On the differential geometry of 3D flow patterns: Generalized helicoids and diffusion MRI analysis

Proceedings of the IEEE International Conference on Computer Vision

Volumn , Issue , 2007, Pages

  Savadjiev, Peter ^a   Zucker, Steven W ^b   Siddiqi, Kaleem ^a  

^a MCGILL UNIVERSITY   (Canada)

^b Yale University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTER NETWORKS; COMPUTER VISION; FLOW PATTERNS; GEOMETRY; IMAGE PROCESSING; MEDICAL IMAGING; SEMICONDUCTOR DOPING; THREE DIMENSIONAL;

INTERNATIONAL CONFERENCES;

COMPUTATIONAL GEOMETRY;

EID: 50649110301     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICCV.2007.4409086     Document Type: Conference Paper

References (26)

1. J. M. Barbosa, M. Dajczer, and L. P. Jorge. Minimal ruled submanifolds in spaces of constant curvature. Indiana University Mathematics Journal, 33:531-547, 1984.
2. A. Barmpoutis, B. C. Vemuri, and J. R. Forder. Robust tensor splines for approximation of diffusion tensor MRI data. In MMBIA'06, pages 86-93, 17-18 June 2006.
3. P.-J. Basser, J. Matiello, and D. Le Bihan. MR diffusion tensor spectroscopy and imaging. Biophysical Journal, 66:259-267, 1994.
4. P. Batchelor, F. Calamante, J. Tournier, D. Atkinson, D. L. G. Hill, and A. Connelly. Quantification of the shape of fiber tracts. Magn. Res. in Medicine, 55:894-903, 2006.
5. O. Ben-Shahar and S. W. Zucker. The perceptual organization of texture flow: A contextual inference approach. IEEE Trans. Pattern Analysis and Machine Intelligence, 25:401-417, 2003.
6. F. Bertails, B. Audoly, M.-P. Cani, B. Querleux, F. Leroy, and J.-L. Lévêque. Super-helices for predicting the dynamics of natural hair. In ACM Transactions on Graphics (Proceedings of SIGGRAPH), August 2006.
7. D. E. Blair and J. R. Vanstone. A generalization of the helicoid. In Minimal Submanifolds and Geodesics, pages 13-16. Kaigai Publications, Tokyo, 1978.
8. I. Corouge, P. T. Fletcher, S. Joshi, S. Gouttard, and G. Gerig. Fiber tract-oriented statistics for quantitative diffusion tensor MRI analysis. Medical Image Analysis, 10(5):786-798, October 2006.
9. F. Dillen. Ruled submanifolds of finite type. Proc. of the American Mathematical Society, 114:795-798, 1992.
10. Z. Ding, J. C. Gore, and A. W. Anderson. Classification and quantification of neuronal fiber pathways using diffusion tensor MRI. Magn. Res. in Medicine, 49:716-721, 2003.
11. H. A. Hayden. On a generalized helix in a Riemannian n-space. Proc. London Math. Soc. 2, 32:337-345, 1930.
12. R. Hummel and S. W. Zucker. On the foundations of relaxation labeling processes. IEEE Trans. Pattern Analysis and Machine Intelligence, 5:267-287, 1983.
13. D. C. Knill. Contour into texture: Information content of surface contours and texture flow. J. Opt. Soc. Am. A, 18(1):12-35, 2001.
14. R. S. Laramee, D. Weiskopf, J. Schneider, and H. Hauser. Investigating swirl and tumble flow with a comparison of visualization techniques. In VIS '04: Proceedings of the conference on Visualization '04, pages 51-58, Washington, DC, USA, 2004. IEEE Computer Society.
15. C. Lenglet, M. Rousson, R. Deriche, and O. Faugeras. Statistics on the manifold of multivariate normal distributions: Theory and applications to diffusion tensor MRI processing. J. Mathematical Imaging and Vision, 25:423-444, 2006.
16. C. P. Lin, V. Wedeen, J. Chen, C. Yao, and W. Tseng. Validation of diffusion spectrum magnetic resonance axonal fiber imaging with manganese-enhanced optic tracts and ex-vivo phantoms. NeuroImage, 19:482-495, 2003.
17. S. Mori and P. C. M. van Zijl. Fiber tracking: principles and strategies - a technical review. NMR in Biomedicine, 15:468-480, 2002.
18. L. J. O'Donnell, M. Kubicki, M. E. Shenton, M. H. Dreusicke, W. E. L. Grimson, and C.-F. Westin. A method for clustering white matter fiber tracts. Am. J. Neuroradiol., 27:1032-1036, 2006.
19. B. O'Neill. Elementary Differential Geometry. Academic Press, 1966.
20. P. Parent and S. W. Zucker. Trace inference, curvature consistency, and curve detection. IEEE Trans. Pattern Analysis and Machine Intelligence, 11:823-839, 1989.
21. P. Savadjiev, J. S. W. Campbell, G. B. Pike, and K. Siddiqi. 3D curve inference for diffusion MRI regularization and fibre tractography. Medical Image Analysis, 10(5):799-813, October 2006.
22. m. Internal Report. Seminar of Higher Geometry, State University of Ghent, 1979.
23. C. Thas. A property of the Veronese surface. Journal of Geometry, 32:157-168, 1988.
24. D. Tuch. Q-ball imaging. Magn. Res. in Medicine, 52:1358-1372, 2004.
25. Z.Wang and B. C. Vemuri. DTI segmentation using an information theoretic tensor dissimilarity measure. IEEE Trans. Medical Imaging, 24:1267-1277, 2005.
26. S. Zhang, Ç. Demiralp, and D. Laidlaw. Visualizing diffusion tensor MR images using streamtubes and streamsurfaces. IEEE Trans. Visualization and Computer Graphics, 9:454-462, 2003.