Overview and State-of-the-Art of Uncertainty Visualization

  • Georges-Pierre Bonneau
  • Hans-Christian Hege
  • Chris R. Johnson
  • Manuel M. Oliveira
  • Kristin Potter
  • Penny Rheingans
  • Thomas Schultz
Chapter
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

The goal of visualization is to effectively and accurately communicate data. Visualization research has often overlooked the errors and uncertainty which accompany the scientific process and describe key characteristics used to fully understand the data. The lack of these representations can be attributed, in part, to the inherent difficulty in defining, characterizing, and controlling this uncertainty, and in part, to the difficulty in including additional visual metaphors in a well designed, potent display. However, the exclusion of this information cripples the use of visualization as a decision making tool due to the fact that the display is no longer a true representation of the data. This systematic omission of uncertainty commands fundamental research within the visualization community to address, integrate, and expect uncertainty information. In this chapter, we outline sources and models of uncertainty, give an overview of the state-of-the-art, provide general guidelines, outline small exemplary applications, and finally, discuss open problems in uncertainty visualization.

References

  1. 1.
    Balabanian, J., Viola, I., Gröller, E.: Interactive illustrative visualization of hierarchical volume data. In: Proceedings of Graphics Interface 2010, Ottawa, Ontario, Canada, pp. 137–144 (2010)Google Scholar
  2. 2.
    Barthelmé, S., Mamassian, P.: Evaluation of objective uncertainty in the visual system. PLoS Comput. Biol. 5(9), e1000504 (2009)CrossRefGoogle Scholar
  3. 3.
    Becketti, S., Gould, W.: Rangefinder box plots. Am. Stat. 41(2), 149 (1987)Google Scholar
  4. 4.
    Benjamini, Y.: Opening the box of a boxplot. Am. Stat. 42(4), 257–262 (1988)Google Scholar
  5. 5.
    Bertin, J.: Sémiologie graphique: Les diagrammes—Les réseaux—Les cartes. Editions de l’Ecole des Hautes Etudes en Sciences (1967)Google Scholar
  6. 6.
    Bertin, J.: Semiology of Graphics. The University of Wisconsin Press (1983) (Translated by William Berg)Google Scholar
  7. 7.
    Bordoloi, U., Kao, D., Shen, H.W.: Visualization techniques for spatial probability density function data. Data Sci. J. 3, 153–162 (2005)CrossRefGoogle Scholar
  8. 8.
    Botchen, R.P., Weiskopf, D., Ertl, T.: Texture-based visualization of uncertainty in flow fields. In: IEEE Visualization 2005, pp. 647–654 (2005)Google Scholar
  9. 9.
    Boukhelifa, N., Duke, D.J.: Uncertainty visualization: why might it fail? In: CHI Extended Abstracts’09, pp. 4051–4056 (2009)Google Scholar
  10. 10.
    Bürger, R., Hauser, H.: Visualization of multi-variate scientific data. Comput. Graph. Forum 28(6), 1670–1690 (2009)CrossRefGoogle Scholar
  11. 11.
    Buttenfield, B., Ganter, J.: Visualization and gis: what should we see? What might we miss? In: 4th International Symposium on Spatial Data Handling, vol. 1, pp. 307–316 (1990)Google Scholar
  12. 12.
    Cai, W., Sakas, G.: Data intermixing and multi-volume rendering. Comput. Graph. Forum 18(3), 359–368 (1999)CrossRefGoogle Scholar
  13. 13.
    Cedilnik, A., Rheingans, P.: Procedural annotation of uncertain information. In: IEEE Proceedings of Visualization 2000, pp. 77–84 (2000)Google Scholar
  14. 14.
    Chambers, J.M., Cleveland, W.S., Kleiner, B., Tukey, P.A.: Graphical Methods for Data Analysis. Wadsworth (1983)Google Scholar
  15. 15.
    Chlan, E.B., Rheingans, P.: Multivariate glyphs for multi-object clusters. In: Proceedings of InfoVis ’05, pp. 141–148 (2005)Google Scholar
  16. 16.
    Choonpradub, C., McNeil, D.: Can the box plot be improved? Songklanakarin J. Sci. Technol. 27(3), 649–657 (2005)Google Scholar
  17. 17.
    Cohen, D.J., Cohen, J.: The sectioned density plot. Am. Stat. 60(2), 167–174 (2006)CrossRefGoogle Scholar
  18. 18.
    Coninx, A., Bonneau, G.P., Droulez, J., Thibault, G.: Visualization of uncertain scalar data fields using color scales and perceptually adapted noise. In: Applied Perception in Graphics and Visualization (2011)Google Scholar
  19. 19.
    Couclelis, H.: The certainty of uncertainty: GIS and the limits of geographic knowledge. Trans. GIS 7(2), 165–175 (2003)CrossRefGoogle Scholar
  20. 20.
    Deitrick, S., Edsall, R.: The influence of uncertainty visualization on decision making: An empirical evaluation. In: Progress in Spatial Data Handling, pp. 719–738. Springer, Berlin (2006)Google Scholar
  21. 21.
    Dietrick, S.: Uncertainty visualization and decision making: Does visualizing uncertain information change decisions? In: Proceedings of the XXII International Cartographic Conference (2007)Google Scholar
  22. 22.
    Djurcilov, S., Kim, K., Lermusiaux, P., Pang, A.: Visualizing scalar volumetric data with uncertainty. Comput. Graph. 26, 239–248 (2002)CrossRefGoogle Scholar
  23. 23.
    Doane, D.P., Tracy, R.L.: Using beam and fulcrum displays to explore data. Am. Stat. 54(4), 289–290 (2000)MathSciNetGoogle Scholar
  24. 24.
    Douceur, J.R.: The sybil attack. In: The First International Workshop on Peer-to-Peer Systems, pp. 251–260 (2002)Google Scholar
  25. 25.
    Ehlschlaeger, C.R., Shortridge, A.M., Goodchild, M.F.: Visualizing spatial data uncertainty using animation. Comput. GeoSci. 23(4), 387–395 (1997)CrossRefGoogle Scholar
  26. 26.
    Esty, W.W., Banfield, J.D.: The box-percentile pot. J. Stat. Softw. 8(17), 1–14 (2003)Google Scholar
  27. 27.
    Feng, D., Kwock, L., Lee II, Y.: R.M.T.: matching visual saliency to confidence in plots of uncertain data. IEEE Trans. Visual. Comput. Graph. 16(6), 980–989 (2010)CrossRefGoogle Scholar
  28. 28.
    Frigge, M., Hoaglin, D.C., Iglewicz, B.: Some implementations of the box plot. Am. Stat. 43(1), 50–54 (1989)Google Scholar
  29. 29.
    Fua, Y.H., Ward, M., Rundensteiner, E.: Hierarchical parallel coordinates for exploration of large datasets. In: Proceedings of Vis ’99, pp. 43–50 (1999)Google Scholar
  30. 30.
    Gershon, N.D.: Visualization of fuzzy data using generalized animation. In: Proceedings of the IEEE Conference on Visualization, pp. 268–273 (1992)Google Scholar
  31. 31.
    Gleicher, M., Albers, D., Walker, R., Jusufi, I., Hansen, C., Roberts, J.: Visual comparison for information visualization. Inf. Visual. 10(4), 289–309 (2011)CrossRefGoogle Scholar
  32. 32.
    Goldberg, K.M., Iglewicz, B.: Bivariate extensions of the boxplot. Technometrics 34(3), 307–320 (1992)CrossRefGoogle Scholar
  33. 33.
    Grigoryan, G., Rheingans, P.: Point-based probabilistic surfaces to show surface uncertainty. In: IEEE Trans. Visual. Comput. Graph. 10(5), 546–573 (2004)Google Scholar
  34. 34.
    Haemer, K.W.: Range-bar charts. Am. Stat. 2(2), 23 (1948)Google Scholar
  35. 35.
    Hagh-Shenas, H., Kim, S., Interrante, V., Healey, C.: Weaving versus blending: a quantitative assessment of the information carrying capacities of two alternative methods for conveying multivariate data with color. IEEE Trans. Visual. Comput. Graph. 13(6), 1270–1277 (2007)CrossRefGoogle Scholar
  36. 36.
    Haroz, S., Ma, K.L., Heitmann, K.: Multiple uncertainties in time-variant cosmological particle data. In: IEEE Pacific Visualization Symposium, pp. 207–214 (2008)Google Scholar
  37. 37.
    Harrison, L., Hu, X., Ying, X., Lu, A., Wang, W., Wu, X.: Interactive detection of network anomalies via coordinated multiple views. In: Proceedings of the 7th International Symposium on Visualization for Cyber Security, VizSec ’10 (2010)Google Scholar
  38. 38.
    Harrower, M.: Representing uncertainty: Does it help people make better decisions? In: UCGISWorkshop: Geospatial Visualization and Knowledge Discovery Workshop (2002)Google Scholar
  39. 39.
    Hintze, J.L., Nelson, R.D.: Violin plots: a box plot-density trace synergism. Am. Stat. 52(2), 181–184 (1998)Google Scholar
  40. 40.
    Interrante, V.: Harnessing natural textures for multivariate visualization. IEEE Comput. Graph. Appl. 20(6), 6–11 (2000)CrossRefGoogle Scholar
  41. 41.
    Jiao, F., Phillips, J.M., Stinstra, J., Krüger, J., Varma, R., Hsu, E., Korenberg, J., Johnson, C.R.: Metrics for uncertainty analysis and visualization of diffusion tensor images. Lect. Notes Comput. Sci. 6326(2010), 179–190 (2010)CrossRefGoogle Scholar
  42. 42.
    Johnson, C.R.: Top scientific visualization research problems. IEEE Comput. Graph. Appl. 24(4), 13–17 (2004)CrossRefGoogle Scholar
  43. 43.
    Johnson, C.R., Sanderson, A.R.: A next step: visualizing errors and uncertainty. IEEE Comput. Graph. Appl. 23(5), 6–10 (2003)CrossRefGoogle Scholar
  44. 44.
    Jones, D.K.: Determining and visualizing uncertainty in estimates of fiber orientation from diffusion tensor mri. Magn. Reson. Med. 49, 7–12 (2003)CrossRefGoogle Scholar
  45. 45.
    Jospeh, A.J., Lodha, S.K., Renteria, J.C., Pang., A.: Uisurf: Visualizing uncertainty in isosurfaces. In: Proceedings of the Computer Graphics and Imaging, pp. 184–191 (1999)Google Scholar
  46. 46.
    Kao, D., Dungan, J.L., Pang, A.: Visualizing 2d probability distributions from eos satellite image-derived data sets: A case study. In: Proceedings of the Conference on Visualization ’01, VIS ’01, pp. 457–460 (2001)Google Scholar
  47. 47.
    Kao, D., Kramer, M., Love, A., Dungan, J., Pang, A.: Visualizing distributions from multi-return lidar data to understand forest structure. Cartograph. J. 42(1), 35–47 (2005)CrossRefGoogle Scholar
  48. 48.
    Kao, D., Luo, A., Dungan, J.L., Pang, A.: Visualizing spatially varying distribution data. In: Information Visualization ’02, pp. 219–225 (2002)Google Scholar
  49. 49.
    Kindlmann, G., Whitaker, R., Tasdizen, T., Moller, T.: Curvature-based transfer functions for direct volume rendering: Methods and applications. In: Proceedings of the 14th IEEE Visualization 2003 (VIS’03), pp. 67–74 (2004)Google Scholar
  50. 50.
    Kniss, J., Kindlmann, G., Hansen, C.: Multidimensional transfer functions for interactive volume rendering. IEEE Trans. Visual. Comput. Graph. 8(3), 270–285 (2002)CrossRefGoogle Scholar
  51. 51.
    Kniss, J.M., Uitert, R.V., Stephens, A., Li, G.S., Tasdizen, T., Hansen, C.: Statistically quantitative volume visualization. In: Proceedings of IEEE Visualization 2005, pp. 287–294 (2005)Google Scholar
  52. 52.
    Lee, B., Robertson, G.G., Czerwinski, M., Parr, C.S.: Candidtree: visualizing structural uncertainty in similar hierarchies. Inf. Visual. 6, 233–246 (2007)CrossRefGoogle Scholar
  53. 53.
    Lenth, R.V.: Comment on rangefinder box plots. Am. Stat. 42(1), 87–88 (1988)CrossRefGoogle Scholar
  54. 54.
    Li, H., Fu, C.W., Li, Y., Hanson, A.J.: Visualizing large-scale uncertainty in astrophysical data. IEEE Trans. Visual. Comput. Graph. 13(6), 1640–1647 (2007)CrossRefGoogle Scholar
  55. 55.
    Lodha, S., Sheehan, B., Pang, A., Wittenbrink, C.: Visualizing geometric uncertainty of surface interpolants. In: Proceedings of the Conference on Graphics Interface ’96, pp. 238–245 (1996)Google Scholar
  56. 56.
    Lodha, S.K., Faaland, N.M., Charaniya, A.P.: Visualization of uncertain particle movement. In: Proceedings of the Computer Graphics and Imaging Conference, pp. 226–232 (2002)Google Scholar
  57. 57.
    Lodha, S.K., Pang, A., Sheehan, R.E., Wittenbrink, C.M.: Uflow: Visualizing uncertainty in fluid flow. In: Proceedings Visualization ’96, pp. 249–254 (1996)Google Scholar
  58. 58.
    Lodha, S.K., Wilson, C.M., Sheehan, R.E.: Listen: sounding uncertainty visualization. In: Proceedings Visualization ’96, pp. 189–195 (1996)Google Scholar
  59. 59.
    Lu, A., Wang, W., Dnyate, A., Hu, X.: Sybil attack detection through global topology pattern visualization. Inf. Visual. 10(1), 32–46 (2011)Google Scholar
  60. 60.
    Lundström, C., Ljung, P., Persson, A., Ynnerman, A.: Uncertainty visualization in medical volume rendering using probabilistic animation. IEEE Trans. Visual. Comput. Graph. 13(6), 1648–1655 (2007)CrossRefGoogle Scholar
  61. 61.
    Luo, A., Kao, D., Pang, A.: Visualizing spatial distribution data sets. In: Proceedings of the Symposium on Data Visualisation 2003, VISSYM ’03, pp. 29–38 (2003)Google Scholar
  62. 62.
    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. Cartograph. Geograph. Inf. Sci. 32(3), 139–160 (2005)CrossRefGoogle Scholar
  63. 63.
    MacEachren, A.M., 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. Cartograph. Geograph. Inf. Sci. 32(3), 139–160 (2005)CrossRefGoogle Scholar
  64. 64.
    Malik, M.M., Heinzl, C., Gröller, M.E.: Comparative visualization for parameter studies of dataset series. IEEE Trans. Visual. Comput. Graph. 16(5), 829–840 (2010)CrossRefGoogle Scholar
  65. 65.
    Masuch, M., Freudenberg, B., Ludowici, B., Kreiker, S., Strothotte, T.: Virtual reconstruction of medieval architecture. In: Proceedings of EUROGRAPHICS 1999, Short Papers, pp. 87–90 (1999)Google Scholar
  66. 66.
    Masuch, M., Strothotte, T.: Visualising ancient architecture using animated line drawings. In: Proceedings of the IEEE Conference on Information Visualization, pp. 261–266 (1998)Google Scholar
  67. 67.
    McGill, R., Tukey, J.W., Larsen, W.A.: Variations of box plots. Am. Stat. 32(1), 12–16 (1978)Google Scholar
  68. 68.
    Miller, J.: Attribute blocks: visualizing multiple continuously defined attributes. IEEE Comput. Graph. Appl. 27(3), 57–69 (2007)CrossRefGoogle Scholar
  69. 69.
    Newman, T.S., Lee, W.: On visualizing uncertainty in volumetric data: techniques and their evaluation. J. Vis. Lang. Comput. 15, 463–491 (2004)CrossRefGoogle Scholar
  70. 70.
    Olston, C., Mackinlay, J.D.: Visualizing data with bounded uncertainty. In: Proceedings of the IEEE Symposium on Information Visualization (InfoVis’02), pp. 37–40 (2002)Google Scholar
  71. 71.
    Osorio, R.A., Brodlie, K.: Contouring with uncertainty. In: 6th Theory and Practice of Computer Graphics Conference, pp. 59–66 (2008)Google Scholar
  72. 72.
    Otto, M., Germer, T., Hege, H.C., Theisel, H.: Uncertain 2d vector field topology. Comput. Graph. Forum 29(2), 347–356 (2010)CrossRefGoogle Scholar
  73. 73.
    Pagendarm, H., Post, F.: Comparative visualization—approaches and examples. In: 5th Eurographics Workshop on Visualization in Scientific Computing, Rostock, Germany (1994)Google Scholar
  74. 74.
    Pang, A., Furman, J.: Data quality issues in visualization. In: SPIE Visual Data Exploration and Analysis, vol. 2278, pp. 12–23 (1994)Google Scholar
  75. 75.
    Pang, A., Wittenbrink, C., Lodha, S.: Approaches to uncertainty visualization. Vis. Comput. 13(8), 370–390 (1997)CrossRefGoogle Scholar
  76. 76.
    Paulus, M., Hozack, N., Zauscher, B., McDowell, J., Frank, L., Brown, G., Braff, D.: Prefrontal, parietal, and temporal cortex networks underlie decision=making in the presence of uncertainty. NeuroImage 13, 91–100 (2001)CrossRefGoogle Scholar
  77. 77.
    Pauly, M., Mitra, N.J., Guibas, L.: Uncertainty and variability in point cloud surface data. In: Symposium on Point-Based Graphics, pp. 77–84 (2004)Google Scholar
  78. 78.
    Politi, M., Han, P., Col, N.: Communicating the uncertainty of harms and benefits of medical interventions. Med. Decis. Mak. 27(5) 681–695 (2007)Google Scholar
  79. 79.
    Pöthkow, K., Hege, H.C.: Positional uncertainty of isocontours: condition analysis and probabilistic measures. IEEE Trans. Visual Comput. Graph. PP(99), 1–15 (2010)Google Scholar
  80. 80.
    Pöthkow, K., Weber, B., Hege, H.C.: Probabilistic marching cubes. Comput. Graph. Forum 30(3), 931–940 (2011)CrossRefGoogle Scholar
  81. 81.
    Potter, K.: Methods for presenting statistical information: The box plot. In: Hagen, H., Kerren, A., Dannenmann, P. (eds.) Visualization of Large and Unstructured Data Sets, GI-Edition, Lecture Notes in Informatics (LNI) S-4, pp. 97–106 (2006)Google Scholar
  82. 82.
    Potter, K., Kniss, J., Riesenfeld, R., Johnson, C.R.: Visualizing summary statistics and uncertainty. In: Computer Graphics Forum, Proceedings of Eurovis 2010, vol. 29(3), pp. 823–831 (2010)Google Scholar
  83. 83.
    Potter, K., Rosen, P., Johnson, C.R.: From quantification to visualization: A taxonomy of uncertainty visualization approaches. IFIP Advances in Information and Communication Technology Series p. (To Appear) (2012). (Invited Paper)Google Scholar
  84. 84.
    Potter, K., Wilson, A., Bremer, P.T., Williams, D., Doutriaux, C., Pascucci, V., Johhson, C.R.: Ensemble-vis: A framework for the statistical visualization of ensemble data. In: IEEE Workshop on Knowledge Discovery from Climate Data: Prediction, Extremes., pp. 233–240 (2009)Google Scholar
  85. 85.
    Praßni, J.S., Ropinski, T., Hinrichs, K.: Uncertainty-aware guided volume segmentation. IEEE Trans. Visual Comput. Graph. 16(6), 1358–1365 (2010)CrossRefGoogle Scholar
  86. 86.
    Rhodes, P.J., Laramee, R.S., Bergeron, R.D., Sparr, T.M.: Uncertainty visualization methods in isosurface rendering. In: EUROGRAPHICS 2003 Short Papers, pp. 83–88 (2003)Google Scholar
  87. 87.
    Riveiro, M.: Evaluation of uncertainty visualization techniques for information fusion. In: 10th International Conference on Information Fusion, pp. 1–8 (2007)Google Scholar
  88. 88.
    Rousseeuw, P.J., Ruts, I., Tukey, J.W.: The bagplot: a bivariate boxplot. Am. Stat. 53(4), 382–387 (1999)Google Scholar
  89. 89.
    Saad, A., Hamarneh, G., Möller, T.: Exploration and visualization of segmentation uncertainty using shape and appearance prior information. IEEE Trans. Visual. Comput. Graph. 16(6), 1366–1375 (2010)CrossRefGoogle Scholar
  90. 90.
    Saad, A., Möller, T., Hamarneh, G.: Probexplorer: uncertainty-guided exploration and editing of probabilistic medical image segmentation. Comput. Graph. Forum 29(3), 1113–1122 (2010)CrossRefGoogle Scholar
  91. 91.
    Sanyal, J., Zhang, S., Bhattacharya, G., Amburn, P., Moorhead, R.J.: A user study to compare four uncertainty visualization methods for 1d and 2d datasets. IEEE Trans. Visual. Comput. Graph. 15(6), 1209–1218 (2009)CrossRefGoogle Scholar
  92. 92.
    Sanyal, J., Zhang, S., Dyer, J., Mercer, A., Amburn, P., Moorhead, R.J.: Noodles: a tool for visualization of numerical weather model ensemble uncertainty. IEEE Trans. Visual. Comput. Graph. 16(6), 1421–1430 (2010)CrossRefGoogle Scholar
  93. 93.
    Schmidt, G.S., Chen, S.L., Bryden, A.N., Livingston, M.A., Rosenblum, L.J., Osborn, B.R.: Multidimensional visual representations for underwater environmental uncertainty. IEEE Comput. Graph. Appl. 24(5), 56–65 (2004)CrossRefGoogle Scholar
  94. 94.
    Spear, M.E.: Charting Statistics. McGraw-Hill, New York (1952)Google Scholar
  95. 95.
    Stokking, R., Zubal, I., Viergever, M.: Display of fused images: methods, interpretation, and diagnostic improvements. Semin. Nucl. Med. 33(3), 219–227 (2003)CrossRefGoogle Scholar
  96. 96.
    Streit, A., Pham, B., Brown, R.: A spreadsheet approach to facilitate visualization of uncertainty in information. IEEE Trans. Visual. Comput. Graph. 14(1), 61–72 (2008)CrossRefGoogle Scholar
  97. 97.
    Strothotte, T., Puhle, M., Masuch, M., Freudenberg, B., Kreiker, S., Ludowici, B.: Visualizing uncertainty in virtual reconstructions. In: Proceedings of Electronic Imaging and the Visual Arts, EVA Europe ’99, p. 16 (1999)Google Scholar
  98. 98.
    Thomson, J., Hetzler, B., MacEachren, A., Gahegan, M., Pavel, M.: A typology for visualizing uncertainty. In: Proceedings of SPIE. vol. SPIE-5669, pp. 146–157 (2005)Google Scholar
  99. 99.
    Tongkumchum, P.: Two-dimensional box plot. Songklanakarin J. Sci. Technol. 27(4), 859–866 (2005)Google Scholar
  100. 100.
    Torsney-Weir, T., Saad, A., Möller, T., Hege, H.C., Weber, B., Verbavatz, J.M.: Tuner: principled parameter finding for image segmentation algorithms using visual response surface exploration. IEEE Trans. Vis. Comput. Graph. (TVCG) 17(12), 1892–1901 (2011)CrossRefGoogle Scholar
  101. 101.
    Tufte, E.: The Visual Display of Quantitative Information, 2nd edn. Graphics Press, Cheshire (2001)Google Scholar
  102. 102.
    Tufte, E.R.: The Visual Display of Quantitative Information. Graphics Press, Cheshire (1983)Google Scholar
  103. 103.
    Tukey, J.W.: Exploratory Data Analysis. Addison-Wesley, Reading (1977)Google Scholar
  104. 104.
    Urness, T., Interrante, V., Marusic, I., Longmire, E., Ganapathisubramani, B.: Effectively visualizing multi-valued flow data using color and texture. Proc. IEEE Visual. Conf. 03, 115–121 (2003)Google Scholar
  105. 105.
    Ware, C.: Information Visualization: Perception for Design, 2nd edn. Morgan Kaufmann Publishers, Los Altos (2004)Google Scholar
  106. 106.
    Wilkinson, L.: Dot plots. Am. Stat. 53(3), 276–281 (1999)Google Scholar
  107. 107.
    Wilkinson, L.: The Grammar of Graphics. Springer, New York, Inc. (1999)Google Scholar
  108. 108.
    Wittenbrink, C., Pang, A., Lodha, S.: Verity visualization: Visual mappings. Technical Report, University of California, Santa Cruz (1995)Google Scholar
  109. 109.
    Wittenbrink, C.M., Pang, A.T., Lodha, S.K.: Glyphs for visualizing uncertainty in vector fields. IEEE Trans. Visual. Comput. Graph. 2(3), 266–279 (1996)CrossRefGoogle Scholar
  110. 110.
    Zehner, B., Watanabe, N., Kolditz, O.: Visualization of gridded scalar data with uncertainty in geosciences. Comput. Geosci. 36(10), 1268–1275 (2010)CrossRefGoogle Scholar
  111. 111.
    Zuk, T., Carpendale, S.: Theoretical analysis of uncertainty visualization. In: SPIE vol. 6060: Visualization and Data Analysis, vol. 2006, pp. 66–79 (2006)Google Scholar
  112. 112.
    Zuk, T., Carpendale, S., Glanzman, W.D.: Visualizing temporal uncertainty in 3d virtual reconstructions. In: Proceedings of the 6th International Symposium on Virtual Reality, Archaeology and Cultural Heritage (VAST 2005), pp. 99–106 (2005)Google Scholar
  113. 113.
    Zuk, T., Downton, J., Gray, D., Carpendale, S., Liang, J.: Exploration of uncertainty in bidirectional vector fields. In: Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 6809 (2008). Published onlineGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Georges-Pierre Bonneau
    • 1
  • Hans-Christian Hege
    • 2
  • Chris R. Johnson
    • 3
  • Manuel M. Oliveira
    • 4
  • Kristin Potter
    • 3
  • Penny Rheingans
    • 5
  • Thomas Schultz
    • 6
    • 7
  1. 1.The University of GrenobleGrenobleFrance
  2. 2.Zuse Institute BerlinBerlinGermany
  3. 3.Scientific Computing and Imaging InstituteUniversity of UtahSalt Lake CityUSA
  4. 4.Instituto de InformáticaUFRGSPorto AlegreBrazil
  5. 5.University of Maryland Baltimore CountyBaltimoreUSA
  6. 6.University of BonnBonnGermany
  7. 7.MPI for Intelligent SystemsTübingenGermany

Personalised recommendations