Robustness for 2D Symmetric Tensor Field Topology

  • Bei Wang
  • Ingrid HotzEmail author
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


Topological feature analysis is a powerful instrument to understand the essential structure of a dataset. For such an instrument to be useful in applications, however, it is important to provide some importance measure for the extracted features that copes with the high feature density and discriminates spurious from important structures. Although such measures have been developed for scalar and vector fields, similar concepts are scarce, if not nonexistent, for tensor fields. In particular, the notion of robustness has been proven to successfully quantify the stability of topological features in scalar and vector fields. Intuitively, robustness measures the minimum amount of perturbation to the field that is necessary to cancel its critical points.

This chapter provides a mathematical foundation for the construction of a feature hierarchy for 2D symmetric tensor field topology by extending the concept of robustness, which paves new ways for feature tracking and feature simplification of tensor field data. One essential ingredient is the choice of an appropriate metric to measure the perturbation of tensor fields. Such a metric must be well-aligned with the concept of robustness while still providing some meaningful physical interpretation. A second important ingredient is the index of a degenerate point of tensor fields, which is revisited and reformulated rigorously in the language of degree theory.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of UtahSalt Lake CityUSA
  2. 2.Linköping UniversityNorrköpingSweden

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