Mathematical foundations of uncertain field visualization

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.