Questions

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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?

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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
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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

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Motivation

• Sources of error abound in visualization
• Consider the typical pipeline of processes

Yet we rarely think about this when we visualize
data!!
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One-dimensional graphs

• The line chart remains the most commonly used
  visualization technique
• but there is often uncertainty

Wikipedia line chart
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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 ()
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Visualizing the Data no uncertaintybut is this
what we want to see?
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Estimating behaviour between the data - but are
we certain?
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Perhaps this is the behaviour but something is
wrong
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At least this is credible..but still we are far
from certain
This is structural uncertainty, or model
uncertainty
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Error bars

• We can also have data uncertainty
• .. error information can be incorporated into a
  graph using 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
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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

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Two Dimensional Data

• We have three classic visualization techniques
• Contour map
• Surface view
• Image plot

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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)
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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
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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 CGA
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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, Visualizin
g Spatial Data Uncertainty using
Animation Computers and Geosciences, 1997
Important to take spatial autocorrelation into
account
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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?
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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

x
1
0
Linear combination of two normal distributions is
another normal distribution
and obvious extensions to 2D bilinear and 3D
trilinear
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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

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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 Earths 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

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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?
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Fuzzy Contours
Here we map probability to intensity zero fuzzy
contour is
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Adding the Mean as a Traditional Contour Line
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Looking at each model
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Comparison
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Contour Bands
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Fuzzy Contours or Contour Bands
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Contour shading

• Often we shade the bands between contour lines

• and we can do the same with uncertainty
  contouring

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Uncertain Contour Shading Colour Blending
Colour blending, using transparency to indicate
level of certainty
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Uncertain Contour Shading Probabilistic Model
Colour chosen according to random variable with
corresponding distribution
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As a Movie
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Looking at each model
Each model rendered with one eighth transparency
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Powerwall for Uncertainty
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Ocean Currents 1943 map
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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

http//www.csit.fsu.edu/futch/iso/
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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
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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
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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
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Uncertainty in Volume Rendering
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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