2D Vector Field Simplification Based on Robustness

Primoz Skraba, Bei Wang, Guoning Chen, Paul Rosen

Research output: Chapter in Book/Report/Conference proceedingConference contribution

27 Scopus citations


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. These geometric metrics do not consider the flow magnitude, an important physical property of the flow. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness, which provides a complementary view on flow structure compared to the traditional topological-skeleton-based approaches. Robustness 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, has fewer boundary restrictions, and so can handle more general cases. Finally, we provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets. © 2014 IEEE.
Original languageEnglish (US)
Title of host publication2014 IEEE Pacific Visualization Symposium
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Number of pages8
ISBN (Print)9781479928743
StatePublished - Mar 2014
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1–016-04
Acknowledgements: We thank Jackie Chen for the combustion datase and Mathew Maltude from LANL and the BER Office of Science UV-CDAT team for the ocean datasets. PR was supported by DOE NETL and KAUST award KUS-C1–016-04. PS was supported by TOPOSYS (FP7-ICT-318493). GC was supported by NSF IIS-1352722. BW was supported in part by INL 00115847 DE-AC0705ID14517 and DOENETL.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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