Modeling, Quantification and Visualization of Probabilistic Features in Fields with Uncertainties
Kai Pöthkow · Universitätsbibliothek der FU Berlin Hochschulschriftenstelle u. Dokumentenserver · 2015
A fundamental property of scientific data is that the true value of a quantity can not be determined with arbitrary precision. It is only possible to enclose it using intervals or characterize the uncertainty using probability distributions. This property is shared by all types of real-valued data, both measurements and simulation results. Examples include measurements of basic physical quantities like velocity as well as long-term temperature forecasts that are computed using climate models. The uncertainty of quantities is an important information that is often indicated using confidence intervals in tables and graphical representations like 1D plots. However, for 2D and 3D data, the uncertainty can not be adequately represented using standard visualization methods in most cases. This thesis proposes methods to facilitate analysis and visualization of uncertain scalar, vector and tensor fields. The focus is on the extraction of spatiotemporal geometric and topological features, e.g. isocontours and critical points, from the fields. The approaches are are well founded on probability theory. We employ parametric and nonparametric random fields as mathematical models for the uncertainty and spatial correlations. The probability distributions are estimated from ensemble data that combine results of multiple simulation runs which are based on, e.g., varying simulation parameters. Furthermore, we introduce condition analysis to feature-based visualization. Condition numbers quantify the sensitivity, i.e. the amplification or attenuation of uncertainty of features relative to the uncertainty of the input fields. We propose a generic approach to probabilistic feature extraction that is the basis for the estimation of spatial distributions of various features in uncertain fields. In this framework, probabilities for the existence of features can be computed from local marginal distributions and formal feature definitions. Numerically, the probabilities can be estimated using Monte Carlo integration. To overcome the high computational cost of this approach, we propose fast approximate methods which employ surrogate functions and lookup tables for the estimate feature probabilities. The proposed methods are evaluated qualitatively and quantitatively using uncertain fields from climate and biofluid mechanics simulations as well as medical imaging.