  Critical point tracking is a core topic in scientific visualization for
understanding the dynamic behavior of time-varying vector field data. The
topological notion of robustness has been introduced recently to quantify the
structural stability of critical points, that is, the robustness of a critical
point is the minimum amount of perturbation to the vector field necessary to
cancel it. A theoretical basis has been established previously that relates
critical point tracking with the notion of robustness, in particular, critical
points could be tracked based on their closeness in stability, measured by
robustness, instead of just distance proximities within the domain. However, in
practice, the computation of classic robustness may produce artifacts when a
critical point is close to the boundary of the domain; thus, we do not have a
complete picture of the vector field behavior within its local neighborhood. To
alleviate these issues, we introduce a multilevel robustness framework for the
study of 2D time-varying vector fields. We compute the robustness of critical
points across varying neighborhoods to capture the multiscale nature of the
data and to mitigate the boundary effect suffered by the classic robustness
computation. We demonstrate via experiments that such a new notion of
robustness can be combined seamlessly with existing feature tracking algorithms
to improve the visual interpretability of vector fields in terms of feature
tracking, selection, and comparison for large-scale scientific simulations. We
observe, for the first time, that the minimum multilevel robustness is highly
correlated with physical quantities used by domain scientists in studying a
real-world tropical cyclone dataset. Such observation helps to increase the
physical interpretability of robustness.
