANL and the BER Office of Science UV-CDAT team for the ocean datasets. P. Rosen was supported by DOE NETL and KAUST award KUS-C1-016-04. P. Skraba was supported by TOPOSYS (FP7-ICT-318493). G. Chen was supported by US National Science Foundation (NSF) IIS-1352722. B. Wang was supported by INL 00115847 DE-AC0705ID14517 and DOE NETL.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.subjectComputational topologyen
dc.subjectFlow visualizationen
dc.subjectRobustnessen
dc.subjectVector field simplificationen
dc.titleRobustness-Based Simplification of 2D Steady and Unsteady Vector Fieldsen
dc.typeArticleen
dc.identifier.journalIEEE Transactions on Visualization and Computer Graphicsen
dc.contributor.institutionJozef Stefan Institute, Ljubljana, Sloveniaen
dc.contributor.institutionUniversity of Utah, Salt Lake City, United Statesen
dc.contributor.institutionUniversity of Houston, Houston, United Statesen
kaust.grant.numberKUS-C1-016-04en

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