Tobias Pfaffelmoser, Rüdiger Westermann
Computer Graphics and Visualization Group, Technische Universität München, Germany
Visualizing correlations, i.e., the tendency of uncertain data values at different spatial positions to change contrarily or according to each other, allows inferring on the possible variations of structures in the data. Visualizing global correlation structures, however, is extremely challenging, since it is not clear how the visualization of complicated long-range dependencies can be integrated into standard visualizations of spatial data. Furthermore, storing correlation information imposes a memory requirement that is quadratic in the number of spatial sample positions. This paper presents a novel approach for visualizing both positive and inverse global correlation structures in uncertain 2D scalar fields, where the uncertainty is modeled via a multivariate Gaussian distribution. We introduce a new measure for the degree of dependency of a random variable on its local and global surroundings, and we propose a spatial clustering approach based on this measure to classify regions of a particular correlation strength. The clustering performs a correlation filtering, which results in a representation that is only linear in the number of spatial sample points. Via cluster coloring the correlation information can be embedded into visualizations of other statistical quantities, such as the mean and the standard deviation. We finally propose a hierarchical cluster subdivision scheme to further allow for the simultaneous visualization of local and global correlations.
A preprint of the article is available for download below. The definitive version is available at http://diglib.eg.org and http://onlinelibrary.wiley.com.
We would like to thank the ECMWF and Thomas Bodin from the RSES at ANU Canberra for providing the data sets used in this work. The work was partly 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.
Visualization of Global Correlation Structures in Uncertain 2D Scalar Fields
T. Pfaffelmoser, R. Westermann, Computer Graphics Forum (Proceedings of EuroVis 2012)