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