1. Semi-Automatic Generation of Transfer Functions
G. Kindlmann, J. Durkin
Cornell University
Presented by Jian Huang, CS594, Spring 2002

2. Direct Volume Rendering
Render the volume by computing the volume integration – Direct Volume Rendering
Iso-surfacing: extract the iso-surfaces from the dataset, and render as surface geometry primitives
Pros and cons: ? depend on who you talk to

3. Example

4. What are we looking for?
look for boundary regions between relatively homogeneous material in the scalar volume
The boundary might be associated with a range of values
Use an opacity function to modulate the parameters corresponding to this range

5. Getting a good transfer function
Transfer function: assign renderable optical properties to the numerical values
This paper focuses on the opacity functions
Getting a good transfer function is tricky

6. Previous work
He et al.,use genetic algorithm to breed a good transfer function
Marks et al., design gallery
Both only look at good-looking renderings, driven by images.
But, good transfer function should come from an analysis of the data set
Work also exists in the iso-surfacing domain

7. Example

8. The Boundary Model Assumption
There exist a sharp, discontinuous change in the physical property of the entity
The data/signal has been low-pass filtered, (band-limited, or, blurred)
The blur is isotropic
The blurring function (low-pass filter) is Gaussian

9. The Boundary Model (2)

10. Directional Derivatives

11. Directional Derivatives (2)

12. Relations between f, f’, f’’

13. Histogram Volume
Measure the relationship between the data value and its derivatives.

14. Histogram Creation
Measure f and its directional derivatives exactly once per voxel, at the original sample points of the data set

15. Implementation First directional derivative
Three ways to compute the gradients

16. Implementation (2) Use central difference
Use method 1 to compute 2nd derivative
Need the 1st directional derivative computed and stored as a volume

17. Implementation (3)

18. Histogram Volume Inspection

19. More examples

20. Boundary Analysis
Based on the assumption of Gaussian profile

21. Where is the boundary?
Average 1st directional derivative of f over all the positions x at which f(x) equals v,
g(v)
Average 2nd directional derivative of f over all the positions x at which f(x) equals v,
h(v)

22. Opacity function

23. Using both data value and gradient magnitude
Extend h(v) to h(v,g).
Benefit:
distinguish between boundaries that have overlapping ranges of values
Capture surface of a material which attains a wide range of values (bone)

24. Results