LOD%20Map%20

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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

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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-on-demand Shneiderman 1992

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Multiresolution Data Representation

• The wavelet tree Guthe et al. 2002
• Octree-based space partition
• Block-wise wavelet transform and compression
• Error metric calculation

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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?

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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
• 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
• where
• 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 mean value
average thickness screen
projection area estimated
visibility
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Distortion
mean value
standard deviation
covariance between bi and bj and small
constants Distortion
(a) covariance (b) luminance distortion (c)
contrast distortion
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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
• maps to the size of rectangle
• maps to its opacity

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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?)

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Results LOD Comparison
MSE-based 67 blocks
entropy 0.163
level-based, 67 blocks
entropy 0.381
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Results LOD Comparison
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Results View Comparison
entropy 0.330
entropy 0.343
entropy 0.384
entropy 0.390
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Results LOD Adjustment
entropy 0.192
entropy 0.386
entropy 0.251
entropy 0.414
before, 90 blocks
after, 90 blocks
before, 108 blocks
after, 108 blocks
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Results Budget Control
before, 365 blocks, entropy 0.448
after, 274 blocks, entropy 0.476
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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

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Acknowledgements

• Data sets
• National Library of Medicine
• Lawrence Livermore National Laboratory
• Funding agencies
• National Science Foundation
• Department of Energy
• Oak Ridge National Laboratory