# Visualization of Uncertain Fields

#### Summary

Almost all data, we want to visualize, suffers from uncertainty. That can happen due to inaccurate meauserments or uncertainty within the data aquisition procedure. Therfore, it is important to know how big the uncertainty is and where in the data uncertainty occurs. Otherwise, we would risk making descisions that rely on data we should not rely on. Thus, it is vital to integrate our knowledge about the uncertainty into our visualizations.

By the time being, we consider two approaches.

**The Discrete Approach****The Continous Approach**

Instead of computing streamlines from single particles, we compute particle distributions. The flow map of the vector field is encoded in a transition matrix (see time-discrete Markov-Chains). This transition matrix can be used to visualize the stationary states of particle distributions in the field (e.g. with colormaps).

A major challenge regarding grid-based, uncertain data is interpolation. The question arises: What is "the best" way to estimate values in between the grid positions? If the uncertainty is normally distributed, Gaussian processes are a possible solution for this problem. They have a well-founded mathematical basis. Therefore they enable us to use well-known visualization techniques (that are based on interpolation) with little to no changes on uncertain data.

Assistants: |

#### Publications:

- Analysis of Streamline Separation at Infinity Using Time-Discrete Markov Chains, 2012
- On the Interpolation of Data with Normally Distributed Uncertainty for Visualization, 2012