LOD Map A Visual Interface for Navigating Multiresolution

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

Large Data Sets – The Visible Woman • 512 * 1728 • Short integer (16 bits) • 864 MB – Richtmyer-Meshkov Instability (RMI) • 2048 * 1920 • Byte integer (8 bits) • 7. 5 GB per time step, 2 TB in total 2

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-ondemand” [Shneiderman 1992] 3

Multiresolution 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 4

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? 5

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 6

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 pi are all equal An example of 3 D probability vector {p 1, p 2, p 3} [Bordoloi and Shen 2005] 7

Probability Definition equal probability! C↑ → D↓ C↓ → D↑ • 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 8

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

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

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/ 11

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 12

LOD Map – A First Look entropy = 0. 238 13

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↑) 14

Results – LOD Comparison MSE-based 67 blocks entropy = 0. 163 level-based, 67 blocks 15 entropy = 0. 381

Results – LOD Comparison 16

Results – View Comparison entropy = 0. 330 entropy = 0. 343 entropy = 0. 384 17 entropy = 0. 390

Results – LOD Adjustment entropy = 0. 192 before, 90 blocks entropy = 0. 386 entropy = 0. 251 after, 90 blocks before, 108 blocks 18 entropy = 0. 414 after, 108 blocks

Results – Budget Control before, 365 blocks, entropy = 0. 448 after, 274 blocks, entropy = 0. 476 19

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 20

Acknowledgements • Data sets – National Library of Medicine – Lawrence Livermore National Laboratory • Funding agencies – National Science Foundation – Department of Energy – Oak Ridge National Laboratory 21