2D Vector Field Simplification Based On Robustness

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.

Primoz Skraba, Bei Wang, Guoning Chen, and Paul Rosen. 2D Vector Field Simplification Based On Robustness. IEEE Pacific Visualization Symposium, 2014.

@inproceedings{skraba20142d,
  title = {2D Vector Field Simplification Based on Robustness},
  author = {Skraba, Primoz and Wang, Bei and Chen, Guoning and Rosen, Paul},
  booktitle = {IEEE Pacific Visualization Symposium},
  series = {PacificVis},
  pages = {49--56},
  year = {2014},
  keywords = {vector field; topology-based techniques; flow visualization},
  note = {Best Paper Award.},
  abstract = {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.}
}