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5 Questions Can we believe what we see? Are there errors in the data? Have we added errors when we created the visualization? What uncertainty is there in the picture?

6 Uncertainty Visualization Ken Brodlie – University of Leeds in collaboration with: Rodolfo Allendes - University of Leeds Keith Haines – University of Reading Adriano Lopes – Universidade Nova de Lisboa NCRM Research Methods Festival 2008

7 Outline Motivation – scope for error in data visualization Simple graphs –Structural versus data uncertainty Two dimensional data –Contouring, surface views and image plots –Visualizing uncertainty –Special look at uncertainty contouring –Case study – oceanographic data from Reading e-Science Centre Three dimensional data –Isosurfacing and volume rendering –Visualizing uncertainty Conclusions

8 Motivation Sources of error abound in visualization Consider the typical pipeline of processes: Input Visualization Algorithm Render Simulation Measurement All data is uncertain! All visualization algorithms are approximations! All rendering is quantised! Yet we rarely think about this when we visualize data!!

9 One-dimensional graphs The line chart remains the most commonly used visualization technique… … but there is often uncertainty Wikipedia – line chart

10 TIME (mins) OXYGEN (%) This table shows the observed oxygen levels in the flue gas, when coal undergoes combustion in a furnace A Simple Example

11 Visualizing the Data – no uncertainty…but is this what we want to see?

12 Estimating behaviour between the data - but are we certain?

13 Perhaps this is the behaviour… but something is wrong

14 At least this is credible..but still we are far from certain This is structural uncertainty, or model uncertainty

15 Error bars We can also have data uncertainty….. error information can be incorporated into a graph using error bars NC State University, LabWrite All you ever want to know about error bars: see: Cumming, Fidler & Vaux (2007) Error bars in experimental biology Journal of Cell Biology, 177, p7-11

16 Summary Statistics for Multiple Values – Box plots Statistics about multiple data values at a point can be summarised using box plots… … or variants such as violin plots

17 Two Dimensional Data We have three classic visualization techniques: –Contour map –Surface view –Image plot

18 Image Plots – Using Saturation Image plots colour each pixel with predicted value Some interpolation methods (here kriging) also deliver measure of prediction error Hengl (2003) has suggested using saturation to encode uncertainty Colour mapping goes from 1D (thickness) to 2D (thickness and uncertainty) Note other studies have argued that saturation is not a good way of encoding uncertainty!! Top-soil thickness (cm)

19 Image Plots - Using Annotation Effects Cedilnik and Rheingans (2000) –Proposed use of annotation to display uncertainty Latitude/longitude lines sharpened to indicate high certainty … focus on perceptual effect … qualitative rather than quantitative IEEE Visualization 2000

20 Image Plots - Augmented Views Uncertainty can be added as a surface layer Ground cover observations at sparse set of points used to generate 250 datasets –Mean is image view –Standard deviation is surface height –Interquartile range is colour –Bar glyphs give mean/median difference Love, Pang, Kao (2005) Visualizing Spatial Multivalue Data IEEE CG&A

21 Surface Views – Using Animation Surface views show 2D data as an elevation view Animation can be used to show a set of possible outcomes from a simulation Here Ehlschlaeger et al (1997) show the impact of potential sea level rise on shoreline of Boston harbour Ehlschlaeger, Shortridge and Goodchild, Visualizing Spatial Data Uncertainty using Animation Computers and Geosciences, 1997 Important to take spatial autocorrelation into account

22 Contouring of 2D Data We have recently been looking at contouring 2D data – and on visualizing the uncertainty associated with that data Rather than a single value at each datapoint (x,y)… f … we have a random variable, F, with an associated probability density function, f(z): Measurement errors: normal distribution Rounding errors: uniform distribution Ensemble computing: distribution derived from data We can contour f… how do we contour F?

23 How do we interpolate uncertainty? Central to much of visualization is interpolation – often we are interested not so much in the data but the bits inbetween Similarly for the uncertain case: 0 1 x 0 1 Y1Y1 Y2Y2 x … and obvious extensions to 2D bilinear and 3D trilinear Linear combination of two normal distributions is another normal distribution

24 Uncertainty Contour Lines In the traditional case, the definition of a contour line is: Set of all points p: In the uncertainty case, the definition could be: Contour bands … or we can map the probability to intensity Fuzzy contours

25 E-Science Application: Ocean Dynamic Topography Mean dynamic ocean topography : difference between average sea surface and its rest-state (the geoid) Measures the ‘steady-state’ circulation of ocean currents that help regulate the Earth’s climate But different models predict different topography! Bingham and Haines (2006) produced a composite MDT from an ensemble of 8 models RMS error for composite MDT is 3.2 cm, on a grid of 829x325

26 Is it easy to understand the error information? Error field overlayed as an image plot … but can we show the uncertainty using just the contouring paradigm?

27 Fuzzy Contours Here we map probability to intensity – zero fuzzy contour is:

28 Adding the Mean as a Traditional Contour Line

29 Looking at each model

30 Comparison

31 Contour Bands

32 Fuzzy Contours or Contour Bands

33 Contour shading Often we shade the bands between contour lines … and we can do the same with uncertainty contouring

34 Uncertain Contour Shading – Colour Blending Colour blending, using transparency to indicate level of certainty

35 Uncertain Contour Shading – Probabilistic Model Colour chosen according to random variable with corresponding distribution

36 As a Movie

37 Looking at each model… Each model rendered with one eighth transparency

38 Powerwall for Uncertainty

39 Ocean Currents – 1943 map

40 Three dimensional data There are two main methods: –Isosurfacing This is the analogy of contouring where a surface of equal threshold value is extracted Marching cubes algorithm works across each grid cell, determining surface separating points above and below threshold –Volume rendering This is the analogy of image plots where transparency is used to ‘see through’ outer layers Imagine data as a gel-like material, with colour and transparency determined by the data

41 Mapping Uncertainty onto Isosurface Rhodes, Bergeron et al (2003) –Multiresolution isosurfacing – error information available at different mesh resolutions –Given error at grid points, interpolate to get error at intersection points –Colour map the isosurface mesh according to the error values Eurographics 2003 …but no indication of spatial distribution of isosurface …no incorporation of type of error distribution

42 Using Volume Rendering Johnson and Sanderson (2003) –Combined isosurface and volume rendering –Isosurface average and volume render error IEEE CG&A - Review paper, no detail …spatial extent shown, but no indication that they have incorporated any probability distribution information

43 Uncertainty in Volume Rendering Djurcilov et al, UCSC (2002) Use the opacity component of volume rendering to encode uncertainty Middle Atlantic Shelf Break – Mean salinity Low opacity = high uncertainty

44 Uncertainty in Volume Rendering

45 Conclusions Important to convey uncertainty information within a visualization We have looked at: –Graphs –Contours, surface views, image plots –Isosurfaces, volume rendering Uncertainty remains a challenging topic for the visualization community