Abstract
Most visualization techniques have been designed on the assumption that the data to be represented are free from uncertainty. Yet this is rarely the case. Recently the visualization community has risen to the challenge of incorporating an indication of uncertainty into visual representations, and in this article we review their work. We place the work in the context of a reference model for data visualization, that sees data pass through a pipeline of processes. This allows us to distinguish the visualization of uncertainty—which considers how we depict uncertainty specified with the data—and the uncertainty of visualization—which considers how much inaccuracy occurs as we process data through the pipeline. It has taken some time for uncertain visualization methods to be developed, and we explore why uncertainty visualization is hard—one explanation is that we typically need to find another display dimension and we may have used these up already! To organize the material we return to a typology developed by one of us in the early days of visualization, and make use of this to present a catalog of visualization techniques describing the research that has been done to extend each method to handle uncertainty. Finally we note the responsibility on us all to incorporate any known uncertainty into a visualization, so that integrity of the discipline is maintained.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aerts, J. C. J. H., Clarke, K. C., & Keuper, A. D. (2003). Testing popular visualization techniques for representing model uncertainty. Cartography and Geographic Information Science, 30(3), 249–261.
Allendes Osorio, R. S. (2010). Visualization of uncertainty in scientific data. PhD thesis, University of Leeds.
Allendes Osorio, R. S., & Brodlie, K. W. (2008). Contouring with uncertainty. In I. S. Lim, & W. Tang (Eds.), Proceedings 6th theory & practice of computer graphics conference (TP.CG.08). Eurographics Association.
Allendes Osorio, R. S., & Brodlie, K. W. (2009). Uncertain flow visualization using LIC. In W. Tang, & J. Collomosse (Eds.), Theory and practice of computer graphics—Eurographics UK chapter proceedings (pp. 215–222).
Berger, W., Piringer, H., Filzmoser, P., & Gröller, E. (2011). Uncertainty-aware exploration of continuous parameter spaces using multivariate prediction. Computer Graphics Forum, 30(3), 911–920.
Bhatia, H., Jadhav, S., Bremer, P.-T., Chen, G., Levine, J. A., Nonato, L. G., & Pascucci, V. (2011). Edge maps: representing flow with bounded error. In Proceedings of IEEE Pacific visualization symposium 2011, March 2011 (pp. 75–82).
Bingham, R. J., & Haines, K. (2006). Mean dynamic topography: intercomparisons and errors. Philosophical Transactions of the Royal Society A, 903–916.
Boller, R. A., Braun, S. A., Miles, J., & Laidlaw, D. H. (2010). Application of uncertainty visualization methods to meteorological trajectories. Earth Science Informatics, 3, 119–126.
Bonneau, G. P., Kindlmann, G., Hege, H. C., Johnson, C. R., Oliveira, M., Potter, K., & Rheinghans, P. (2012, in preparation). Overview and state-of-the-art of uncertainty visualization. In M. Chen, H. Hagen, C. Hansen, C. Johnson, & A. Kaufmann (Eds.), Scientific visualization: challenges for the future.
Botchen, R. P., Weiskopf, D., & Ertl, T. (2005). Texture-based visualization of uncertainty in flow fields. In Proceedings of IEEE visualization 2005 (pp. 647–654).
Boukhelifa, N., & Duke, D. J. (2007). The uncertain reality of underground assets. In Proceedings of ISPRS/ICA/DGfK joint workshop on visualization and exploration of geospatial data. ISPRS.
Brodlie, K. (1993). A classification scheme for scientific visualization. In R. A. Earnshaw, & D. Watson (Eds.), Animation and scientific visualization (pp. 125–140). San Diego: Academic Press.
Brodlie, K. W., Carpenter, L. A., Earnshaw, R. A., Gallop, J. R., Hubbold, R. J., Mumford, A. M., Osland, C. D., & Quarendon, P. (Eds.) (1992). Scientific visualization—techniques and applications. Berlin: Springer.
Brown, R. A. (2004). Animated visual vibrations as an uncertainty visualisation technique. In International conference on computer graphics and interactive techniques in Australasia and South East Asia (pp. 84–89).
Buttenfield, B., & Beard, M. K. (1994). Graphical and geographical components of data quality. In H. M. Hearnshaw, & D. J. Unwin (Eds.), Visualization in graphical information systems (pp. 150–157). New York: Wiley.
Carr, H., Moller, T., & Snoeyink, J. (2006). Artifacts caused by simplicial subdivision. IEEE Transactions on Visualization and Computer Graphics, 12(2), 231–242.
Cedilnik, A., & Rheingans, P. (2000). Procedural annotation of uncertain information. In Proceedings of visualization 2000 (pp. 77–84). Los Alamitos: IEEE Computer Society Press.
Coninx, A., Bonneau, G.-P., Droulez, J., & Thibault, G. (2011). Visualization of uncertain scalar data fields using color scales and perceptually adapted noise. In Applied perception in graphics and visualization. Toulouse, France.
Coppola, G., Sherwin, S. J., & Peiro, J. (2001). Nonlinear particle tracking for high-order elements. Journal of Computational Physics, 172(1), 356–386.
Correa, C. D., Chan, Y.-H., & Ma, K.-L. (2009). A framework for uncertainty-aware visual analytics. In Proceedings of IEEE symposium on visual analytics science and technology VAST 09.
Cox, M. G., & Harris, P. M. (2004). Uncertainty evaluation (Technical Report). National Physical Laboratory, March 2004. Software Support for Metrology. Best Practice Guide No. 6.
Cumming, G., Fidler, F., & Vaux, D. L. (2007). Error bars in experimental biology. The Journal of Cell Biology, 177(1), 7–11.
Daradkeh, M., McKinnon, A., & Churcher, C. (2010). Visualisation tools for exploring the uncertainty-risk relationship in the decision-making process: a preliminary empirical evaluation. In Proceedings of the eleventh Australasian conference on user interface, Auic ’10 (Vol. 106, pp. 42–51). Darlinghurst: Australian Computer Society
Davis, T. J., & Keller, C. P. (1997). Modelling and visualizing multiple spatial uncertainties. Computers and Geosciences, 23(4), 397–408. Exploratory Cartographic Visualisation.
Djurcilov, S., Kim, K., Lermusiaux, P., & Pang, A. (2002). Visualizing scalar volumetric data with uncertainty. Computers & Graphics, 26, 239–248.
Ehlschlaeger, C. R., Shortridge, A. M., & Goodchild, M. F. (1997). Visualizing spatial data uncertainty using animation. Computers and Geosciences, 23(4), 387–395.
Feng, D., Kwock, L., Lee, Y., & Taylor, R. M. (2010). Matching visual saliency to confidence in plots of uncertain data. IEEE Transactions on Visualization and Computer Graphics, 16(6), 980–989.
Fisher, P. (1994). Animation and sound for the visualization of uncertain spatial information. In Visualization in graphical information systems (pp. 181–185). New York: Wiley.
Goodchild, M., Buttenfield, B., & Wood, J. (1994). Introduction to visualizing data validity. In H. M. Hearnshaw, & D. J. Unwin (Eds.), Visualization in graphical information systems (pp. 141–149). New York: Wiley.
Griethe, H., & Schumann, H. (2006). The visualization of uncertain data: methods and problems. In Proceedings of the 17th simulation and visualization conference.
Grigoryan, G., & Rheingans, P. (2004). Point-based probabilistic surfaces to show surface uncertainty. IEEE Transactions on Visualization and Computer Graphics, 10(5), 564–573.
Haber, R. B., & McNabb, D. A. (1990). Visualization idioms: a conceptual model for scientific visualization systems. In B. Shriver, G. M. Nielson, & L. J. Rosenblum (Eds.), Visualization in scientific computing (pp. 74–93). IEEE.
Hengl, T. (2003). Visualisation of uncertainty using the hsi colour model: computation with colours. In Proceedings of the 7th international conference on geocomputation (pp. 8–17). Southampton, United Kingdom.
Hlawatsch, M., Leube, P., Nowak, W., & Weiskopf, D. (2011). Flow radar glyphs—static visualization of unsteady flow with uncertainty. IEEE Transactions on Visualization and Computer Graphics, 17(12), 1949–1958.
Jänicke, H., Wiebel, A., Scheuermann, G., & Kollmann, W. (2007). Multifield visualization using local statistical complexity. IEEE Transactions on Visualization and Computer Graphics, 13(6), 1384–1391.
Johnson, C. (2004). Top scientific visualization research problems. IEEE Computer Graphics and Applications, July/August, 13–17.
Johnson, C. R., & Sanderson, A. R. (2003). A next step: visualizing errors and uncertainties. IEEE Computer Graphics and Applications, 6–10.
Juang, K.-W., Chen, Y.-S., & Lee, D.-Y. (2004). Using sequential indicator simulation to assess the uncertainty of delineating heavy-metal contaminated soils. Environmental Pollution, 127, 229–238.
Kahl, J. D., & Sampson, P. J. (1986). Uncertainty in trajectory calculations due to low resolution meteorological data. Journal of Climate and Applied Meteorology, 25, 1816–1831.
Kipfer, P., Reck, F., & Greiner, G. (2003). Local exact particle tracing on unstructured grids. Computer Graphics Forum, 22, 133–142.
Kniss, J. M., Uitert, R. V., Stephens, A., Li, G.-S., Tasdizen, T., & Hansen, C. (2005). Statistically quantitative volume visualization. In IEEE visualization 2005.
Li, H., Fu, C.-W., Li, Y., & Hanson, A. J. (2007). Visualizing large-scale uncertainty in astrophysical data. IEEE Transactions on Visualization and Computer Graphics, 13(6), 1640–1647.
Lodha, S. K., Wilson, C. M., & Sheehan, R. E. (1996a). LISTEN: sounding uncertainty visualization. In Proceedings of visualization 96 (pp. 189–195).
Lodha, S. K., Pang, A., Sheehan, R. E., & Wittenbrink, C. M. (1996b). UFLOW: visualizing uncertainty in fluid flow. In R. Yagel, & G. M. Nielson (Eds.), IEEE visualization ’96 (pp. 249–254).
Lopes, A., & Brodlie, K. (1998). Accuracy in contour drawing. In Proceedings of Eurographics (pp. 301–312).
Lopes, A., & Brodlie, K. (1999). Accuracy in 3D particle tracing. In H. C. Hege, & K. Polthier (Eds.), Mathematical visualization: algorithms, applications and numerics (pp. 329–341). Berlin: Springer.
Lopes, A., & Brodlie, K. (2003). Improving the robustness and accuracy of the marching cubes algorithm for isosurfacing. IEEE Transactions on Visualization and Computer Graphics, 9, 16–29.
Love, A. L., Pang, A. T., & Kao, D. L. (2005). Visualizing spatial multivalue data. IEEE Computer Graphics and Applications, 69–79.
Lundstrom, C., Ljung, P., Persson, A., & Ynnerman, A. (2007). Uncertainty visualization in medical volume rendering using probabilistic animation. IEEE Transactions on Visualization and Computer Graphics, 13(6), 1648–1655.
Luo, A., Kao, D., & Pang, A. (2003). Visualizing spatial distribution data sets. In Proceedings of VISSYM ’03—Eurographics and IEEE TVCG symposium on visualization (pp. 29–38). Eurographics Association.
MacEachren, A. M. (1992). Visualizing uncertain information. Cartographic Perspective, Fall 13, 10–19.
MacEachren, A. M., Robinson, A., Hopper, S., Gardner, S., Murray, R., Gahegan, M., & Hetzler, E. (2005). Visualizing geospatial information uncertainty: what we know and what we need to know. Cartography and Geographic Information Science, 32(8), 139–160.
Nelson, B., & Kirby, R. M. (2006). Ray-tracing polymorphic multidomain spectral/hp elements for isosurface rendering. IEEE Transactions on Visualization and Computer Graphics, 12(1), 114–126.
Nelson, B., Kirby, R. M., & Haimes, R. (2011). Gpu-based interactive cut-surface extraction from high-order finite element fields. IEEE Transactions on Visualization and Computer Graphics, 17(12), 1803–1811.
Newman, T. S., & Lee, W. (2004). On visualizing uncertainty in volumetric data: techniques and their evaluation. Journal of Visual Languages and Computing, 15, 463–491.
Nielson, G. M., & Jung, I.-H. (1999). Tools for computing tangent curves for linearly varying vector fields over tetrahedral domains. IEEE Transactions on Visualization and Computer Graphics, 5(4), 360–372.
Olston, C., & Mackinlay, J. D. (2002). Visualizing data with bounded uncertainty. In INFOVIS (p. 37).
Otto, M., Germer, T., Hege, H.-C., & Theisel, H. (2010). Uncertain 2d vector field topology. Computer Graphics Forum, 29(2), 347–356.
Otto, M., Germer, T., & Theisel, H. (2011). Uncertain topology of 3d vector fields. In Visualization symposium (pp. 67–74). IEEE Pacific.
Pang, A. T., Wittenbrink, C. M., & Lodha, S. K. (1997). Approaches to uncertainty visualization. The Visual Computer, 13(8), 370–390.
Post, F. H., Vrolijk, B., Hauser, H., Laramee, R. S., & Doleisch, H. (2003). The state of the art in flow visualisation: feature extraction and tracking. Computer Graphics Forum, 22(4), 775–792.
Pöthkow, K., & Hege, H.-C. (2010). Positional uncertainty of isocontours: condition analysis and probabilistic measures. IEEE Transactions on Visualization and Computer Graphics.
Pöthkow, K., Weber, B., & Hege, H.-C. (2011). Probabilistic marching cubes. Computer Graphics Forum, 30(3), 931–940.
Potter, K., Wilson, A., Bremer, P.-T., Williams, D., Doutriaux, C., Pascucci, V., & Johnson, C. R. (2009). Ensemble-vis: a framework for the statistical visualization of ensemble data. In Proceedings of the 2009 IEEE international conference on data mining workshops (pp. 233–240). Los Alamitos: IEEE Computer Society.
Potter, K., Kniss, J., Riesenfeld, R., & Johnson, C. R. (2010). Visualizing summary statistics and uncertainty. Computer Graphics Forum, 29(3), 823–831.
Prabni, J.-S., Ropinski, T., & Hinrichs, K. (2010). Uncertainty-aware guided volume segmentation. IEEE Transactions on Visualization and Computer Graphics, 16(6), 1358–1365.
Preusser, A. (1989). Algorithm 671: Farb-e-2d: fill area with bicubics on rectangles—a contour plot program. ACM Transactions on Mathematical Software, 15, 79–89.
Rhodes, P. J., Laramee, R. S., Bergeron, R. D., & Sparr, T. M. (2003). Uncertainty visualization methods in isosurface rendering. In M. Chover, H. Hagen, & D. Tost (Eds.), Proceedings of Eurographics. The Eurographics Association.
Sanyal, J., Zhang, S., Bhattacharya, G., Amburn, P., & Moorhead, R. J. (2009). A user study to compare four uncertainty visualization methods for 1D and 2D datasets. IEEE Transactions on Visualization and Computer Graphics, 15(6), 1209–1218.
Sanyal, J., Zhang, S., Dyer, J., Mercer, A., Amburn, P., & Moorhead, R. J. (2010). Noodles: a tool for visualization of numerical weather model ensemble uncertainty. IEEE Transactions on Visualization and Computer Graphics, 16(6), 1421–1430.
Thomson, J., Hetzler, B., MacEachren, A., Gahegan, M., & Pavel, M. (2005). A typology for visualizing uncertainty. In Proceedings of the SPIE, visualization and data analysis (pp. 146–157).
Tory, M., & Moeller, T. (2004). Rethinking visualization: a high-level taxonomy. In Proceedings of IEEE symposium on information visualization (pp. 151–158).
Tukey, J. W. (1977). Exploratory data analysis. Reading: Addison-Wesley.
USGS (1977). Spatial data transfer standard (SDTS): logical specifications.
Wittenbrink, C. M., Pang, A. T., & Lodha, S. K. (1996). Glyphs for visualizing uncertainty in vector fields. IEEE Transactions on Visualization and Computer Graphics, 2, 266–279.
Wright, H., Brodlie, K., & David, T. (2000). Navigating high-dimensional spaces to support design steering. In Proceedings of IEEE visualization 2000 (pp. 291–296).
Xie, Z., Huang, S., Ward, M. O., & Rundensteiner, E. A. (2006). Exploratory visualization of multivariate data with variable quality. In IEEE symposium on visual analytics science and technology (pp. 183–190).
Zehner, B., Watanabe, N., & Kolditz, O. (2010). Visualization of gridded scalar data with uncertainty in geosciences. Computers and Geosciences, 36(10), 1268–1275.
Zuk, T. (2008). Visualizing uncertainty. PhD thesis, Department of Computer Science, University of Calgary.
Zuk, T., & Carpendale, S. (2006). Theoretical analysis of uncertainty visualizations. In Visualization and data analysis.
Zuk, T., Downton, J., Gray, D., Carpendale, S., & Liang, J. D. (2008). Exploration of uncertainty in bidirectional vector fields. In K. Börner, M. T. Grönh, J. Park, & J. C. Roberts (Eds.), Visualization and data analysis 2008, proceedings of SPIE-IS&T electronic imaging. Bellingham: SPIE and IS&T.
Acknowledgements
We have many people to thank: Alan McKinnon of Lincoln University, NZ, who helped us during his sabbatical at Leeds in 2009; Roger Payne, of VSNi Ltd, showed us how t-tests could help draw uncertain contours; Rory Bingham and Keith Haines who lent us the ocean data we have used in most of our uncertainty studies; Christian Hege who gave permission for us to use Fig. 6.8; Robert Moorhead, Jibonananda Sanyal and Hamish Carr who created images especially for this article; and members past and present of the VVR group at University of Leeds.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag London Limited
About this chapter
Cite this chapter
Brodlie, K., Allendes Osorio, R., Lopes, A. (2012). A Review of Uncertainty in Data Visualization. In: Dill, J., Earnshaw, R., Kasik, D., Vince, J., Wong, P. (eds) Expanding the Frontiers of Visual Analytics and Visualization. Springer, London. https://doi.org/10.1007/978-1-4471-2804-5_6
Download citation
DOI: https://doi.org/10.1007/978-1-4471-2804-5_6
Publisher Name: Springer, London
Print ISBN: 978-1-4471-2803-8
Online ISBN: 978-1-4471-2804-5
eBook Packages: Computer ScienceComputer Science (R0)