Questions

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

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

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

10. A Simple Example This table shows the observed oxygen levels in the flue gas, when coal undergoes combustion in a furnace TIME (mins) 0 2 4 10 28 30 32 20.8 8.8 4.2 0.5 3.9 6.2 9.6 OXYGEN (%)

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. We can also have data uncertainty… .. error information can be incorporated into a graph using error bars Error bars 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 NC State University, LabWrite

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

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

18. 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!! Image Plots – Using Saturation 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 IEEE Visualization 2000 … focus on perceptual effect … qualitative rather than quantitative

20. 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 Image Plots - Augmented Views 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. 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: Y1 1 x 0 Y2 How do we interpolate uncertainty? x 1 0 Linear combination of two normal distributions is another normal distribution … and obvious extensions to 2D bilinear and 3D trilinear

24. 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 Uncertainty Contour Lines

25. 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 E-Science Application: Ocean Dynamic Topography

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

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. 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 Three dimensional data http://www.csit.fsu.edu/~futch/iso/

41. Eurographics 2003 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 …but no indication of spatial distribution of isosurface …no incorporation of type of error distribution

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

43. Djurcilov et al, UCSC (2002) Use the opacity component of volume rendering to encode uncertainty Uncertainty in Volume Rendering 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