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.