information-theoretic framework for flow visualization
DESCRIPTION
A summary of the Vis paper, "A Information-Theoretic Framework for Flow Visualization"TRANSCRIPT
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An Information-Theoretic Framework for Flow Visualization
Vis2010
2010/12/14ked
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Authors
Lijie Xu Teng-Yok Lee Han-Wei Shen
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Flow visualization
“Flow visualization is the art of making flow patterns visible.” – wiki
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Vector field
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Streamline
Streamlines are a family of curves that are instantaneously tangent to the velocity vector of the flow.
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Streamline
Different streamlines do not intersect. because a fluid particle cannot have two different
velocities at the same point.
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Streamline placement algorithm
evenly-spaced seeding method
farthest-point seeding method
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Streamline placement algorithm
evenly-spaced seeding method
farthest-point seeding method
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Information-aware streamline placement
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Information-aware streamline placement
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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
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Entropy field
Shannon’s entropy: A histogram is create from vectors:
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Entropy field
Shannon’s entropy: A histogram is create from vectors:
5.79 5.82
2.42 4.36
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Entropy field
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Information-aware streamline placement
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Important-based seed sampling1. Compute conditional entropy, h(x, y)
2. Place seeds in high conditional entropy
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Conditional entropy
0.56
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Interpolation
Streamline diffusion Generate a vector field Y(x) with respect to the
field that minimize the energy function
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Streamline diffusion
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Information-aware streamline placement
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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.
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2D results
initial seeds 1st seeding result
conditional entropy
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2D results
initial seeds 1st seeding result
conditional entropy
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3D results
initial seeds 50 streamlines 200 streamlines
conditional entropy
entropy field
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3D results
initial seeds 50 streamlines 200 streamlines
conditional entropy
entropy field
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3D results
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Performance
in seconds
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Limitations and feature work
Entropy measures consider the statistical properties but not spatial distribution
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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
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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
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Thx.