Correlation Visualization for Structural Uncertainty Analysis

Tobias Pfaffelmoser, Rüdiger Westermann

Computer Graphics and Visualization Group, Technische Universität München, Germany


In uncertain scalar fields, where the values at every point can be assumed 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 on 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 3D 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 motivate, 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 visually distinguishing 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.

A preprint of the article is available for download below. The definitive version is available at


The work was funded by the European Union under the ERC Advanced Grant 291372: SaferVis - Uncertainty Visualization for Reliable Data Discovery, and the Munich Centre for Advanced Computing (MAC) and the International Graduate School of Science and Engineering (IGSSE) at the Technische Universität München.

Associated Publications

Correlation Visualization for Structural Uncertainty Analysis
T. Pfaffelmoser, R. Westermann,  International Journal of Uncertainty Quantification IJUQ Pfaffelmoser [Download] [Bibtex]