This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Anisotropic Noise Samples
March/April 2008 (vol. 14 no. 2)
pp. 342-354
ASCII Text
x 
 
Louis Feng, Ingrid Hotz, Bernd Hamann, Kenneth Joy, "Anisotropic Noise Samples," IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 2, pp. 342-354, March/April, 2008.
 
 
BibTex
x
 
@article{ 10.1109/TVCG.2007.70434,
author = {Louis Feng and Ingrid Hotz and Bernd Hamann and Kenneth Joy},
title = {Anisotropic Noise Samples},
journal ={IEEE Transactions on Visualization and Computer Graphics},
volume = {14},
number = {2},
issn = {1077-2626},
year = {2008},
pages = {342-354},
doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2007.70434},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Visualization and Computer Graphics
TI - Anisotropic Noise Samples
IS - 2
SN - 1077-2626
SP342
EP354
EPD - 342-354
A1 - Louis Feng,
A1 - Ingrid Hotz,
A1 - Bernd Hamann,
A1 - Kenneth Joy,
PY - 2008
KW - Flow visualization
KW - Computer Graphics
KW - Picture/Image Generation
KW - Sampling
KW - Relaxation
VL - 14
JA - IEEE Transactions on Visualization and Computer Graphics
ER -
 
We present a practical approach to generate stochastic anisotropic samples with Poisson-disk characteristic over a two-dimensional domain. In contrast to isotropic samples, we understand anisotropic samples as non-overlapping ellipses whose size and density match a given anisotropic metric. Anisotropic noise samples are useful for many visualization and graphics applications. The spot samples can be used as input for texture generation, e.g., line integral convolution (LIC), but can also be used directly for visualization. The definition of the spot samples using a metric tensor makes them especially suitable for the visualization of tensor fields that can be translated into a metric. Our work combines ideas from sampling theory and mesh generation. To generate these samples with the desired properties we construct a first set of non-overlapping ellipses whose distribution closely matches the underlying metric. This set of samples is used as input for a generalized anisotropic Lloyd relaxation to distribute noise samples more evenly. Instead of computing the Voronoi tessellation explicitly, we introduce a discrete approach which combines the Voronoi cell and centroid computation in one step. Our method supports automatic packing of the elliptical samples, resulting in textures similar to those generated by anisotropic reaction-diffusion methods. We use Fourier analysis tools for quality measurement of uniformly distributed samples.

[1] V. Ostromoukhov, “A Simple and Efficient Error-Diffusion Algorithm,” Proc. ACM SIGGRAPH '01, pp. 567-572, 2001.
[2] D.E. Knuth, “Digital Halftones by Dot Diffusion,” ACM Trans. Graphics, vol. 6, no. 4, pp. 245-273, 1987.
[3] R. Ulichney, Digital Halftoning. MIT Press, 1987.
[4] L. Velho and J. de Miranda Gomes, “Digital Halftoning with Space Filling Curves,” Proc. ACM SIGGRAPH '91, pp. 81-90, 1991.
[5] P. Alliez, É. Colin de Verdière, O. Devillers, and M. Isenburg, “Isotropic Surface Remeshing,” Proc. Int'l Conf. Shape Modeling and Applications (SMI '03), p. 49, 2003.
[6] Q. Du and D. Wang, “Anisotropic Centroidal Voronoi Tessellations and Their Applications,” SIAM J. Scientific Computing, vol. 26, no. 3, pp. 737-761, 2005.
[7] F. Labelle and J.R. Shewchuk, “Anisotropic Voronoi Diagrams and Guaranteed-Quality Anisotropic Mesh Generation,” Proc. 19th Ann. Symp. Computational Geometry (SCG '03), pp. 191-200, 2003.
[8] K. Shimada, A. Yamada, and T. Itoh, “Anisotropic Triangulation of Parametric Surfaces via Close Packing of Ellipsoids,” Int'l J.Computational Geometry Applications, vol. 10, no. 4, pp. 417-440, 2000.
[9] V. Ostromoukhov, C. Donohue, and P.-M. Jodoin, “Fast Hierarchical Importance Sampling with Blue Noise Properties,” ACM Trans. Graphics, vol. 23, no. 3, pp. 488-495, 2004.
[10] D.P. Mitchell, “Spectrally Optimal Sampling for Distribution Ray Tracing,” Proc. ACM SIGGRAPH '91, pp. 157-164, 1991.
[11] B. Cabral and L. Leedom, “Imaging Vector Fields Using Line Integral Convolution,” Proc. ACM SIGGRAPH '93, vol. 27, pp. 263-272, Aug. 1993.
[12] M.-H. Kiu and D.C. Banks, “Multi-Frequency Noise for LIC,” Proc. Seventh IEEE Conf. Visualization (VIS '96), pp. 121-126, 1996.
[13] A.J.S. Hin and F.H. Post, “Visualization of Turbulent Flow with Particles,” Proc. Fourth IEEE Conf. Visualization (VIS '93), pp. 46-53, 1993.
[14] R.M. Kirby, H. Marmanis, and D.H. Laidlaw, “Visualizing Multivalued Data from 2D Incompressible Flows Using Concepts from Painting,” Proc. 10th IEEE Conf. Visualization (VIS '99), pp.333-340, citeseer.ist.psu.edukirby99visualizing.html , 1999.
[15] G. Kindlmann, D. Weinstein, and D. Hart, “Strategies for Direct Volume Rendering of Diffusion Tensor Fields,” IEEE Trans. Visualization and Computer Graphics, vol. 6, no. 2, pp. 124-138, , Apr.-June 2000.
[16] 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.
[17] I. Hotz, L. Feng, H. Hagen, B. Hamann, B. Jeremic, and K.I. Joy, “Physically Based Methods for Tensor Field Visualization,” Proc. 15th IEEE Conf. Visualization (VIS '04), pp. 123-130, Oct. 2004.
[18] A.S. Glassner, “Principles of Digital Image Synthesis,” Morgan Kaufmann Series in Computer Graphics and Geometric Modeling, vol. 2, Morgan Kaufmann, 1995.
[19] R.L. Cook, “Stochastic Sampling in Computer Graphics,” ACM Trans. Graphics, vol. 5, no. 1, pp. 51-72, 1986.
[20] S.P. Lloyd, “Least Square Quantization in PCM,” IEEE Trans. Information Theory, vol. 28, no. 2, pp. 129-137, Mar. 1982.
[21] Q. Du, V. Faber, and M. Gunzburger, “Centroidal Voronoi Tessellations: Applications and Algorithms,” SIAM Rev., vol. 41, no. 4, pp. 637-676, 1999.
[22] S. Hiller, H. Hellwig, and O. Deussen, “Beyond Stippling— Methods for Distributing Objects on the Plane,” Computer Graphics Forum, vol. 22, no. 3, pp. 515-522, 2003.
[23] A. Hausner, “Simulating Decorative Mosaics,” Proc. ACM SIGGRAPH '01, pp. 573-578, citeseer.ist.psu.edu/kindlmann00strategies.htmlhttp:/ /citeseer.ist.psu.eduhausner 01simulating.html , 2001.
[24] L.-P. Fritzsche, H. Hellwig, S. Hiller, and O. Deussen, “Interactive Design of Authentic Looking Mosaics Using Voronoi Structures,” Proc. Second Int'l Symp. Voronoi Diagrams in Science and Eng. (VD'05), http://citeseer.ist.psu.edu744345.html, 2005.
[25] K.E. Hoff, J. Keyser, M. Lin, D. Manocha, and T. Culver, “Fast Computation of Generalized Voronoi Diagrams Using Graphics Hardware,” Proc. ACM SIGGRAPH '99, vol. 33, pp. 277-286, , 1999.
[26] D.H. Laidlaw, E.T. Ahrens, D. Kremers, M.J. Avalos, R.E. Jacobs, and C. Readhead, “Visualizing Diffusion Tensor Images of the Mouse Spinal Cord,” Proc. Ninth IEEE Conf. Visualization (VIS '98), pp. 127-134, , Oct. 1998.
[27] G. Turk and D. Banks, “Image-Guided Streamline Placement,” Proc. ACM SIGGRAPH '96, vol. 30, pp. 453-460, citeseer.ist.psu.edu/hoff99fast.htmlhttp:/ /visinfo.zib.de/EVlib/Show?EVL-1998-331citeseer.csail.mit. edu turk96imageguided.html , 1996.
[28] A.R. Sanderson, C.R. Johnson, and R.M. Kirby, “Display of Vector Fields Using a Reaction-Diffusion Model,” Proc. 15th IEEE Conf. Visualization (VIS '04), pp. 115-122, 2004.
[29] E.N. Gilbert, “Gray Codes and Paths on the N-Cube,” Bell System Technical J., vol. 37, no. 3, pp. 815-826, 1958.
[30] G. Kindlmann, “Superquadric Tensor Glyphs,” Proc. IEEE TCVG/EG Symp. Visualization, pp. 147-154, May 2004.

Index Terms:
Flow visualization, Computer Graphics, Picture/Image Generation, Sampling, Relaxation
Citation:
Louis Feng, Ingrid Hotz, Bernd Hamann, Kenneth Joy, "Anisotropic Noise Samples," IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 2, pp. 342-354, March-April 2008, doi:10.1109/TVCG.2007.70434
Usage of this product signifies your acceptance of the Terms of Use.