Visualisation of uncertainty. Kai-Mikael Jää-Aro

Transcription

1 Visualisation of uncertainty Kai-Mikael Jää-Aro

2 Why is this important? Visualising uncertainty Means and Methods Scalar data Vector data Volume data Generic methods

3 Let us talk about the weather A weather forecast is based on sensor readings, which are fed into numerical models, the output from which is used to draw weather maps.

4 Uncertainty and error At each step in the forecasting process, errors creep in: Sensors have limited resolution, readings contain noise, their positions may be uncertain, sampling is sparse in time and space. Converting the raw data to suitable input for numerical models may involve averaging, interpolation, resampling. The numerical models are approximate, further, discrete computation introduces errors, some algorithms increase errors. Visualisation of computation results introduces quantisation errors, data are interpolated, additional numerical integration may be used. To help interpreting the results we should indicate the level of uncertainty and error in the visualisation.

5 How can we describe uncertainty? An uncertainty parameter can be given as (for example): statistic The probability distribution of data. range Minimum and maximum values for data. error Estimated or known differences between true and computed values of data. In addition, data may be missing.

6 Visualising uncertainty We can treat uncertainty as simply another variable to be visualised, but it is preferrable if the viewer has to do as few mental transformations as possible to understand the image. We have to use the free parameters of our visualisation space to indicate the uncertainty, this may occasionally conflict with the indication of other variables. We need to consider how easily the user will interpret what is shown as uncertainty, and how easy it is to detect the quantitative values of uncertainty? Do we wish to emphasise uncertain parts of our data set, or should these be downplayed?

7 One-dimensional scalar data 1D scalars have the most effective and well-used methods for indicating uncertainty. (Why should this be?) Simple scatterplots will show data distribution.

8 We can gain further understanding by indicating statistical properties in a box-and-whisker plot. This plot is overlaid on a scatterplot. The box often indicates median and 25th and 75th percentiles, the whiskers 10th and 90th percentiles, but could equally well be average, ± 1 and 2 standard deviations, or 90 and 95% confidence intervals or whatever is meaningful for the statistic.

9 We can add more statistical indicators by making the box shape more complex.

10 On the other hand, box-and-whisker plots do not give any indication of how successive data ranges are related to each other. We may want to see envelopes of the ranges. Note that we are introducing uncertainty in the visualisation step.

11 2D scalar data As data move up in dimension, we get fewer dimensions in which to show uncertainty. One option is to use colour. A difference image with a good colour scale shows areas with small deviations in black and large deviations in brighter colour. =

12 Over a surface we can indicate increasing uncertainty of data values by e g decreasing the saturation or increasing the transparency, but note that this changes the colour, which may affect its interpretation, especially for shaded 3D surfaces.

13 Vector data Vectors can have uncertainty in magnitude and direction, which both have to be shown. We can generalise standard vector visualisation methods to show uncertainty. We will show methods from C. M. Wittenbrink, A. T. Pang, and S. K. Lodha. Glyphs for visualizing uncertainty in vector fields. IEEE Transactions on Visualization and Computer Graphics, 2(3): , Sept

14 We often use arrow-shaped glyphs to show vector fields, with the obvious mappings for magnitude and direction.

15 A number of possible generalisations of arrow glyphs are possible. They have to be tested to see which one(s) behave best in a real situation.

16 A version where the width of the arrowhead shows the uncertainty of direction and multiple arrowheads show the uncertainty of magnitude makes the glyphs too large.

17 Remapping so that area indicates magnitude gives better-behaved glyphs.

18 A side-by-side comparison of uncertain and certain visualisations.

19 We can also adapt stream ribbons and stream tubes to show uncertainty in vector fields.

20 Volume data The simplest way of rendering volume data is by isosurfaces. Fat surfaces directly show the range of possible shapes of an isosurface.

21 Following G. Grigoryan and P. Rheingans. Point-based probabilistic surfaces to show surface uncertainty. IEEE Transactions on Visualization and Computer Graphics, 10(5): , Sept./Oct we will look at several methods of isosurface uncertainty visualisation. Problem: Finding the boundaries of tumours. Setting a distinct boundary may miss the edges where the tumour blends in with normal cells.

22 We begin by looking at a simple isosurface.

23 We may attempt to indicate uncertainty by colour coding. But precisely how uncertain are these surfaces?

24 Instead, let us show uncertain surfaces by an uncertain surface. Make the surface of points instead of polygons, displace the points by a random amount proportional to the uncertainty in that region.

25 Instead of points, we may use lines to directly show the range of uncertainty. They can be rendered with varying opacity depending on the certainty value along the line.

26 We can speed up rendering and improve the image by combining polygonal surfaces and points or lines.

27 All this can be enhanced with colours showing other parameters, such as cell age.

28 Volume visualisation We may also perform direct volume visualisation. Following S. Djurcilova, K. Kim, P. Lermusiaux, and A. Pang. Visualizing scalar volumetric data with uncertainty. Computers & Graphics, 26: , 2002, we can map uncertainty to transparency.

29 Generic methods Many methods are common for all types of data. Showing the range of possible values in side-by-side displays is often the easiest for the designer, if not always for the viewer.

30 Animating through the range of values is another option. A simple animation is simply blinking back and forth between the min and max values, the parts that flicker most are most uncertain.

31 Using other modalities If we have difficulty with fitting in the uncertainty information in available dimensions, we can try using haptic or aural presentation. Both these require active probing by the viewer/listener/toucher; this is not necessarily a problem.

32 Useful links: ehlschl/paper.htm ICAvis_working.html