Dynamic View Selection for Time-Varying Volumes

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Dynamic View Selection for Time-Varying Volumes

• Guangfeng Ji and Han-Wei Shen
• The Ohio State University
• Now at Vital Images

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Visualization of Time-Varying Volumes

• Time-varying features are often highly dynamic,
  with their positions, orientations, and shapes
  changing continuously.
• It is important to select dynamic views that can
  follow the features so that maximum information
  can be perceived from the time sequence.

Time-varying features (Terascale Supernova
Initiative) seen from a fixed view
A better dynamic view
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Contributions

• An improved static view selection algorithm
• The quality of a static view is determined by
  measuring the opacity, color, and curvature
  distribution of the corresponding rendering
  images.
• Use the information theory approach.
• Dynamic view selection
• Maximize the information perceived from the time
  sequence.
• Follow the smooth-movement constraint.
• Use the dynamic programming approach.

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Assumption of Viewing Setting

• All views are located on the surface of a viewing
  sphere.
• The volume is located at the center of the
  sphere.

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Previous Work on View Selection

• Takahashi et al
• Decompose the whole volume into a set of feature
  interval volumes.
• Use the surface-based view selection technique
  propose by Vazquez et al to find the optimal view
  for each component.
• The globally best view is a compromise among all
  the locally optimal views.

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Previous Work (contd)

• Bordoloi et al
• A full volume rendering approach
• In a good view, the visibility of a voxel should
  be proportional to the noteworthiness value of
  the voxel.
• If the visibility of a voxel can be maximized, it
  does not have to be proportional to the
  noteworthiness value.

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The Improved Static View Selection Algorithm

• An image-based view selection algorithm
• Opacity image
• Prefers even opacity distribution, and larger
  projection size.
• Color image
• Prefers a larger area of salient features
  colors, with an even distribution among all
  salient colors.
• Curvature image
• Prefers more perceived curvature information.

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Shannon Entropy Function

• A random sequence of symbols occur in the set
  a0, a1, , an-1 with the occurrence probability
  p0, p1, pn-1, the Shannon entropy (average
  information) of the sequence is defined as
• The entropy function reaches the maximum value
  log2(n) when p0p1 pn-11/n

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Measurement of Opacity Distribution and
Projection Size

• A good view prefers an even opacity distribution
  and a larger projection size.

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Opacity (contd)

• How to achieve this?
• Use the entropy function
• Given an opacity image a0, a1, an-1, the
  probability pi of each pixel is
• Why is it correct?
• Background pixels (a0) do not contribute to the
  entropy.
• The maximum of the entropy is log2(f), where f is
  foreground size. It is reached when all the
  foreground pixels have the same opacity values.

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Measurement of the Color Distribution

• Color transfer functions are often used to
  highlight salient features.
• A good view prefers a larger area of salient
  colors, with even distribution among these
  colors.

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Color (contd)

• How to achieve this?
• Use the entropy function
• Suppose there are n colors C0, C1, Cn-1,
  where C0 is the background color and the other
  colors appear in the color transfer function to
  highlight salient feature, the probability of Ci
  is piAi/T(Ai is area of Ci, and T is total area)
• Why is it correct?
• Entropy reaches maximum value when A0 A1 An-1
• Details
• CIELUV color space
• Lighting model without specular

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Measurement of the Curvature Information

• A good view should also reflect the curvature
  information
• Low curvature means flat area, and high curvature
  means highly irregular surfaces.
• How to present the curvature information in the
  rendering image?
• The curvature of a voxel determines the color
  intensity of the voxel.
• The overall intensity of the rendering images
  reflects the amount of perceived curvature
  information.

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The Final Utility Function

• Scenario 1 Sophisticated opacity transfer
  function, but simple gray-scale or rainbow color
  transfer function.
• Scenario 2 Different colors are used to
  highlight different features in a segmented
  volume
• Put large weight to
  

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Dynamic View Selection

• The optimal dynamic view should satisfy
• It should move at a near-constant speed.
• It should not change its direction abruptly.
• It should maximize the amount of information the
  user can perceive from the time-varying dataset.
• A brute-force algorithm can take exponential
  running time.

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Algorithm if only Considering Constraint I and III

• The view moves at speed V, with VminltVltVmax
• Pi,j is the position of jth view at ti
• Max(Pi,j) is the maximum information perceived
  from Pi,j to some view at the final time step
• u(Pi,j) measures the information perceived at the
  view Pi,j

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Dynamic Programming
A backward procedure
Time complexity O(nvv)
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Solution Considering All the Constraints

• How to take the movement direction into account?
• Partition a views local tangent plane and
  specify the allowed turns.

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Dynamic Programming

• MaxInfo(Pi,j,r) is the maximal information
  perceived from Pi,j to some view at the final
  timestep, and Pi,j was entered from region r from
  its previous view.

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Dynamic Programming (contd)

• A backward procedure
• Time Complexity O(nrvv)

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Results

• Static view for shockwave data set
• Opacity as the criterion
• 6.92 seconds to compute the opacity entropies for
  all 256 views

Worst view Best view
The corresponding opacity images
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Tooth Data Set

• Opacity as the criterion
• 7.18 seconds to compute the opacity entropies for
  all 256 views

Worst view Best view
The corresponding opacity images
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Vortex Data Set

• Color as the criterion
• 16.3 seconds to compute the color entropies for
  all 256 views

Worst view Best view
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TSI Dataset

• Utility 0.8Curvature 0.2Opacity
• 18.7 seconds to compute curvature and opacity
  entropies for all 256 views

Worst view Best view
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Dynamic View for TSI Data Set
4.31 seconds for the dynamic programming process
Dynamic view selected by the
dynamic programming algorithm
The
images at the original fixed view
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Conclusions and Future Work

• An improved static view selection method
• A dynamic view selection method
• Future work
• Lighting design for time-varying polygonal and
  volumetric data sets.

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Acknowledgements

• NSF ITR Grant ACI-0325934
• NSF RI Grant CNS-0403342
• DOE Early Career Principal Investigator Award
• DE-FG02-03ER25572
• NSF Career Award CCF-0346883
• Oak Ridge National Laboratory Contract 400045529
• John M. Blondin (NCSU), Anthony Mezzacappa
  (ORNL), and Ross J. Toedte (ORNL) for providing
  the TSI data set.
• Kwan-Liu Ma for the vortex data set.