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

1. An Information-Theoretic Framework
for Flow Visualization
Vis2010
2010/12/14
ked

2. Authors
 Lijie Xu Teng-Yok Lee Han-Wei Shen

3. Flow visualization
 “Flow visualization is the art of making flow
patterns visible.” – wiki

4. Vector field


5. Streamline
 Streamlines are a family of curves that are
instantaneously tangent to the velocity vector
of the flow.

6. Streamline
 Different streamlines do not intersect.
 because a fluid particle cannot have two different
velocities at the same point.

7. Streamline placement algorithm
evenly-spaced
seeding method
farthest-point
seeding method

8. Streamline placement algorithm
evenly-spaced
seeding method
farthest-point
seeding method

9. Information-aware streamline placement

10. Information-aware streamline placement

11. 1. Detect local maxima in the entropy field
2. Discard points whose entropy are too small
3. Place initial seeds
 The seed are distributed using diamond shape
template
Template based seed selection

12. Entropy field
 Shannon’s entropy:
 A histogram is create from vectors:

13. Entropy field
 Shannon’s entropy:
 A histogram is create from vectors:
5.79 5.82
2.42 4.36

14. Entropy field

15. Information-aware streamline placement

16. Important-based seed sampling
1. Compute conditional entropy, h(x, y)
2. Place seeds in high conditional entropy

17. Conditional entropy

0.56

18. Interpolation
 Streamline diffusion
 Generate a vector field Y(x) with respect to the
field that minimize the energy function

19. Streamline diffusion

20. Information-aware streamline placement

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 streamline
that is closer than threshold, the streamline is
pruned.

22. 2D results
initial seeds 1st
seeding result
conditional
entropy

23. 2D results
initial seeds 1st
seeding result
conditional
entropy

24. 3D results
initial seeds 50 streamlines 200 streamlines
conditional
entropy
entropy field

25. 3D results
initial seeds 50 streamlines 200 streamlines
conditional
entropy
entropy field

26. 3D results

27. Performance
in seconds

28. Limitations and feature work
 Entropy measures consider the statistical
properties but not spatial distribution

29. Limitations and feature work
 Entropy measures consider the statistical
properties but not spatial distribution
 A region with high error magnitudes can still
have a low conditional entropy

30. Limitations and feature work
 Entropy measures consider the statistical
properties but not spatial distribution
 A region with high error magnitudes can still
have a low conditional entropy
 The magnitude of vectors are not considered

31. Thx.