Tensor splines for interpolation and approximation of DT-MRI with applications to segmentation of isolated rat hippocampi

IEEE Transactions on Medical Imaging

Volumn 26, Issue 11, 2007, Pages 1537-1546

  Barmpoutis, Angelos ^a   Vemuri, Baba C ^a   Shepherd, Timothy M ^b   Forder, John R ^b  

^a UNIVERSITY OF FLORIDA   (United States)

^b UNIVERSITY OF FLORIDA COLLEGE OF MEDICINE   (United States)

Author keywords

Affine invariance; Approximation; Diffusion tensors; Interpolation; Segmentation

Indexed keywords

APPROXIMATION ALGORITHMS; DIFFUSION; IMAGE SEGMENTATION; INTERPOLATION; MAGNETIC RESONANCE IMAGING; PROBABILITY;

AFFINE INVARIANCE; DIFFUSION TENSORS; SYMMETRIC POSITIVE DEFINITE (SPD); TENSOR SPLINES;

TENSORS;

ALGORITHM; ANIMAL; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; COMPUTER ASSISTED DIAGNOSIS; DIFFUSION WEIGHTED IMAGING; HIPPOCAMPUS; HISTOLOGY; IMAGE ENHANCEMENT; IN VITRO STUDY; MATHEMATICAL COMPUTING; METHODOLOGY; RAT; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; THREE DIMENSIONAL IMAGING;

ALGORITHMS; ANIMALS; ARTIFICIAL INTELLIGENCE; DIFFUSION MAGNETIC RESONANCE IMAGING; HIPPOCAMPUS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; PATTERN RECOGNITION, AUTOMATED; RATS; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY;

EID: 35648986676     PISSN: 02780062     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMI.2007.903195     Document Type: Article

References (32)

1. P. Basser, J. Mattiello, and D. Lehihan, "Estimation of the effective self-diffusion tensor from the NMR spin echo.," J. Magn. Reson. B, vol. 103, pp. 247-254, 1994.
2. A. Terras, Harmonic Analysis on Symmetric Spaces and Applications. New York: Springer-Verlag, 1988, vol. II.
3. P. Fletcher and S. Joshi, "Principal geodesic analysis on symmetric spaces: Statistics of diffusion tensors.," Proc. CVAMIA, pp. 87-98, 2004.
4. Z. Wang and B. C. Vemuri, "An affine invariant tensor dissimilarity measure and its applications to tensor-valued image segmentation," in Proc. IEEE Comput. Soc. Int. Conf. Comput. Vision Pattern Recognit., 2004, vol. 1, pp. 228-233.
5. Z. Wang and B. C. Vemuri, "DTT segmentation using an information theoretic tensor dissimilarity measure," IEEE Trans. Med. Imag., vol. 24, no. 10, pp. 1267-1277, Oct. 2005.
6. C. Lenglet et al., "Statistics on multivariate normal distributions: A geometric approach and its application to diffusion tensor MRI," INRIA Res. Rep. 5242, 2004.
7. X. Pennec et al., "A Riemannian framework for tensor computing," Int. J. Comput. Vis., vol. 65, 2005.
8. R. San-Jose Estepar et al., "Riemannian mean curvature flow," in First International Symposium, ISVC 2005. New York: Springer-Verlag, 2005, vol. 3804, Lecture Notes in Computer Science, pp. 613-620.
9. D. Amaral and M. Witter, "Hippocampal formation," in The Rat Nervous System. New York: Academic, 1995, pp. 443-493.
10. L. Squire, C. Stark, and R. Clark, "The medial temporal lobe.," Annu. Rev. Neurosci., vol. 27, pp. 279-306, 2004.
11. T. M. Shepherd et al., "Structural insights from, high-resolution diffusion tensor imaging and tractography of the isolated rat hippocampus," NeuroImage, vol. 32, no. 4, pp. 1499-1509, 2006.
12. S. Pajevic et al., "A continuous tensor field approximation of discrete DT-MRI data for extracting microstructural and architectural features of tissue," J. Magn. Reson., vol. 154, no. 1, pp. 85-100, 2002.
13. A. H. Barr, B. Currin, S. Gabriel, and J. F. Hughes, "Smooth, interpolation of orientations with angular velocity constraints using quaternions," Proc. SIGGRAPH, pp. 313-320, 1992.
14. P. G. Batchelor et al., "A rigorous framework for diffusion tensor calculus," Magn. Reson. Med., vol. 53, pp. 221-225, 2005.
15. C. Lenglet et al., "DTI segmentation by statistical surface evolution," IEEE Trans. Med. Imag., vol. 25, no. 6, pp. 685-700, Jun. 2006.
16. V. Arsigny, P. Fillard, X. Pennec, and N. Ayache, "Fast and simple calculus on tensors in. the log-Euclidean framework," in Proceedings of MICCAI. New York: Springer, 2005, Lecture Notes in Computer Science, pp. 259-267.
17. J. Weickert and M. Welk, "Tensor field interpolation with PDEs," Preprint 142, Saarland Univ., 2005.
18. C.-F. Westin, M. Martin-Fernandez, C. Alberola-Lopez, J. Ruiz-Alzola, and H. Knutsson, "Tensor field regularization using normalized convolution and markov random, fields in a bayesian framework," in Visualization Image Processing of Tensor Fields, J. Weickert and H. Hagen, Eds. New York: Springer-Verlag, 2005.
19. D. C. Alexander, C. Pierpaoli, P. J. Basser, and J. C. Gee, "Spatial transformations of diffusion tensor magnetic resonance images," IEEE Trans. Med. Imag., vol. 20, no. 1.1, pp. 1131-1139, Nov. 2001.
20. L. Zhukov, K. Museth, D. Breen, B. A. H., andR. Whitaker, "Level set segmentation and modeling of DT-MRI human brain data," J. Electron. Imag., vol. 12, no. 1, pp. 125-133, 2003.
21. C. Feddern, J. Weickert, and B. Burgeth, "Level-set methods for tensorvalued images," in IEEE Workshop Variational, Geometric Level Set Methods Computer Vision, 2003, pp. 65-72.
22. S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces. Providence, RI: Amer. Math. Soc., 2001.
23. E. O. Stejskal and J. E. Tanner, "Spin diffusion measurements: Spin echoes in the presence of a time-dependent field gradient," J. Chem. Phys., vol. 42, pp. 288-292, 1965.
24. C. de Boor, "On calculating with b-splines," J. Approx. Theory, vol. 6, pp. 50-62, 1972.
25. Z. Wang, B. Vemuri, Y. Chen, and T. Mareei, "A constrained variational principle for direct estimation and smoothing of the diffusion tensor field from. DWL," Inf. Process. Med. Imag., pp. 660-671, 2003.
26. M. Rivera, O. Ocegueda, and J. L. Marroquí, "Entropy controlled Gauss-Markov random measure field models for early vision," VLSM, pp. 137-148, 2005.
27. J. L. Marroquí, F. A. Velasco, M. Rivera, and M. Nakamura, "Gauss-Markov measure field models for low-level vision," IEEE Trans. Pattern Anal. Mach. Intell., vol. 23, no. 4, pp. 337-348, Apr. 2001.
28. J. Zhang, "The mean field theory in EM procedure for Markov random fields," IEEE Trans. Signal Process., vol. 40, no. 10, pp. 2570-2583, Oct. 1992.
29. R. Neal and R. Barry, "A vew of the EM algorithm, that justifies incremental, sparse, and others variants," in Learning in Graphical Models. Dordrecht, The Netherlands: Kluwer, 1998, pp. 355-368.
30. O. Söderman and B. Jönsson, "Restricted diffusion in cylindrical geometry," J. Magn. Reson., vol. A, no. 117, pp. 94-97, 1995.
31. M. J. Black et al., "Robust anisotropic diffusion," IEEE Trans. Image Process., vol. 7, no. 3, pp. 421-432, Mar. 1998.
32. R. Insausti and D. Amaral, "Hippocampal formation," in The Human Nervous System. New York: Elsevier, 2004, pp. 871-914.