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Interpreting Feature Tracking Through the Lens of Robustness

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Topological Methods in Data Analysis and Visualization III

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

A key challenge in the study of a time-varying vector fields is to resolve the correspondences between features in successive time steps and to analyze the dynamic behaviors of such features, so-called feature tracking. Commonly tracked features, such as volumes, areas, contours, boundaries, vortices, shock waves and critical points, represent interesting properties or structures of the data. Recently, the topological notion of robustness, a relative of persistent homology, has been introduced to quantify the stability of critical points. Intuitively, the robustness of a critical point is the minimum amount of perturbation necessary to cancel it. In this chapter, we offer a fresh interpretation of the notion of feature tracking, in particular, critical point tracking, through the lens of robustness. We infer correspondences between critical points based on their closeness in stability, measured by robustness, instead of just distance proximities within the domain. We prove formally that robustness helps us understand the sampling conditions under which we can resolve the correspondence problem based on region overlap techniques, and the uniqueness and uncertainty associated with such techniques. These conditions also give a theoretical basis for visualizing the piecewise linear realizations of critical point trajectories over time.

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Acknowledgements

This work was funded in part by the EU project TOPOSYS (FP7-ICT-318493-STREP), NSF OCI-0906379, NSF OCI- 0904631, DOE/NEUP 120341, DOE/MAPD DESC000192, DOE/LLNL B597476, DOE/Codesign P01180734, and DOE/SciDAC DESC0007446. The authors would like to thank Guoning Chen and Paul Rosen for developing the tool for robustness-based visualization. We thank Jackie Chen for the combustion dataset. We also thank Mathew Maltude from the Climate, Ocean and Sea Ice Modeling program at Los Alamos National Laboratory (LANL) and the BER Office of Science UV-CDAT team for providing us the ocean datasets. The authors would also like to thank the anonymous reviewers for many useful comments to improve the readability of the paper.

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Authors and Affiliations

  1. Jozef Stefan Institute, Ljubljana, Slovenia

    Primoz Skraba

  2. Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT, USA

    Bei Wang

Authors
  1. Primoz Skraba
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  2. Bei Wang
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Correspondence to Bei Wang .

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Editors and Affiliations

  1. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, California, USA

    Peer-Timo Bremer

  2. Comparative Visualization Group, Konrad-Zuse-Zentrum für Informationstechnik, Berlin, Germany

    Ingrid Hotz

  3. School of Computing and SCI Institute, University of Utah, Salt Lake City, Utah, USA

    Valerio Pascucci

  4. Department of Computer Science, ETH Zürich, Zürich, Switzerland

    Ronald Peikert

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© 2014 Springer International Publishing Switzerland

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Skraba, P., Wang, B. (2014). Interpreting Feature Tracking Through the Lens of Robustness. In: Bremer, PT., Hotz, I., Pascucci, V., Peikert, R. (eds) Topological Methods in Data Analysis and Visualization III. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-04099-8_2

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