The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.05 - May (2011 vol.17)
pp: 612-625
Markus van Almsick , Eindhoven University of Technology, Eindhoven
Tim H.J.M. Peeters , Eindhoven University of Technology, Eindhoven
Vesna Prčkovska , Eindhoven University of Technology, Eindhoven
Anna Vilanova , Eindhoven University of Technology, Eindhoven
Bart ter Haar Romeny , Eindhoven University of Technology, Eindhoven
ABSTRACT
Any sufficiently smooth, positive, real-valued function \psi : S^2 \rightarrow {\hbox{\rlap{I}\kern 2.0pt{\hbox{R}}}}^+ on a sphere S^2 can be expanded by a Laplace expansion into a sum of spherical harmonics. Given the Laplace expansion coefficients, we provide a CPU and GPU-based algorithm that renders the radial graph of \psi in a fast and efficient way by ray-casting the glyph of \psi in the fragment shader of a GPU. The proposed rendering algorithm has proven highly useful in the visualization of high angular resolution diffusion imaging (HARDI) data. Our implementation of the rendering algorithm can display simultaneously thousands of glyphs depicting the local diffusivity of water. The rendering is fast enough to allow for interactive manipulation of large HARDI data sets.
INDEX TERMS
Computer graphics, viewing algorithms, three-dimensional graphics and realism, computer applications, life and medical sciences.
CITATION
Markus van Almsick, Tim H.J.M. Peeters, Vesna Prčkovska, Anna Vilanova, Bart ter Haar Romeny, "GPU-Based Ray-Casting of Spherical Functions Applied to High Angular Resolution Diffusion Imaging", IEEE Transactions on Visualization & Computer Graphics, vol.17, no. 5, pp. 612-625, May 2011, doi:10.1109/TVCG.2010.61
REFERENCES
[1] P.J. Basser, J. Mattiello, and D. Lebihan, “MR Diffusion Tensor Spectroscopy and Imaging,” Biophysical J., vol. 66, no. 1, pp. 259-267, Jan. 1994.
[2] H.C. Torrey, “Bloch Equations with Diffusion Terms,” Physical Rev., vol. 194, pp. 563-565, 1956.
[3] D.S. Tuch, “Diffusion MRI of Complex Tissue Structure,” PhD dissertation, Harvard Univ., 2002.
[4] L.R. Frank, “Anisotropy in High Angular Resolution Diffusion-Weighted MRI,” Magnetic Resonance in Medicine, vol. 45, no. 6, pp. 935-939, 2001.
[5] D. Tuch, “Q-Ball Imaging,” Magnetic Resonance in Medicine, vol. 52, pp. 1358-1372, 2004.
[6] E. Özarslan, T.M. Shepherd, B.C. Vemuri, S.J. Blackband, and T.H. Mareci, “Resolution of Complex Tissue Microarchitecture Using the Diffusion Orientation Transform (DOT),” NeuroImage, vol. 36, no. 3, pp. 1086-1103, July 2006.
[7] E. Özarslan and T.H. Mareci, “Generalized Diffusion Tensor Imaging and Analytical Relationships between Diffusion Tensor Imaging and High Angular Resolution Diffusion Imaging,” Magnetic Resonance in Medicine, vol. 50, no. 5, pp. 955-965, 2003.
[8] R. Deriche and M. Descoteaux, “Splitting Tracking through Crossing Fibers: Multidirectional Q-Ball Tracking,” Proc. Fourth IEEE Int'l Symp. Biomedical Imaging: From Nano to Macro (ISBI), pp. 756-759, 2007.
[9] M. Perrin, C. Poupon, Y. Cointepas, B. Rieul, N. Golestani, D. Rivière, A. Constantinesco, D.L. Bihan, and J.-F. Mangin, “Fiber Tracking in Q-Ball Fields Using Regularized Particle Trajectories,” Proc. 19th Int'l Conf. Information Processing in Medical Imaging, vol. 19, pp. 52-63, 2005.
[10] S. Jbabdi, M.W. Woolrich, J.L.R. Andersson, and T.E.J. Behrens, “A Bayesian Framework for Global Tractography,” NeuroImage, vol. 37, no. 1, pp. 116-129, Aug. 2007.
[11] G. Kindlmann, “Visualization and Analysis of Diffusion Tensor Fields,” PhD dissertation, School of Computing, Univ. of Utah, Sept. 2004.
[12] G. Kindlmann and C.-F. Westin, “Diffusion Tensor Visualization with Glyph Packing,” IEEE Trans. Visualization and Computer Graphics, vol. 12, no. 5, pp. 1329-1336, Sept.-Oct. 2006.
[13] M. Hlawitschka, G. Scheuermann, and B. Hamann, “Interactive Glyph Placement for Tensor Fields,” Advances in Visual Computing, pp. 331-340, Springer, 2007.
[14] N.A. for Medical Image Computing. Slicer. http://www.na-mic. org/Wiki/index.phpSlicer , 2009.
[15] I.P.O. 2004, “QBall Plug-In for Slicer3D,” http://www-sop.inria. fr/odyssee/en/software QBallSlicer, 2009.
[16] U.C.L.C.S. Department, “Camino,” http://www.cs.ucl.ac.uk/ research/medic camino/, 2009.
[17] D.W. Shattuck, M.-C. Chiang, M. Barysheva, K.L. McMahon, G.I. de Zubicaray, M. Meredith, M.J. Wright, A.W. Toga, and P.M. Thompson, “Visualization Tools for High Angular Resolution Diffusion Imaging,” Proc. Medical Image Computing and Computer-Assisted Intervention (MICCAI '08), pp. 298-305, 2008.
[18] T. Schultz, HARDI Glyph Rendering, Max-Planck-Institut für Informatik, Saarbrücken, personal comm., June 2009.
[19] M. Hlawitschka, G. Scheuermann, A. Anwander, T. Knösche, M. Tittgemeyer, and B. Hamann, “Tensor Lines in Tensor Fields of Arbitrary Order,” Proc. Third Int'l Symp. Visual Computing (ISVC), vol. 1, pp. 341-350, 2007.
[20] S. Gumhold, “Splatting Illuminated Ellipsoids with Depth Correction,” Proc. Vision, Modelling, and Visualization, pp. 245-252, 2003.
[21] C. Sigg, T. Weyrich, M. Botsch, and M. Gross, “GPU-Based Ray-Casting of Quadratic Surfaces,” Proc. Eurographics Symp. Point-Based Graphics, pp. 59-65, 2006.
[22] S.E. Mario Hlawitschka and G. Scheuermann, “Fast and Memory Efficient GPU-Based Rendering of Tensor Data,” Proc. IADIS Int'l Conf. Computer Graphics and Visualization '08, pp. 28-30, 2008.
[23] G. Kindlmann, “Superquadric Tensor Glyphs,” Proc. Joint Eurographics/IEEE TCVG Symp. Visualization, O. Deussen, C. Hansen, D. Keim, and D. Saupe, eds., pp. 147-154, 2004.
[24] T. Peeters, V. Prčkovska, M. van Almsick, A. Vilanova, and B. ter Haar Romeny, “Fast and Sleek Glyph Rendering for Interactive Hardi Data Exploration,” Proc. IEEE Pacific Visualization Symp., pp. 153-160, 2009.
[25] W. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes, third ed., Cambridge Univ. Press, 2007.
[26] D.A. Varshalovich, A.N. Moskalev, and V.K. Khersonskii, Quantum Theory of Angular Momentum. World Scientific Publishing Co., 1988.
[27] M. Descoteaux, E. Angelino, S. Fitzgibbons, and R. Deriche, “Regularized, Fast and Robust Analytical Q-Ball Imaging,” Magnetic Resonance in Medicine, vol. 58, pp. 497-510, 2007.
[28] O. Söderman and B. Jönsson, “Restricted Diffusion in Cylindrical Geometry,” J. Magnetic Resonance, Series A, vol. 117, no. 1, pp. 94-97, 1995.
28 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool