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 Multiresolution Data Representation low-pass filtered subblockwavelet 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

7 Shannon Entropy The source takes a sequence of finite symbols {a 1, a 2, a 3, …, a M } with probabilities {p 1, p 2, p 3, …, p M } The amount of information contained is defined as The entropy function is maximized when p i are all equal An example of 3D probability vector {p 1, p 2, p 3 } [Bordoloi and Shen 2005]

8 Probability Definition Entropy: where C i : contribution of data block i to the image D i : 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

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

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

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 …… …

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 blocksentropy = 0.163level-based, 67 blocksentropy = 0.381

16 Results – LOD Comparison

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

18 Results – LOD Adjustment entropy = 0.192entropy = 0.386entropy = 0.251entropy = before, 90 blocksafter, 90 blocksbefore, 108 blocksafter, 108 blocks

19 Results – Budget Control before, 365 blocks, entropy = 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