Correlation Visualization for Structural Uncertainty Analysis

In uncertain scalar fields, where the values at every point can be assumed as realizations of a random variable, standard deviations indicate the strength of possible variations of these values from their mean values, independently of the values at any other point in the domain. To infer the possible variations at different points relative to each other, and thus to predict the possible structural occurrences, i.e., the structural variability, of particular features in the data, the correlation between the values at these points has to be considered. The purpose of this paper is to shed light on the use of correlation as an indicator for the structural variability of isosurfaces in uncertain three-dimensional scalar fields. In a number of examples, we first demonstrate some general conclusions one can draw from the correlations in uncertain data regarding its structural variability. We will further explain, why an adequate correlation visualization is crucial for a comprehensive uncertainty analysis. Then, our focus is on the visualization of local and usually anisotropic correlation structures in the vicinity of uncertain isosurfaces. Therefore, we propose a model that can represent anisotropic correlation structures on isosurfaces and allows visual distinguishing of the local correlations between points on the surface and along the surface’s normal directions. A glyph-based approach is used to simultaneously visualize these dependencies. The practical relevance of our work is demonstrated in artificial and real-world examples using standard random distributions and ensemble simulations.