Visualization of Global Correlation Structures in Uncertain 2D Scalar Fields (English)

In: Computer Graphics Forum   ;  31 ,  3pt2  ;  1025-1034  ;  2012

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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.

Table of contents – Volume 31, Issue 3pt2

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Using Signposts for Navigation in Large Graphs
May, T. / Steiger, M. / Davey, J. / Kohlhammer, J. | 2012
Comparative Evaluation of an Interactive Time‐Series Visualization that Combines Quantitative Data with Qualitative Abstractions
Aigner, W. / Rind, A. / Hoffmann, S. | 2012
A Qualitative Study on the Exploration of Temporal Changes in Flow Maps with Animation and Small‐Multiples
Boyandin, Ilya / Bertini, Enrico / Lalanne, Denis | 2012
Conceptualizing Visual Uncertainty in Parallel Coordinates
Dasgupta, Aritra / Chen, Min / Kosara, Robert | 2012
Visualization of Global Correlation Structures in Uncertain 2D Scalar Fields
Pfaffelmoser, Tobias / Westermann, Rüdiger | 2012
Vortex Analysis in Uncertain Vector Fields
Otto, Mathias / Theisel, Holger | 2012
Probabilistic Local Features in Uncertain Vector Fields with Spatial Correlation
Petz, Christoph / Pöthkow, Kai / Hege, Hans‐Christian | 2012
Reliable Adaptive Modelling of Vascular Structures with Non‐Circular Cross‐Sections
Kretschmer, Jan / Beck, Thomas / Tietjen, Christian / Preim, Bernhard / Stamminger, Marc | 2012
Visualization of 4D Blood‐Flow Fields by Spatiotemporal Hierarchical Clustering
van Pelt, R. F. P. / Jacobs, S. S. A. M. / ter Haar Romeny, B. M. / Vilanova, A. | 2012
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Biopsy Planner – Visual Analysis for Needle Pathway Planning in Deep Seated Brain Tumor Biopsy
Herghelegiu, P. C. / Manta, V. / Perin, R. / Bruckner, S. / Gröller, E. | 2012
Automatic Stream Surface Seeding: A Feature Centered Approach
Edmunds, M. / Laramee, R.S. / Malki, R. / Masters, I. / Croft, T.N. / Chen, G. / Zhang, E. | 2012
Visualization of Advection‐Diffusion in Unsteady Fluid Flow
Karch, Grzegorz Karol / Sadlo, Filip / Weiskopf, Daniel / Munz, Claus‐Dieter / Ertl, Thomas | 2012