The Visualization of Uncertainty

The graphical depiction of uncertainty information is emerging as a problem of great importance in the field of visualization. Scientific data sets are not considered complete without indications of error, accuracy, or levels of confidence, and this information is often presented as charts and tables alongside visual representations of the data. Uncertainty measures are often excluded from explicit representation within data visualizations because the increased visual complexity incurred can cause clutter, obscure the data display, and may lead to erroneous conclusions or false predictions. However, uncertainty is an essential component of the data, and its display must be integrated in order for a visualization to be considered a true representation of the data. The growing need for the addition of qualitative information into the visual representation of data, and the challenges associated with that need, command fundamental research on the visualization of uncertainty. This dissertation seeks to advance approaches for uncertainty visualization by exploring techniques from scientific and information visualization, creating new visual devices to handle the complexities of uncertainty data, and combining the most effective display methods into the Ensemble-Vis framework for visual data analysis. Many techniques exist for graphical data display. However, their usage on data with uncertainty information is not straightforward. This work begins by first exploring existing methods for data visualization and assessing their application to uncertainty. New visual metaphors are then presented for the depiction of salient features of data distributions, including indications of uncertainty. These new methods are inspired by proven visual data analysis techniques, but account for the requirements of large, complex data sets. Finally, Ensemble-Vis is presented, which combines effective uncertainty visualization techniques with interactive selection, linking, and querying to provide a user-driven, component-based framework for data investigation, exploration, and analysis.

[1]  Thomas Nocke,et al.  Visual exploration and evaluation of climate-related simulation data , 2007, 2007 Winter Simulation Conference.

[2]  J. Dungan,et al.  Visualizing Distributions from Multi-Return Lidar Data to Understand Forest Structure , 2005 .

[3]  Issei Fujishiro,et al.  The elements of graphing data , 2005, The Visual Computer.

[4]  Heidrun Schumann,et al.  Visualizing Statistical Properties of Smoothly Brushed Data Subsets , 2008, 2008 12th International Conference Information Visualisation.

[5]  Matthew O. Ward,et al.  Hierarchical parallel coordinates for exploration of large datasets , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

[6]  A. Raftery,et al.  Atmospheric science. Weather forecasting with ensemble methods. , 2005, Science.

[7]  Matthew O. Ward,et al.  Exploratory Visualization of Multivariate Data with Variable Quality , 2006, 2006 IEEE Symposium On Visual Analytics Science And Technology.

[8]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[9]  Richard A. Becker,et al.  Brushing scatterplots , 1987 .

[10]  Don McNeil,et al.  Can the box plot be improved , 2005 .

[11]  Jean Nicolau.  SHORT-RANGE ENSEMBLE FORECASTING , 2002 .

[12]  Jock D. Mackinlay,et al.  Visualizing data with bounded uncertainty , 2002, IEEE Symposium on Information Visualization, 2002. INFOVIS 2002..

[13]  Alex T. Pang,et al.  Glyphs for Visualizing Uncertainty in Vector Fields , 1996, IEEE Trans. Vis. Comput. Graph..

[14]  Ken Brodlie,et al.  Contouring with Uncertainty , 2008, TPCG.

[15]  J. Bonet,et al.  Comparison between Spatial Interactions in Perceived Contrast and Perceived Brightness , 1997, Vision Research.

[16]  David L. Kao,et al.  Visualizing spatial multivalue data , 2005, IEEE Computer Graphics and Applications.

[17]  Alex T. Pang,et al.  Visualizing Geometric Uncertainty of Surface Interpolants , 1996, Graphics Interface.

[18]  Penny Rheingans.  Task-based color scale design , 2000, Applied Imaging Pattern Recognition.

[19]  Yoav Benjamini,et al.  Opening the Box of a Boxplot , 1988 .

[20]  Penny Rheingans,et al.  Procedural annotation of uncertain information , 2000, Proceedings Visualization 2000. VIS 2000 (Cat. No.00CH37145).

[21]  William L. Hibbard,et al.  The VIS-5D system for easy interactive visualization , 1990, Proceedings of the First IEEE Conference on Visualization: Visualization `90.

[22]  David Borland,et al.  Rainbow Color Map (Still) Considered Harmful , 2007, IEEE Computer Graphics and Applications.

[23]  Zoltan Toth,et al.  An Ensemble Forecasting Primer , 1997 .

[24]  David P. Doane,et al.  Using Beam and Fulcrum Displays to Explore Data , 2000 .

[25]  Suresh K. Lodha,et al.  VERITY VISUALIZATION: VISUAL MAPPINGS , 1995 .

[26]  P. Diggle.  Analysis of Longitudinal Data , 1995 .

[27]  Chris R. Johnson,et al.  A Next Step: Visualizing Errors and Uncertainty , 2003, IEEE Computer Graphics and Applications.

[28]  Alex T. Pang,et al.  Volume Rendering Data with Uncertainty Information , 2001, VisSym.

[29]  Joe Michael Kniss,et al.  Resolution Independent NPR‐Style 3D Line Textures , 2009, Comput. Graph. Forum.

[30]  Victoria Interrante,et al.  Harnessing natural textures for multivariate visualization , 2000, IEEE Computer Graphics and Applications.

[31]  Anders Ynnerman,et al.  Uncertainty Visualization in Medical Volume Rendering Using Probabilistic Animation , 2007, IEEE Transactions on Visualization and Computer Graphics.

[32]  J.C. Roberts,et al.  State of the Art: Coordinated & Multiple Views in Exploratory Visualization , 2007, Fifth International Conference on Coordinated and Multiple Views in Exploratory Visualization (CMV 2007).

[33]  Jon Cohen,et al.  The Sectioned Density Plot , 2006 .

[34]  Peter L. Brooks,et al.  Visualizing data , 1997 .

[35]  J. Tukey,et al.  Variations of Box Plots , 1978 .

[36]  Chris R. Johnson.  Top Scientific Visualization Research Problems , 2004, IEEE Computer Graphics and Applications.

[37]  Michael F. Goodchild,et al.  Visualizing spatial data uncertainty using animation , 1997 .

[38]  Edward Rolf Tufte,et al.  The visual display of quantitative information , 1985 .

[39]  J. Hannan,et al.  Introduction to probability and mathematical statistics , 1986 .

[40]  P. Rousseeuw,et al.  The Bagplot: A Bivariate Boxplot , 1999 .

[41]  John M. Chambers,et al.  Graphical Methods for Data Analysis , 1983 .

[42]  Alex T. Pang,et al.  Visualizing scalar volumetric data with uncertainty , 2002, Comput. Graph..

[43]  B. Iglewicz,et al.  Bivariate extensions of the boxplot , 1992 .

[44]  Hans Hagen,et al.  Methods for Presenting Statistical Information: The Box Plot , 2006, VLUDS.

[45]  Kenneth W. Haemer.  Range-Bar Charts , 1948 .

[46]  Robert Michael Kirby,et al.  Application of Stochastic Finite Element Methods to Study the Sensitivity of ECG Forward Modeling to Organ Conductivity , 2008, IEEE Transactions on Biomedical Engineering.

[47]  O Leg S Mirnov,et al.  Visualizing Multivariate Spatial Correlation with Dynamically Linked Windows , 2002 .

[48]  Rüdiger Westermann,et al.  Acceleration techniques for GPU-based volume rendering , 2003, IEEE Visualization, 2003. VIS 2003..

[49]  M. Braga,et al.  Exploratory Data Analysis , 2018, Encyclopedia of Social Network Analysis and Mining. 2nd Ed..

[50]  Jennifer L. Dungan,et al.  Visualizing 2D probability distributions from EOS satellite image-derived data sets: a case study , 2001, Proceedings Visualization, 2001. VIS '01..

[51]  R. Haber,et al.  Visual Perception , 2018, Encyclopedia of Database Systems.

[52]  Matthias Gruber,et al.  Moment-Based Image Normalization With High Noise-Tolerance , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[53]  Jennifer L. Dungan,et al.  Visualizing Spatial Distribution Data Sets , 2003, VisSym.

[54]  Robert S. Laramee,et al.  Uncertainty Visualization Methods in Isosurface Rendering , 2003, Eurographics.

[55]  Ted Mihalisin,et al.  Visualization and analysis of multi-variate data: a technique for all fields , 1991, Proceeding Visualization '91.

[56]  Mark Bailey,et al.  The Grammar of Graphics , 2007, Technometrics.

[57]  Irving Roshwalb,et al.  Charting Statistics , 1954 .

[58]  Phattrawan Tongkumchum.  Two-dimensional box plot , 2005 .

[59]  Jennifer L. Dungan,et al.  Visualizing spatially varying distribution data , 2002, Proceedings Sixth International Conference on Information Visualisation.

[60]  Barry N. Taylor,et al.  Guidelines for Evaluating and Expressing the Uncertainty of Nist Measurement Results , 2017 .

[61]  Alex T. Pang,et al.  Approaches to uncertainty visualization , 1996, The Visual Computer.

[62]  Yoon-ha Lee,et al.  Uncertainty Quantification for Multiscale Simulations , 2002 .

[63]  P. Rheingans,et al.  Multivariate glyphs for multi-object clusters , 2005, IEEE Symposium on Information Visualization, 2005. INFOVIS 2005..

[64]  John Shalf,et al.  Query-driven visualization of large data sets , 2005, VIS 05. IEEE Visualization, 2005..

[65]  Penny Rheingans,et al.  Point-based probabilistic surfaces to show surface uncertainty , 2004, IEEE Transactions on Visualization and Computer Graphics.

[66]  David L. Kao,et al.  Visualization techniques for spatial probability density function data , 2004, Data Sci. J..

[67]  Mark Gahegan,et al.  Visualizing Geospatial Information Uncertainty: What We Know and What We Need to Know , 2005 .

[68]  J. Hintze,et al.  Violin plots : A box plot-density trace synergism , 1998 .

[69]  Andreas Buja,et al.  Interactive High-Dimensional Data Visualization , 1996 .