LOD Map – A Visual Interface for Navigating Multiresolution Volume Visualization

1. 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

3. 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]

4. low-pass filtered subblock wavelet coefficients Multiresolution Data Representation • 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

7. 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]

8. 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↑

9. Contribution Contribution: : mean value : average thickness : screen projection area : estimated visibility

10. (a) (b) (c) i j Distortion : mean value : standard deviation : covariance between bi and bj and : small constants Distortion: (a) covariance (b) luminance distortion (c) contrast distortion

11. … … … 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/

12. 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

13. LOD Map – A First Look entropy = 0.238

14. 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↑)

15. Results – LOD Comparison MSE-based 67 blocks entropy = 0.163 level-based, 67 blocks entropy = 0.381

16. Results – LOD Comparison

17. Results – View Comparison entropy = 0.330 entropy = 0.343 entropy = 0.384 entropy = 0.390

18. 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

19. Results – Budget Control before, 365 blocks, entropy = 0.448 after, 274 blocks, entropy = 0.476

20. 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