Visualization of topological structures in uncertain fields

标量场和矢量场在许多科学学科中扮演着重要的角色。可以找到重要的例子，例如在流体动力学和气候研究中。模拟和测量产生了大量的数据集，如果没有可视化，人类就无法理解这些数据集。在可视化研究中，提取和显示基本结构的方法在创建相关图像方面发挥着越来越大的作用。由于所有的数据都带有来自计算误差、测量误差或未知参数的不确定性，因此基于结构的可视化应该考虑不确定性。本项目旨在开发基于这种结构的可视化方法，特别是考虑不确定性的拓扑可视化方法。一项重要的任务是将随机数据建模为随机过程，这也是在前期工作中所做的。新方法将与领域专家一起进行评估。

Scalar and vector fields play a prominent role in many scientific disciplines. Important examples can be found, e.g. in fluid dynamics and climate research. Simulations andmeasurements create large data sets that can not be understood by humans withoutvisualization. In visualization research, methods to extract and show essential structuresplay a increasing role to create relevant images. Since all data comes with uncertainty from computing errors, measurement errors or not exactly known parameters, structure-based visualization should take uncertainty into account. This project aims at the development of such structure-based, especially topological visualization methods that take uncertainty into account. An important task is the modelling of stochastic data as stochastic processes which was also done in preliminary work. The new methods will be evaluated with domain experts.