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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

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

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.

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.

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.

Previous Work (cont’d)

- 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.

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.

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 p0=p1=…= pn-1=1/n

Measurement of Opacity Distribution and Projection Size

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

Opacity (cont’d)

- 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 (a=0) 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.

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.

Color (cont’d)

- 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 pi=Ai/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

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.

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

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.

Algorithm if only Considering Constraint I and III

- The view moves at speed V, with Vmin
- Pi,j is the position of jth view at t=i
- 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

Solution Considering All the Constraints

- How to take the movement direction into account?
- Partition a view’s local tangent plane and specify the allowed turns.

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.

Dynamic Programming (cont’d)

- A backward procedure:
- Time Complexity: O(n*r*v*v)

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

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

Vortex Data Set

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

Worst view Best view

TSI Dataset

- Utility = 0.8*Curvature + 0.2*Opacity
- 18.7 seconds to compute curvature and opacity entropies for all 256 views

Worst view Best view

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

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.

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.

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