Interpreting Galilean Invariant Vector Field Analysis Via Extended Robustness

The topological notion of robustness introduces mathematically rigorous approaches to interpret vector field data. Robustness quantifies the structural stability of critical points with respect to perturbations and has been shown to be useful for increasing the visual interpretability of vector fields. However, critical points, which are essential components of vector field topology, are defined with respect to a chosen frame of reference. The classical definition of robustness, therefore, depends also on the chosen frame of reference. We define a new Galilean invariant robustness framework that enables the simultaneous visualization of robust critical points across the dominating reference frames in different regions of the data. We also demonstrate a strong connection between such a robustness-based framework with the one recently proposed by Bujack et al., which is based on the determinant of the Jacobian. Our results include notable observations regarding the definition of stable features within the vector field data.

Bei Wang, Roxana Bujack, Paul Rosen, Primoz Skraba, Harsh Bhatia, and Hans Hagen. Interpreting Galilean Invariant Vector Field Analysis Via Extended Robustness. Topological Methods in Data Analysis and Visualization V, 2020.

@article{wang2019interpreting,
  title = {Interpreting Galilean Invariant Vector Field Analysis via Extended Robustness},
  author = {Wang, Bei and Bujack, Roxana and Rosen, Paul and Skraba, Primoz and Bhatia,
    Harsh and Hagen, Hans},
  journal = {Topological Methods in Data Analysis and Visualization V},
  year = {2020},
  note = {textit{Presented at TopoInVis 2017.}},
  abstract = {The topological notion of robustness introduces mathematically rigorous
    approaches to interpret vector field data. Robustness quantifies the structural
    stability of critical points with respect to perturbations and has been shown to be
    useful for increasing the visual interpretability of vector fields. However, critical
    points, which are essential components of vector field topology, are defined with
    respect to a chosen frame of reference. The classical definition of robustness,
    therefore, depends also on the chosen frame of reference. We define a new Galilean
    invariant robustness framework that enables the simultaneous visualization of robust
    critical points across the dominating reference frames in different regions of the data.
    We also demonstrate a strong connection between such a robustness-based framework with
    the one recently proposed by Bujack et al., which is based on the determinant of the
    Jacobian. Our results include notable observations regarding the definition of stable
    features within the vector field data.}
}