Robustness-Based Simplification Of 2D Steady And Unsteady Vector Fields

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.

Primoz Skraba, Bei Wang, Guoning Chen, and Paul Rosen. Robustness-Based Simplification Of 2D Steady And Unsteady Vector Fields. IEEE Transactions on Visualization and Computer Graphics (TVCG), 2015.

@article{skraba2015robustness,
  title = {Robustness-Based Simplification of 2D Steady and Unsteady Vector Fields},
  author = {Skraba, Primoz and Wang, Bei and Chen, Guoning and Rosen, Paul},
  journal = {IEEE Transactions on Visualization and Computer Graphics (TVCG)},
  volume = {21},
  pages = {930--944},
  year = {2015},
  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. 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.}
}