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. 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 talk, I will give an overview on some of my recent work in studying the stability of critical points within vector fields data.
This includes: (a) a new visualization framework which enables interactive exploration of robustness of critical points for time-varying 2D vector fields;
(b) feature tracking under the notion of robustness;
(c) vector field simplification based on robustness, which provides a complementary view on flow structure compared to the traditional topological-skeleton-based approaches.
I will end my talk by discussing some future directions in the study of dynamic systems: robustness quantification with uncertainty, etc.