Global curvature analysis and segmentation of volumetric data sets using trivariate B-spline functions

Proceedings - Geometric Modeling and Processing 2004

Volumn , Issue , 2004, Pages 217-226

  Soldea, Octavian ^a   Elber, Gershon ^a   Rivlin, Ehud ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

CURVATURE COMPUTATION; DATA SETS; GAUSSIAN CURVATURES; VOLUMETRIC IMAGES;

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; CONSTRAINT THEORY; DATA REDUCTION; FUNCTIONS; IMAGE SEGMENTATION; LASER APPLICATIONS; MAGNETIC RESONANCE IMAGING; SCANNING;

IMAGE ANALYSIS;

EID: 4544292584     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/GMAP.2004.1290043     Document Type: Conference Paper

References (23)

1. Gaussian Curvature of Volumetric Data Sets. http://www.cs.technion.ac.il/~octavian/gaussian_ curvature.vol.
2. E. Cohen, R. F. Riesenfeld, and G. Elber. Geometric Modeling with Splines: An Introduction. A. K. Peters, July 2001.
3. R. M. Corless. Essential Maple 7. An Introduction for Scientific Programmers, second edition. www.maplesoft.com, Spinger, ISBN: 0-387-95352-3, 2002.
4. G. Dahlquist and Å. Björck. Numerical Methods. Prentice-Hall, Englewood Cliffs, New Jersey, 1974.
5. G. Elber. Irit Version 9.0. http://www.cs.technion.ac.il/~irit.
6. G. Elber and M.-S. Kim. Geometric Constraint Solver Using Multivariate Spline Functions. Proceedings of the Sixth ACM Symposium on Solid Modeling and Computer Graphics, pp. 171-175, October 11-12 2001.
7. G. Farin. Curves and Surfaces for Computer Aided Geometric Design, A Practical Guide. Fourth Edition, Academic Press, 1996.
8. Gene H. Golub and Charles F. Van Loan. Matrix Computations. Third Edition, The Johns Hopkins University Press, pp. 180-181, 1996.
9. B. Hamann, Visualization and Modeling Contours of Trivariate Functions, PhD Thesis. Arizona State University, 1991.
10. Jiří Hladuvka, Andreas König, and Eduard Gröllet. Curvature-Based Transfer Functions for Direct Volume Rendering. Proceedings of Spring Conference on Computer Graphics and its Applications, SCCG 2000, pp. 58-65, 2000.
11. A. Hoover, G. Jean-Baptiste, X. Jiang, P. J. Flynn, H. Bumke, D. B. Goldgof, K. Bowyer, D. W. Eggert, A. Fitzgibbon, and R. B. Fischer. An Experimental Comparison of Range Image Segmentation Algorithms. IEEE Transactions on Pattern Analysis and Machine Intelligence. Volume 18, Number 7, pp. 673-689, July 1996.
12. Roger A. Horn and Charles R. Johnson. Matrix Analysis. Cambridge University Press, pp. 336, 338-339, 1985.
13. V. Interrante. Illustrating Surface Shape in Volume Data via Principal Direction-Driven 3D Line Integral Convolution. Computer Graphics (Proceedings of SIGGRAPH 97), pp. 109-116, 1997.
14. A. Kaufman. Volume Visualization (Tutorial). IEEE Computer Society Press, Los Alamitos, CA., 1991.
15. Gordon Kindlmann, Ross Whitaker, Tolga Tasdizen, and Torsten Möller. Curvature-Based Transfer Functions for Direct Volume Rendering: Methods and Applications. IEEE Visualization, accepted for publication, October 2003.
16. S. Lakare, M. Wan, M. Sato, and A. Kaufman. 3D Digital Cleansing Using Segmentation Rays. IEEE Visualization Annual Conference, pp. 37-44, 2000.
17. Charles F. Van Loan. The Ubiquitous Kronecker Product, to appear in Journal of Computational and Applied Mathematics, 2003.
18. W. E. Lorensen and H. E. Cline. Marching cubes: A high resolution 3D surface construction algorithm. Computer Graphics (Proceedings of SIGGRAPH 87), Volume 21, Number 4, pp. 163-169, July 1987.
19. J.-P. Thirion and A. Gourdon. The 3D Marching Lines Algorithm and its Application to Crest Lines Extraction. Rapports de Recherche, No. 1672, Programme 4, Robotique, Image et Vision, Unité de Recherche Inria-Rocquencourt, Inria, May 1992.
20. J.-P. Thirion and A. Gourdon. Intrinsic surface properties from surface triangulation. Differential Characteristics of Isointensity Surfaces. Computer Vision and Image Understanding, Volume 61, Number 2, pp. 190-202, March 1995.
21. Visualization Toolkit, http://www.vtk.org.
22. Volume Visualization, http://www.volvis.org.
23. T. Weinkauf and H. Theisel. Curvature Measures of 3D Vector Fields and Their Applications. V. Skala (editor): Journal of WSCG'2002, International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, Plzen, Czech Republic, Number 10, pp. 507-514, February 2002.