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An Information-Theoretic Frameworkfor Flow VisualizationVis20102010/12/14ked
Authors Lijie Xu Teng-Yok Lee Han-Wei Shen
Flow visualization “Flow visualization is the art of making flowpatterns visible.” – wiki
Vector field
Streamline Streamlines are a family of curves that areinstantaneously tangent to the velocity vectorof the flow.
Streamline Different streamlines do not intersect. because a fluid particle cannot have two differentvelocities at the s...
Streamline placement algorithmevenly-spacedseeding methodfarthest-pointseeding method
Streamline placement algorithmevenly-spacedseeding methodfarthest-pointseeding method
Information-aware streamline placement
Information-aware streamline placement
1. Detect local maxima in the entropy field2. Discard points whose entropy are too small3. Place initial seeds The seed a...
Entropy field Shannon’s entropy: A histogram is create from vectors:
Entropy field Shannon’s entropy: A histogram is create from vectors:5.79 5.822.42 4.36
Entropy field
Information-aware streamline placement
Important-based seed sampling1. Compute conditional entropy, h(x, y)2. Place seeds in high conditional entropy
Conditional entropy0.56
Interpolation Streamline diffusion Generate a vector field Y(x) with respect to thefield that minimize the energy function
Streamline diffusion
Information-aware streamline placement
Redundant streamline pruning Low entropy region: Fewer streamlines are needed Large distance threshold High entropy re...
2D resultsinitial seeds 1stseeding resultconditionalentropy
2D resultsinitial seeds 1stseeding resultconditionalentropy
3D resultsinitial seeds 50 streamlines 200 streamlinesconditionalentropyentropy field
3D resultsinitial seeds 50 streamlines 200 streamlinesconditionalentropyentropy field
3D results
Performancein seconds
Limitations and feature work Entropy measures consider the statisticalproperties but not spatial distribution
Limitations and feature work Entropy measures consider the statisticalproperties but not spatial distribution A region w...
Limitations and feature work Entropy measures consider the statisticalproperties but not spatial distribution A region w...
Thx.
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Information-theoretic framework for flow visualization

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A summary of the Vis paper, "A Information-Theoretic Framework for Flow Visualization"

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Information-theoretic framework for flow visualization

  1. 1. An Information-Theoretic Frameworkfor Flow VisualizationVis20102010/12/14ked
  2. 2. Authors Lijie Xu Teng-Yok Lee Han-Wei Shen
  3. 3. Flow visualization “Flow visualization is the art of making flowpatterns visible.” – wiki
  4. 4. Vector field
  5. 5. Streamline Streamlines are a family of curves that areinstantaneously tangent to the velocity vectorof the flow.
  6. 6. Streamline Different streamlines do not intersect. because a fluid particle cannot have two differentvelocities at the same point.
  7. 7. Streamline placement algorithmevenly-spacedseeding methodfarthest-pointseeding method
  8. 8. Streamline placement algorithmevenly-spacedseeding methodfarthest-pointseeding method
  9. 9. Information-aware streamline placement
  10. 10. Information-aware streamline placement
  11. 11. 1. Detect local maxima in the entropy field2. Discard points whose entropy are too small3. Place initial seeds The seed are distributed using diamond shapetemplateTemplate based seed selection
  12. 12. Entropy field Shannon’s entropy: A histogram is create from vectors:
  13. 13. Entropy field Shannon’s entropy: A histogram is create from vectors:5.79 5.822.42 4.36
  14. 14. Entropy field
  15. 15. Information-aware streamline placement
  16. 16. Important-based seed sampling1. Compute conditional entropy, h(x, y)2. Place seeds in high conditional entropy
  17. 17. Conditional entropy0.56
  18. 18. Interpolation Streamline diffusion Generate a vector field Y(x) with respect to thefield that minimize the energy function
  19. 19. Streamline diffusion
  20. 20. Information-aware streamline placement
  21. 21. Redundant streamline pruning Low entropy region: Fewer streamlines are needed Large distance threshold High entropy region: Smaller distance threshold If a streamline have a neighboring streamlinethat is closer than threshold, the streamline ispruned.
  22. 22. 2D resultsinitial seeds 1stseeding resultconditionalentropy
  23. 23. 2D resultsinitial seeds 1stseeding resultconditionalentropy
  24. 24. 3D resultsinitial seeds 50 streamlines 200 streamlinesconditionalentropyentropy field
  25. 25. 3D resultsinitial seeds 50 streamlines 200 streamlinesconditionalentropyentropy field
  26. 26. 3D results
  27. 27. Performancein seconds
  28. 28. Limitations and feature work Entropy measures consider the statisticalproperties but not spatial distribution
  29. 29. Limitations and feature work Entropy measures consider the statisticalproperties but not spatial distribution A region with high error magnitudes can stillhave a low conditional entropy
  30. 30. Limitations and feature work Entropy measures consider the statisticalproperties but not spatial distribution A region with high error magnitudes can stillhave a low conditional entropy The magnitude of vectors are not considered
  31. 31. Thx.

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