1. Wei Chen1, Song Zhang2, Stephan Correia3, and David S. Ebert4
Abstractive Representation and Exploration of Hierarchically Clustered Diffusion Tensor Fiber Tracts
Wei Chen1, Song Zhang2, Stephan Correia3, and David S. Ebert4
1State Key Lab of CAD&CG, Zhejiang University, 2Mississippi State University, 3Brown University, 4Purdue University

2. Road map
Introduction
Method
Results
Conclusion/Future work

3. Diffusion tensor imaging

4. DTI fiber model

5. Problems Crowded, hard to see inside structures
Hard to see the shape, boundary and orientation of individual fiber tracts

6. Previous work on DTI fiber illustration
Seed placement/culling [Vilanova et al. 2004]
Clustering [Moberts et al. 2005, Brun et al. 2004, Zhang et al. 2007]
Hulls [Enders et al. 2005, Merhof et al. 2007]
Topology [Schultz et al. 2007]
GPU acceleration [Petrovic et al. 2007, Merhof et al. 2006]

7. Previous work on thin line illustration
Anisotropic voxel representation [Schussman et al. 2004]
Appearance texture [Weiskopf et al. 2007]
Volume rendering [Wenger et al. 2004]

8. Data Two human subjects
1.5T Simens scanner, 12 gradient directions, two b-values (0, 1000)

9. Hierarchical clustering
Proximity threshold
Zhang et al. TVCG 2008

10. Parameter Setting proximity threshold = 1.5 mm 2.5 mm 3.5 mm 4.5 mm
cluster size > 10

11. Smoothed geometric hulls
Alpha shape
A fiber cluster
We use the standard alpha shape algorithm to build a tightly approximated hull for each fiber cluster. It ensure that all vertices are inside the built hull. We then use the Poisson mesh reconstruction algorithm to generate a visually pleasing smoothed hull.
After smoothing
Fiber cluster + smoothed alpha shape

12. Principal fibers
Standard principal curve works for points, and do not consider the line length.
All tracts in a bundle are distributed samples of a smooth principal fiber C = f(λ), which is arc-length parameterized.
For points in a fiber, we estimate the λ values for two end points, and optimize rest points’ λ.
Standard principal curve algorithm applies on points. We extend it to work for a sequence of curves. All tracts in a bundle are independent and are distributed….

13. Principal fibers
where E denotes the expectation, i is the arc length of Ci, and j i is the arc length from the first vertex to V ji . Equation
(1) is known as the self-consistency property, which states that f (λ) is the average of all points that have the parameter value λ. The first formula of Equation (2) computes
the λ values for two end points of the underlying curve. The λ values of other points are estimated with the second formula of Equation (2).

14. Principal fibers
Principal fiber

15. Principal fibers
Several principal fibers

16. Principal fibers in hierarchical clusters
Calculate principal fibers at this level

17. Principal fibers

18. The multi-valued volume
The encoded information in the multi-valued volume

19. Visual exploration Original model Hierarchy level 6 Hierarchy level 9

20. Results

21. Expert evaluation
Our expert is a neuropsychologist with strong knowledge of white matter architecture.
With unclustered model, he was able to identify big and coherent structures but have trouble with others.
With clustered model, he was able to identify more anatomical structures but have trouble with overall shapes and boundaries.
With geometric hulls and principal curves, he was able to identify the shapes, boundaries, and orientations of the fiber tracts.

22. Conclusion
Abstraction of DTI fibers helps identification of anatomical structures.
Alpha shapes, principal curves, and the hierarchical structure of the fibers create a meaningful DTI fiber abstraction.

23. Future work
We would like to extend the hierarcical structures and the expressiveness of volume illustration to display muscles. Here we show some initial results.

24. Future work
We would like to extend the hierarcical structures and the expressiveness of volume illustration to display muscles. Here we show some initial results.

25. Acknowledgment We would like to thank Nvidia for equipment donations.
This work is partially supported by NSF of China (No ), the NOAA Northern Gulf Cooperative Institute (NA06OAR ), the Research Initiation Program, Mississippi State University, the NIA PAR , the Alzheimer’s Association (NIRG ), the Ittleson Fund, Brown University, NSF Grants , , , and the U.S. Department of Homeland Security.

26. End of presentation, the following slides will not show.

27. Introduction Diffusion tensor imaging Scientific illustration
Visualization techniques
Problems
Clustering
Scientific illustration
No data altering
Data altering

28. Principal fibers