Visualizing Robustness Of Critical Points For 2D Time-Varying Vector Fields

Visualizing Robustness Of Critical Points For 2D Time-Varying Vector Fields
Bei Wang, Paul Rosen, Primoz Skraba, Harsh Bhatia, and Valerio Pascucci
Computer Graphics Forum, 2013

Abstract

Analyzing critical points and their temporal evolutions plays a crucial role in understanding the behavior of vector fields. A key challenge is to quantify the stability of critical points: more stable points may represent more important phenomena or vice versa. The topological notion of robustness is a tool which allows us to quantify rigorously the stability of each critical point. Intuitively, the robustness of a critical point is the minimum amount of perturbation necessary to cancel it within a local neighborhood, measured under an appropriate metric. In this paper, we introduce a new analysis and visualization framework which enables interactive exploration of robustness of critical points for both stationary and time-varying 2D vector fields. This framework allows the end-users, for the first time, to investigate how the stability of a critical point evolves over time. We show that this depends heavily on the global properties of the vector field and that structural changes can correspond to interesting behavior. We demonstrate the practicality of our theories and techniques on several datasets involving combustion and oceanic eddy simulations and obtain some key insights regarding their stable and unstable features.

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Bei Wang, Paul Rosen, Primoz Skraba, Harsh Bhatia, and Valerio Pascucci. Visualizing Robustness Of Critical Points For 2D Time-Varying Vector Fields. Computer Graphics Forum, 2013.

Bibtex


@article{wang2013visualizing,
  title = {Visualizing Robustness of Critical Points for 2D Time-Varying Vector Fields},
  author = {Wang, Bei and Rosen, Paul and Skraba, Primoz and Bhatia, Harsh and Pascucci,
    Valerio},
  journal = {Computer Graphics Forum},
  series = {EuroVis},
  volume = {32},
  pages = {221--230},
  year = {2013},
  abstract = {Analyzing critical points and their temporal evolutions plays a crucial
    role in understanding the behavior of vector fields. A key challenge is to quantify the
    stability of critical points: more stable points may represent more important phenomena
    or vice versa. The topological notion of robustness is a tool which allows us to
    quantify rigorously the stability of each critical point. Intuitively, the robustness of
    a critical point is the minimum amount of perturbation necessary to cancel it within a
    local neighborhood, measured under an appropriate metric. In this paper, we introduce a
    new analysis and visualization framework which enables interactive exploration of
    robustness of critical points for both stationary and time-varying 2D vector fields.
    This framework allows the end-users, for the first time, to investigate how the
    stability of a critical point evolves over time. We show that this depends heavily on
    the global properties of the vector field and that structural changes can correspond to
    interesting behavior. We demonstrate the practicality of our theories and techniques on
    several datasets involving combustion and oceanic eddy simulations and obtain some key
    insights regarding their stable and unstable features.}
}