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An Information-theoretic Framework for Visualization

An Information-theoretic Framework for Visualization. University of Calgary Department of Computer Science Yang Liu. …about. presentation outline. Introduction. Content. Conclusion. Future Discussion. Related Work. Introduction. data compression. data abstraction.

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An Information-theoretic Framework for Visualization

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  1. An Information-theoretic Framework for Visualization University of Calgary Department of Computer Science Yang Liu

  2. …about presentation outline Introduction Content Conclusion Future Discussion Related Work

  3. Introduction data compression data abstraction • Information theory • The science of quantification, coding and communication of information VS • Visualization • Visually coding and communicating information information discovery process creating and viewing a visualization probabilistic experiments quality of a visualization

  4. Introduction • Is a visualization system a communication system? Example: a visual communication system

  5. Related Work • scene and shape complexity analysis • various ways to apply information-theoretic theories, strategies, and techniques to find the dots, make sense of them, and differentiate them at different levels of abstraction—from macroscopic to microscopic. • An information theory framework for the analysis of scene complexity • integral geometry and information theory tools(Mutual Information)have been applied to quantify the shape complexity from two different perspectives • Shape Complexity Based on Mutual Information terrorism-research literature (1995–97)

  6. Related Work • light source placement • A safe and a fast global optimization procedure were designed to place light sources by maximizing the illumination information with entropy functions. • Maximum Entropy Light Source Placement fitted perceptual entropy function and selected light source directions

  7. Related Work • view selection in mesh rendering • Use viewpoint entropy measure to automatically select the camera positions that allow to minimize the amount of images used as an Image-Based representation. • Automatic View Selection Using Viewpoint Entropy and its Application to Image-Based Modelling • defined a unified framework for viewpoint selection and mesh saliency based on an information channel between a set of viewpoints and the set of polygons of an object. • An Unified Information-Theoretic Framework for Viewpoint Selection and Mesh Saliency six most representative views selected by the VMI-based algorithm Three images of a balloon, bad viewpoints, good viewpoint

  8. feature highlighting in unsteady multi-field visualization and …… view selection in volume rendering More Related Work focus of attention in volume rendering feature highlighting in time-varying volume visualization multi-resolution volume visualization

  9. Content

  10. Models of communication and visualization Ω: machine-representable data, information and knowledge, human brains G : Ω → Ω D: all machine-representable data F: D→D

  11. Relevance: Infor-theory and Visualization

  12. Quantifying Visual Information • Random variable • X • Takes a finite number of values • x1, x2, . . . , xm • Probability mass function • P( xi ) • Entropy • H(X) = - • Mutual Information • I(X;Y) = I(Y;X) Claude Elwood Shannon (1916–2001)

  13. Entropy • Time Series • 64 independent samples • each sample is an integer in [0, 255] • probability mass function is i.i.d. • Entropy • Time Series Plot • Minimal 256x64 pixels (214 pixels)

  14. Entropy • The most compact: • 64 bytes (512 bits) • One pixel per bit isn’t readable • 4x4 pixels per bit: 213 bits • Samples only in lower half • 448 bits, not 512 bits • 64*128*7*1/27 = 448 bits

  15. Three Measures for Visualization • Entropy of Input Data Space: H(X) • Visualization Capacity: V(G) • Display Capacity: D • Visual Mapping Ratio (VMR) = • Information Loss Ratio (ILR) = • Display Space Utilization (DSU) =

  16. Information Loss Ratio (ILR) • Display Space Restriction • 64x64 pixels • Evenly distributed probability mass function • Linear visual mapping • ILR is a probabilistic measure about • a data space X • not an instance xi

  17. Unevenly Distribution • Linear visual mapping

  18. Unevenly Distribution • Nonlinear visual mapping • [0,63] to [0,31] • [64,127] to [32,47] • [128,191] to [48,55] • [192,255] to [56,63]

  19. Unevenly Distribution • Logarithmic visual mapping

  20. Logarithmic Pattern

  21. Redundancy • P. Rheingans and C. Landreth. Perceptual principles for effective visualizations. 1995. • different parameters of a visual mapping convey different types of information with different efficiency • multiple display parameters can overcome visual deficiencies • multiple display parameters reinforce each other

  22. Interaction and User Studies • I(Overview;Detail) = I(Detail;Overview) • The information about an overview in one of its detailed view is the same as that about that detailed view in the overview.

  23. Example 1 • MutualInformation I = 0.147

  24. Example 1 • Example 1: I(X;Y) = 0.147 • Example 2: I(X;Y) = 0.278 Example 2

  25. A white brick? A mobile? An iphone? An iphone 5? …If I change the shell? What is In my hand?

  26. The Role of User Studies • quantitative measurements VS user studies • Interaction allows users to provide a visualization system with additional information • Pre-stored knowledge includes hard-coded knowledge (not stochastic) and human knowledge (stochastic) • If fundamental statistical findings from visualization user studies, then transfer information theory to practice in visualization

  27. Data Processing Inequality • “No clever manipulation of data can improve the inferences that can be made from the data” ----Thomas M. Cover • Markov chain conditions • Closed coupling: (X,Y), (Y,Z) • X and Z are conditionally independent • What if the condition is broken? • I (X;Y) I (X;Z) • I (X;Y) I (X;Z)

  28. “The purpose of computing is insight, not numbers.” Conclusion • Information theory can explain many phenomena in visualization: • including but not limited to visual mapping, interaction, user studies, quality metrics, and knowledge-assisted visualization • Drawbacks: • assumption of memoryless • visualization user studies • different emphasis (eg. Readable vs Efficiency) Richard Wesley Hamming (February 11, 1915 – January 7, 1998)

  29. Future Discussion Visualization Information Theory

  30. References • M Chen, H Jaenicke. An Information-theoretic Framework for Visualization. Some content in this presentation may from the author’s website and corresponding materials. • M. Feixas, E. del Acebo, P. Bekaert, and M. Sbert. An information theory framework for the analysis of scene complexity. • J. Rigau, M. Feixas, and M. Sbert. Shape complexity based on mutual information. • S. Gumhold. Maximum entropy light source placement. • P.-P. V′azquez, M. Feixas, M. Sbert, andW. Heidrich. Automatic view selection using viewpoint entropy and its application to image-based modelling. • M. Feixas, M. Sbert, and F. Gonz′alez. A unified information-theoretic framework for viewpoint selection and mesh saliency. • U. Bordoloi and H.-W. Shen. View selection for volume rendering. • S. Takahashi and Y. Takeshima. A feature-driven approach to locating optimal viewpoints for volume visualization. • ……

  31. The End Thank you …any questions

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