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List of Figures

1. Data processing path
2. Bipolar pulsed gradient experiment (adapted from [22] and [9])
3. Diffusion in myelinated fibers (adapted from [22])
4. Diffusion tensor overlying two crossing fibertracts
5. Sagittal view showing acquisition positions
6. Random tensorfield
7. Smoothing with Gauss filter of length 5
8. Random tensorfield with bias in one direction
9. Smoothing with Gauss filter of length 3
10. Interpolation of single components of two tensors in 9 steps
11. Interpolation of two tensors in 9 steps by keeping the shape
12. Visualization of tensors using ellipsoids
13. Visualizing tensors with headless arrows and dots representing $c_l\hat{\mathbf{e}}_1$
14. Visualizing tensors by color-encoding the largest eigenvalue, -vector
15. Grayscale representation of the measurement close-line $c_l$
16. Grayscale representation of the measurement close-plane $c_p$
17. Grayscale representation of the measurement close-sphere $c_s$
18. Orthogonalization of the eigenvectors
19. Original synthetic square
20. Rigid rotation of synthetic example with nearest neighbor interpolation
21. Rigid rotation of synthetic example with linear interpolation
22. Rigid rotation of synthetic example with nearest neighbor interpolation and local transformation of tensors
23. Rigid rotation of synthetic example with linear interpolation and local transformation of tensors
24. Notation conventions used
25. Eigensystem decomposition of the correlation matrix
26. Variogram parameters
27. Plot of common parametric correlation forms used for Kriging interpolation
28. Example of using Kriging interpolation
29. Synthetic displacement
30. Distorted synthetic square with full local warping
31. Distorted synthetic square with local warping but without scaling
32. Distorted synthetic square only with local rotation of the tensors
33. Multi-scale matching
34. Chessboard example for the nonrigid matching process
35. MRI scan example for the nonrigid matching process
36. Classification Examples
37. C++ Class hierarchy
38. Local transformation of tensors
39. Diffusion tensor image of an adult human brain
40. Diffusion tensor image of the corpus callosum of an adult human brain
41. 3D representation of the frontal lobe of the corpus callosum
42. 3D representation of the frontal lobe of the corpus callosum