Tobias Pfaffelmoser and Rüdiger Westermann.
Visualization of Global Correlation Structures in Uncertain 2D Scalar Fields.
In Computer Graphics Forum, vol. 31, no. 3, pp. 1025--1034, 2012.

Links:

Abstract:

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.

Bibtex:

@Article{        pfaffelmoser:2012:VGCS,
  author = 	 {Tobias Pfaffelmoser and R{\"u}diger Westermann},
  title =        {Visualization of Global Correlation Structures in
                  Uncertain 2D Scalar Fields},
  journal =      {Computer Graphics Forum},
  volume =       {31},
  number =       {3},
  pages =        {1025--1034},
  year =         {2012},
}

Images:

References:

[ACN08] AILON N., CHARIKAR M., NEWMAN A.: Aggregating inconsistent information: ranking and clustering. Journal of the ACM (JACM) 55, 5 (2008), 23. 3, 4
[BAF08] BOSTROM A., ANSELIN L., FARRIS J.: Visualizing Seismic Risk and Uncertainty. Annals of the New York Academy of Sciences 1128, 1 (2008), 29-40. 2
[BBC04] BANSAL N., BLUM A., CHAWLA S.: Correlation clustering. Machine Learning 56, 1 (2004), 89-113. 3
[BKKZ04] BÖHM C., KAILING K., KRÖGER P., ZIMEK A.: Computing clusters of correlation connected objects. In Proceedings of the 2004 ACM SIGMOD international conference on Management of data (2004), ACM, pp. 455-466. 3
[Bro04] BROWN R.: Animated visual vibrations as an uncertainty visualisation technique. In GRAPHITE (2004), ACM, pp. 84-89. 3
[CWMW11] CHEN C., WANG C., MA K., WITTENBERG A.: Static correlation visualization for large time-varying volume data. In Pacific Visualization Symposium (PacificVis), 2011 IEEE (2011), IEEE, pp. 27-34. 3
[DKLP02] DJURCILOV S., KIM K., LERMUSIAUX P., PANG A.: Visualizing scalar volumetric data with uncertainty. Computers & Graphics 26, 2 (2002), 239-248. 3
[GR04] GRIGORYAN G., RHEINGANS P.: Point-based probabilistic surfaces to show surface uncertainty. Visualization and Computer Graphics, IEEE Transactions on 10, 5 (2004), 564-573. 3
[GS06] GRIETHE H., SCHUMANN H.: The visualization of uncertain data: Methods and problems. In Proceedings of SimVis 2006 (2006), pp. 143-156. 2
[Hol11] HOLY T.:. http://www.mathworks.com/matlabcentral/fileexchange/29702, 2011. 4
[JPR04] JEN D., PARENTE P., ROBBINS J., WEIGLE C., TAYLOR II R., BURETTE A., WEINBERG R.: Imagesurfer: A tool for visualizing correlations between two volume scalar fields. 3
[JS03] JOHNSON C., SANDERSON A.: A next step: Visualizing errors and uncertainty. Computer Graphics and Applications, IEEE 23, 5 (2003), 6-10. 1, 2
[KKZ09] KRIEGEL H., KRÖGER P., ZIMEK A.: Clustering highdimensional data: A survey on subspace clustering, pattern-based clustering, and correlation clustering. ACM Transactions on Knowledge Discovery from Data (TKDD) 3, 1 (2009), 1. 3
[KWL] KINDLMANN G., WEINSTEIN D., LEE A., TOGA A., THOMPSON P.: Visualization of anatomic covariance tensor fields. In Engineering in Medicine and Biology Society, 2004. IEMBS'04. 26th Annual International Conference of the IEEE, vol. 1, IEEE, pp. 1842-1845. 3
[KWTM03] KINDLMANN G., WHITAKER R., TASDIZEN T., MOLLER T.: Curvature-based transfer functions for direct volume rendering: Methods and applications. In Visualization, 2003. VIS 2003. IEEE (2003), IEEE, pp. 513-520. 3
[LFLH07] LI H., FU C., LI Y., HANSON A.: Visualizing largescale uncertainty in astrophysical data. Visualization and Computer Graphics, IEEE Transactions on 13, 6 (2007), 1640-1647.2
[LLPY07] LUNDSTROM C., LJUNG P., PERSSON A., YNNERMAN A.: Uncertainty visualization in medical volume rendering using probabilistic animation. Visualization and Computer Graphics, IEEE Transactions on 13, 6 (2007), 1648-1655. 3
[MRH05] MACEACHREN A., ROBINSON A., HOPPER S., GARDNER S., MURRAY R., GAHEGAN M., HETZLER E.: Visualizing Geospatial Information Uncertainty: What We Know and What We Need to Know. Cartography and Geographic Information Science 32, 3 (2005), 139-161. 2
[PH10] PÖTHKOW K., HEGE H.: Positional uncertainty of isocontours: Condition analysis and probabilistic measures. Visualization and Computer Graphics, IEEE Transactions on, 99(2010), 1-1. 3
[Pot] POTTER K.:. http://www.sci.utah.edu/~kpotter/library/uncertainVis/index.html.2
[PRW11] PFAFFELMOSER T., REITINGER M., WESTERMANN R.: Visualizing the positional and geometrical variability of isosurfaces in uncertain scalar fields. In Computer Graphics Forum (2011), vol. 30, Wiley Online Library, pp. 951-960. 3, 7
[PWH11] PÖTHKOW K., WEBER B., HEGE H.: Probabilistic marching cubes. In Computer Graphics Forum (2011), vol. 30, Wiley Online Library, pp. 931-940. 3
[PWL97] PANG A., WITTENBRINK C., LODHA S.: Approaches to uncertainty visualization. The Visual Computer 13, 8 (1997), 370-390. 1, 2, 3
[RLBS03] RHODES P., LARAMEE R., BERGERON R., SPARR T.: Uncertainty visualization methods in isosurface rendering. In Eurographics (2003), Citeseer, pp. 83-88. 3
[STS06] SAUBER N., THEISEL H., SEIDEL H.: Multifieldgraphs: An approach to visualizing correlations in multifield scalar data. Visualization and Computer Graphics, IEEE Transactions on 12, 5 (2006), 917-924. 3
[SWMW09] SUKHAREV J., WANG C., MA K., WITTENBERG A.: Correlation study of time-varying multivariate climate data sets. In Visualization Symposium, 2009. PacificVis' 09. IEEE Pacific (2009), IEEE, pp. 161-168. 3
[SZD10] SANYAL J., ZHANG S., DYER J., MERCER A., AMBURN P., MOORHEAD R.: Noodles: A Tool for Visualization of Numerical Weather Model Ensemble Uncertainty. IEEE Transactions on Visualization and Computer Graphics (2010). 3
[Tar05] TARANTOLA A.: Inverse problem theory and methods for model parameter estimation. Society for Industrial Mathematics, 2005. 3
[THM05] THOMSON J., HETZLER E., MACEACHREN A., GAHEGAN M., PAVEL M.: A typology for visualizing uncertainty. In Proc. SPIE (2005), vol. 5669, Citeseer, pp. 146-157. 2
[WPL02] WITTENBRINK C., PANG A., LODHA S.: Glyphs for visualizing uncertainty in vector fields. Visualization and Computer Graphics, IEEE Transactions on 2, 3 (2002), 266-279. 3
[YXK11] YANG C., XIU D., KIRBY R. M.: Visualization of Covariance and Cross-covariance Fields. International Journal for Uncertainty Quantification (to appear) (2011). 3
[Zim08] ZIMEK A.: Correlation Clustering. PhD thesis, LMU München, 2008. 3
[ZWK10] ZEHNER B., WATANABE N., KOLDITZ O.: Visualization of gridded scalar data with uncertainty in geosciences. Computers & Geosciences (2010). 3