Coloring 3D Line fields using Boy's real projective plane immersion

IEEE Transactions on Visualization and Computer Graphics

Volumn 15, Issue 6, 2009, Pages 1457-1463

  Demiralp, Çaǧatay ^a   Hughes, John F ^a   Laidlaw, David H ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

colormapping; DTI; Line field; orientation; real projective plane; tensor field

Indexed keywords

COLORMAPPING; DTI; LINE FIELD; ORIENTATION; REAL PROJECTIVE PLANE; TENSOR FIELD;

THREE DIMENSIONAL;

TENSORS;

ARTICLE; BRAIN; COMPUTER GRAPHICS; DIFFUSION WEIGHTED IMAGING; HISTOLOGY; HUMAN; IMAGE PROCESSING; METHODOLOGY; NERVE FIBER; THREE DIMENSIONAL IMAGING;

BRAIN; COMPUTER GRAPHICS; DIFFUSION MAGNETIC RESONANCE IMAGING; HUMANS; IMAGE PROCESSING, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; NERVE FIBERS;

EID: 70350630743     PISSN: 10772626     EISSN: None     Source Type: Journal    
DOI: 10.1109/TVCG.2009.125     Document Type: Conference Paper

References (16)

1. B. Alpern, L. Carter, M. Grayson, and C. Pelkie. Orientation maps: techniques for visualizing rotations (a consumer's guide). In VIS '93: Proceedings of the 4th conference on Visualization '93, pages 183-188, 1993.
2. F. Apery. Models of the Real Projective Plane. Friedrich Vieweg & Sohn Verlag, 1987.
3. P. J. Basser, J. Mattiello, and D. LeBihan. Estimation of the effective self-diffusion tensor from the nmr spin echo. J Magn Reson B, 103(3):247-254, March 1994.
4. W. Boy. Über die Curvatura Integra und dieTopologie der Geschlossener Flachen. PhD thesis, Universität Göttingen, Göttingen, 1901.
5. R. L. Bryant. Surfaces in conformal geometry. In The mathematical heritage of Hermann Weyl (Durham, NC, 1987), volume 48 of Proc. Sympos. Pure Math., pages 227-240. Amer. Math. Soc., Providence, RI, 1988.
6. W. E. Byerly. An Elementary Treatise on Fourier's Series, and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics. Dover, New York, 1959
7. G. K. Francis. A Topological Picture Book. Springer, 2006.
8. R. Kusner. Conformal geometry and complete minimal surfaces. Bull. Amer. Math. Soc. (N.S.), 17(2):291-295, 1987
9. W. S. Massey. Algebraic Topology: An Introduction. Number 56 in Graduate Texts in Mathematics. Springer-Verlag, New York, NY, 1967.
10. V. Mineev. Topological objects in nematic liquid crystals. In Intuitive Combinatorial Topology. Springer, July 2001.
11. S. Mori and J. Zhang. Principles of diffusion tensor imaging and its applications to basic neuroscience research. Neuron, 51:527-539, 2006.
12. B. Morin. Équations du retournement de la sphère. C. R. Acad. Sci. Paris S é r. A-B, 287(13):A879-A882, 1978.
13. S. Pajevic and C. Pierpaoli. Color schemes to represent the orientation of anisotropic tissues from diffusion tensor data: Application to white matter fiber tract mapping in the human brain. MRM, 42:526-540, 1999.
14. C. Pierpaoli. Oh no! one more method for color mapping of fiber tract direction using diffusion mr imaging data. In Proceedings of 5th ISMRM, page 1741, 1997.
15. http://www.cs.brown.edu/̃cad/rp2coloring/.
16. B. Yamrom, J. A. Sutliff, and A. P. Woodfield. Visualizing polycrys-talline orientation microstructures with spherical color maps. In VIS '94: Proceedings of the conference on Visualization '94, pages 46-51, Los Alamitos, CA, USA, 1994. IEEE Computer Society Press.