LOD Map – A Visual Interface for
Navigating Multiresolution Volume
Visualization
Chaoli Wang and Han-Wei Shen
The Ohio State University
Presented at
IEEE Visualization 2006
2
Large Data Sets
– The Visible Woman
• 512 * 512 * 1728
• Short integer (16 bits)
• 864MB
– Richtmyer-Meshkov Instability (RMI)
• 2048 * 2048 * 1920
• Byte integer (8 bits)
• 7.5 GB per time step, 2TB in total
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Motivation
• Large data size makes interactive visualization
difficult
– High main / texture memory requirement
– Slower rendering speed
• Multiresolution volume visualization
– Adaptive data exploration
– “Overview first, zoom and filter, and then details-ondemand” [Shneiderman 1992]
4
Multiresolution Data Representation
low-pass filtered subblock
wavelet coefficients
• The wavelet tree [Guthe et al. 2002]
– Octree-based space partition
– Block-wise wavelet transform and compression
– Error metric calculation
5
Research Questions
• How to measure and compare the quality
of different LOD selections?
• Are the computing resources effectively
distributed?
• Can we visualize what are being selected
and make changes?
6
Our Approach
• LOD entropy – LOD quality index
– Employ information theory
– Measure information contained in the LOD
• LOD map – visual representation of LOD quality
– A single number vs. a visual interface
– Immediate suggestions for LOD improvement
– Interactive techniques for LOD adjustment
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Shannon Entropy
• The source takes a sequence of finite symbols {a1, a2,
a3, …, aM} with probabilities {p1, p2, p3, …, pM}
• The amount of information contained is defined as
M
H ( X )   pi log pi
i 1
• The entropy function is maximized when pi are all equal
An example of 3D probability vector {p1, p2, p3}
[Bordoloi and Shen 2005]
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Probability Definition
• Entropy:
M
H ( X )   pi log pi
i 1
C D
pi  i i
S
M
where
S   Ci  Di
i 1
Ci : contribution of data block i to the image
Di : distortion of data block i with its child blocks
M : total number of data blocks in the hierarchy
• A global quality index
– Quality of rendered images
– Probability distribution of all data blocks
equal probability!
C↑ → D↓
C↓ → D↑
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Contribution
Contribution:

t
a

Ci    t  a  v
: mean value
: average thickness
: screen projection area
: estimated visibility
thickness
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Distortion
i2   2j  C1  i2   2j  C2
d ij   ij 

2i  j  C1 2 i j  C2
(a)
(b)
(c)
(a) covariance
(b) luminance distortion
(c) contrast distortion
 : mean value
 : standard deviation
 ij : covariance between bi and bj
C1 and C2 : small constants
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Distortion:
Di   dij  max{ D j |7j 0 }
j 0
i
j
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Treemap
• A space-filling method to visualize hierarchical
information [Shneiderman et al. 1992]
– Recursive subdivision of a given display area
– Information of each individual node
• Color and size of its bounding rectangle
…
…
…
http://www.cs.umd.edu/hcil/treemap-history/
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LOD Map
• Treemap representation of a LOD
– User interface for visual LOD selections
– Observe individual blocks and make adjustments
– Information mapping
• Distortion D : maps to the color of rectangle
• Contribution C :
– (   t  a) maps to the size of rectangle
–
maps to its opacity

LOD Map – A First Look
entropy = 0.238
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How Can LOD Map Help?
• Balance probability distribution
• Large rectangles with bright red colors
– Highly-visible
– High contribution, large distortion
– Split to increase resolutions (C↑ → D↓)
• Small blue rectangles
– Low contribution, small distortion
– Join to decrease resolutions (C↓ → D↑)
• Dark rectangles
– Lowest visibility
– Join to decrease resolutions (C↓ → D↑)
Results – LOD Comparison
MSE-based 67 blocks
entropy = 0.163
level-based, 67 blocks
15
entropy = 0.381
Results – LOD Comparison
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Results – View Comparison
entropy = 0.330
entropy = 0.343
entropy = 0.384
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entropy = 0.390
Results – LOD Adjustment
entropy = 0.192
before, 90 blocks
entropy = 0.386 entropy = 0.251
after, 90 blocks before, 108 blocks
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entropy = 0.414
after, 108 blocks
Results – Budget Control
before, 365 blocks, entropy = 0.448
after, 274 blocks, entropy = 0.476
19
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Summary & Future Work
• Summary
– LOD entropy – quality measure
– LOD map – visual navigation interface
– Effectiveness and efficiency
• Future work
– Time-critical rendering
– Eye-tracking application
– Time-varying data visualization
21
Acknowledgements
• Data sets
– National Library of Medicine
– Lawrence Livermore National Laboratory
• Funding agencies
– National Science Foundation
– Department of Energy
– Oak Ridge National Laboratory