# Colloquium of the Department and the PhD Program

## title

*Probabilistic Features in Uncertain Scalar and Vector Fields*

## speaker

## date & place

Wednesday, 09.01.2013, 15:15 h

Room G 309

## abstract

Spatial and spatiotemporal fields are often afflicted with uncertainties. In a probabilistic modeling such fields can be described by discrete random fields. A standard task in visual analysis of fields is to extract and visualize geometrical or topological characteristics -- often called 'features'. Examples are locally defined features, like patches of iso-contours, critical points or vortex indicators, or globally defined ones, like topological skeletons. In this talk I will focus on locally defined features in correlated random fields. While in a crisp field, at some given location, a feature is either present or absent, in a random field it is present with some probability. It will be shown, how such probabilities can be computed. For Gaussian random fields the computation simplifies substantially, since only locally defined marginal density functions need to be integrated. The higher-dimensional integrals can be calculated using Monte Carlo methods. I will also sketch shortly, how to deal with the non-Gaussian case. Potential applications will be illustrated, using 2D and 3D examples from climate research, fluid dynamics and medicine.