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LOD Map – A Visual Interface for LOD Map – A Visual Interface for Navigating Multiresolution Volume Navigating Multiresolution Volume
VisualizationVisualization
Chaoli Wang and Han-Wei ShenChaoli Wang and Han-Wei Shen
The Ohio State UniversityThe Ohio State University
Presented atPresented at
IEEE Visualization 2006IEEE Visualization 2006
22
Large Data SetsLarge 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
33
MotivationMotivation
• 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]
44
Multiresolution Data RepresentationMultiresolution 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
55
Research QuestionsResearch 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?
66
Our ApproachOur 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
77
Shannon EntropyShannon 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}
M
iii ppXH
1
log)(
[Bordoloi and Shen 2005]
88
Probability DefinitionProbability 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
M
iii ppXH
1
log)(
S
DCp iii
M
iii DCS
1
equal probability!C↑ → D↓C↓ → D↑
99
Contribution:
: mean value : average thickness : screen projection area : estimated visibility
ContributionContribution
vatCi
ta
thickness
1010
: mean value : standard deviation
: covariance between bi and bj
and : small constants
Distortion:
(a) covariance(b) luminance distortion(c) contrast distortion
DistortionDistortion
2
222
1
122
22 C
C
C
Cd
ji
ji
ji
jiijij
(a)
(b)
(c)
ij
1C 2C
7
0
70}|max{
jjjiji DdD
i
j
1111
TreemapTreemap
• 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/
1212
LOD MapLOD 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
)( at
1313
LOD Map – A First LookLOD Map – A First Look
entropy = 0.238
1414
How Can LOD Map Help?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↑)
1515
Results – LOD ComparisonResults – LOD Comparison
MSE-based 67 blocks entropy = 0.163 level-based, 67 blocks entropy = 0.381
1616
Results – LOD ComparisonResults – LOD Comparison
1717
Results – View ComparisonResults – View Comparison
entropy = 0.330 entropy = 0.343 entropy = 0.384 entropy = 0.390
1818
Results – LOD AdjustmentResults – 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
1919
Results – Budget ControlResults – Budget Control
before, 365 blocks, entropy = 0.448
after, 274 blocks, entropy = 0.476
2020
Summary & Future WorkSummary & 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
2121
AcknowledgementsAcknowledgements
• Data sets– National Library of Medicine– Lawrence Livermore National Laboratory
• Funding agencies– National Science Foundation– Department of Energy– Oak Ridge National Laboratory