Mathematical Foundations of Uncertain Field Visualization

  • Gerik Scheuermann
  • Mario Hlawitschka
  • Christoph Garth
  • Hans Hagen
Chapter
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

Uncertain field visualization is currently a hot topic as can be seen by the overview in this book. This article discusses a mathematical foundation for this research. To this purpose, we define uncertain fields as stochastic processes. Since uncertain field data is usually given in the form of value distributions on a finite set of positions in the domain, we show for the popular case of Gaussian distributions that the usual interpolation functions in visualization lead to Gaussian processes in a natural way. It is our intention that these remarks stimulate visualization research by providing a solid mathematical foundation for the modeling of uncertainty.

Keywords

Covariance 

References

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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Gerik Scheuermann
    • 1
  • Mario Hlawitschka
    • 1
  • Christoph Garth
    • 2
  • Hans Hagen
    • 2
  1. 1.University of LeipzigLeipzigGermany
  2. 2.TU KaiserslauternKaiserslauternGermany

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