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A summary of the Vis paper, "A Information-Theoretic Framework for Flow Visualization"
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An Information-Theoretic Framework for Flow Visualization
Vis2010
2010/12/14ked
Authors
Lijie Xu Teng-Yok Lee Han-Wei Shen
Flow visualization
“Flow visualization is the art of making flow patterns visible.” – wiki
Vector field
Streamline
Streamlines are a family of curves that are instantaneously tangent to the velocity vector of the flow.
Streamline
Different streamlines do not intersect. because a fluid particle cannot have two different
velocities at the same point.
Streamline placement algorithm
evenly-spaced seeding method
farthest-point seeding method
Streamline placement algorithm
evenly-spaced seeding method
farthest-point seeding method
Information-aware streamline placement
Information-aware streamline placement
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
Entropy field
Shannon’s entropy: A histogram is create from vectors:
Entropy field
Shannon’s entropy: A histogram is create from vectors:
5.79 5.82
2.42 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 the
field 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 region: Smaller distance threshold
If a streamline have a neighboring streamline that is closer than threshold, the streamline is pruned.
2D results
initial seeds 1st seeding result
conditional entropy
2D results
initial seeds 1st seeding result
conditional entropy
3D results
initial seeds 50 streamlines 200 streamlines
conditional entropy
entropy field
3D results
initial seeds 50 streamlines 200 streamlines
conditional entropy
entropy field
3D results
Performance
in seconds
Limitations and feature work
Entropy measures consider the statistical properties but not spatial distribution
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
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
Thx.