Visualizing Uncertainty in
Volume Rendering
Suzana Djurcilov*, Kwansik Kim*,
Pierre Lermusiaux† and Alex Pang*
* UC Santa Cruz
† Harvard University
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OVERVIEW
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Introduction
Inline Approach
Post-Processing Approach
Future Directions
Uncertainty in Volume
Rendering
• Volume Rendering is a single value
method
• Need to add a second parameter
without diminishing the output of the
volume rendered image
• Want a task-specific visualization
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Application Domain
• Ocean Model (Mid-atlantic) from
Harvard
• Focus: temperature and salinity
along the shelf-break
• Uncertainty is the standard
deviation over several time steps
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Inline Approach
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Direct Volume Rendering (DVR)
1D Transfer Function
Opacity mapping of uncertainties
2D Transfer function
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Inline Approach
Direct Volume Rendering (DVR)
C ( a , b)  
b
a
 : opacity
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s

E ( s)  e a
  ( x ) dx
ds
Example visualization of
Salinity data using DVR
C: color intensity E: emission
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1D Transfer function
• Thresholding
• Map uncertainty to opacity
• Leave color transfer intact
• High uncertainty areas more
noticeable
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1D Transfer Function :
uncertainty thresholding
DVR of uncertainty > 0.2
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DVR of uncertainty > 0.5
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1D Transfer Function : mapping
uncertainties to opacity values
Transfer function
Increasing opacity with
uncertainty
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salinity
temperature
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1D Transfer Function : higher contrast
Transfer function
Increasing opacity with
uncertainty
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salinity
temperature
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2D Transfer function Histogram
• Create a graph of data vs.
uncertainty
• Map different regions to different
colors
• Override the transfer function
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2D Transfer Function : histogram
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2D Transfer Functions
2D transfer function
Salinity data
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2D Transfer Functions
2D transfer function
Salinity data
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Post-processing approach
• Get a separate volume rendering of
the primary data value and of
uncertainty
• Combine the two renderings into a
single image
• Primary value still discernible
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• Color background is
preserved
• Multi-variable
representation
specific to uncertainty
• Holes can be larger if
needed
• Hole color can not be
part of the transfer
function
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Variable hole size
1 pixel
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4 pixels
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Speckle intensity
• Higher uncertainty
--> darker hole
• Gray-scale color
•Vary both density
and shade of hole
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Using Texture
• Rough textures naturally convey uncertainty
• Random elements introduced into the image
• Textures can be from nature (sandstone, gravel)
or procedurally created
• Higher contrast -> higher uncertainty
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2D textures
• Create textures for 5
different uncertainty levels
• Quantize uncertainty and
map to different texture
levels
• Blend the texture with the
original DVR
• Shade the original pixel
color according to the
matching texture
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Texture Examples
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Adding Noise
• Change the DVR image directly
• Alter pixels in areas of high uncertainty
• Distance in color space proportional to
uncertainty
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Noise Example
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Future Work
• Extend the application domain
• Incorporate depth information into
post-processing
• Non-scalar (range, distribution)
uncertainty
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Acknowledgements
• ONR N00014-00-1-0764 and N00014-00-10771
• NASA NCC2-5281
• DOE W-7405-ENG-48
• NSF ACI-9908881
• DARPA grant N66001-97-8900
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