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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\u2010varying 2D vector fields. This framework allows the end\u2010users, 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.<\/jats:p>","DOI":"10.1111\/cgf.12109","type":"journal-article","created":{"date-parts":[[2013,7,1]],"date-time":"2013-07-01T16:13:39Z","timestamp":1372695219000},"page":"221-230","update-policy":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/http\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Visualizing Robustness of Critical Points for 2D Time\u2010Varying Vector Fields"],"prefix":"10.1111","volume":"32","author":[{"given":"B.","family":"Wang","sequence":"first","affiliation":[]},{"given":"P.","family":"Rosen","sequence":"additional","affiliation":[]},{"given":"P.","family":"Skraba","sequence":"additional","affiliation":[]},{"given":"H.","family":"Bhatia","sequence":"additional","affiliation":[]},{"given":"V.","family":"Pascucci","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2013,7]]},"reference":[{"key":"e_1_2_9_2_2","unstructured":"BrambillaA. 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