Critical Point Cancellation In 3D Vector Fields: Robustness And Discussion

Vector field topology has been successfully applied to represent the structure of steady vector fields. Critical points, one of the essential components of vector field topology, play an important role in describing the complexity of the extracted structure. Simplifying vector fields via critical point cancellation has practical merit for interpreting the behaviors of complex vector fields such as turbulence. However, there does not exist an effective technique that allows direct cancellation of critical points in 3D. This work fills this gap and introduces the emph{first} framework to directly cancel pairs or groups of 3D critical points in a hierarchical manner with guaranteed minimum amount of perturbation based on their robustness, a quantitative measure of their stability. In addition, our framework does not require the extraction of the entire 3D topology, which contains nontrivial separation structure, and thus is computationally effective. Furthermore, our algorithm can remove critical points in any subregions of the domain whose degree is zero and handle complex boundary configurations, making it capable of addressing challenging scenarios that may not be resolved otherwise. We apply our methods to synthetic and simulation datasets to demonstrate its effectiveness.

Primoz Skraba, Paul Rosen, Bei Wang, Guoning Chen, Harsh Bhatia, and Valerio Pascucci. Critical Point Cancellation In 3D Vector Fields: Robustness And Discussion. IEEE Transactions on Visualization and Computer Graphics (TVCG), 2016.

@article{skraba2016critical,
  title = {Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion},
  author = {Skraba, Primoz and Rosen, Paul and Wang, Bei and Chen, Guoning and Bhatia,
    Harsh and Pascucci, Valerio},
  journal = {IEEE Transactions on Visualization and Computer Graphics (TVCG)},
  volume = {22},
  pages = {1683--1693},
  year = {2016},
  note = {textit{Presented at PacificVis 2014. Best Paper Award.}},
  abstract = {Vector field topology has been successfully applied to represent the
    structure of steady vector fields. Critical points, one of the essential components of
    vector field topology, play an important role in describing the complexity of the
    extracted structure. Simplifying vector fields via critical point cancellation has
    practical merit for interpreting the behaviors of complex vector fields such as
    turbulence. However, there does not exist an effective technique that allows direct
    cancellation of critical points in 3D. This work fills this gap and introduces the
    emph{first} framework to directly cancel pairs or groups of 3D critical points in a
    hierarchical manner with guaranteed minimum amount of perturbation based on their
    robustness, a quantitative measure of their stability. In addition, our framework does
    not require the extraction of the entire 3D topology, which contains nontrivial
    separation structure, and thus is computationally effective. Furthermore, our algorithm
    can remove critical points in any subregions of the domain whose degree is zero and
    handle complex boundary configurations, making it capable of addressing challenging
    scenarios that may not be resolved otherwise. We apply our methods to synthetic and
    simulation datasets to demonstrate its effectiveness.}
}