© 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.
|Original language||English (US)|
|Number of pages||15|
|Journal||IEEE Transactions on Visualization and Computer Graphics|
|State||Published - Aug 1 2015|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.