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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

Probability Space Covariance Function Gaussian Process Multivariate Gaussian Distribution Continuous Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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