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Spherical Parameterization of Marching Cubes IsoSurfaces Based upon Nearest Neighbor Coordinates

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Abstract

We present some new methods for parameterizing the triangle mesh surface (TMS) which result from the Marching Cubes (MC) algorithm. The methods apply to surfaces of genus zero and the parameter domain is a unit sphere. We take advantage of some special properties of the TMS resulting from the MC algorithm to obtain simple, computational efficient representations of the nearest neighbor coordinates and utilize these coordinates in the characterization of the parameterization by means of systems of equations which are solved iteratively. Examples and comparisons are presented.

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References

  1. Nielson G M, Zhang L, Lee K, Huang A. Parameterizing marching cubes isosurfaces with natural neighbor coordinates. Advances in Geometric Modeling and Processing, Chen FL, Jüttler B (eds.), Springer, 2008, pp.315–328.

  2. Hormann K, Greiner G. MIPS: An efficient global parameterization method. Curve and Surface Design: Saint-Malo. Laurent P J, Sablonniere P, Schumaker L L (eds.), Vanderbilt University Press, Nashville, 1999, pp.153–162.

    Google Scholar 

  3. Meyer D M, Alliez P. Intrinsic parameterizations of surface meshes. Eurographics, Computer Graphics Forum, 2002, 21(2): 209–218.

    Google Scholar 

  4. Haker S, Angenent S, Tannenbaum A, Kikinis R, Sapiro G. Conformal surface parameterization for texture mapping. Transactions on Visualization and Computer Graphics, 2000, 6(2): 181–189.

    Article  Google Scholar 

  5. Haker S, Angenent S, Tannenbaum A, Kikinis R. Nondistorting flattening for virtual colonoscopy. In Proc. MICCAI, Utrecht, The Netherlands, Springer, Oct. 14–17, 2001, pp.358–366.

  6. Pinkall U, Polthier K. Computing discrete minimal surfaces and their conjugates. Exp. Math., 1993, 2: 15–36.

    MATH  MathSciNet  Google Scholar 

  7. Floater M S. Parametrization and smooth approximation of surface triangulations. Computer Aided Geometric Design, 1997, 14(3): 231–250.

    Article  MATH  MathSciNet  Google Scholar 

  8. Wachpress E. A Rational Finite Element Basis. Academic Press, 1975.

  9. Floater M S. Mean value coordinates. Computer Aided Geometric Design, 2003, 20(1): 19–27.

    Article  MATH  MathSciNet  Google Scholar 

  10. Floater M S, Hormann K. Parameterization of Triangulations and Unorganized Points. Tutorial on Multiresolution in Geometric Modelling. Iske A, Quak E, Floater M S (eds.), Springer, 2002, pp.287–314.

  11. Meyer M, Barr A, Lee H, Desbrun M. Generalized barycentric coordinates or irregular polygons. Journal of Graphical Tools, 2002, 17: 13–22.

    Google Scholar 

  12. Floater M S, Hormann K. Surface Parameterization: A Tutorial and Survey. Advances in Multiresolution for Geometric Modelling, Dodgson N A, Floater M S, Sabin M A (eds.), Springer, 2006, pp.913–1943.

  13. Tutte W F. Convex representation of graphs. Proc. London Math. Soc., 1960, 10: 304–320.

    Article  MATH  MathSciNet  Google Scholar 

  14. Tutte W. How to draw a graph. Proc. London Math. Soc., 1963, 13: 743–768.

    Article  MATH  MathSciNet  Google Scholar 

  15. Nielson G M. MC*: Star functions for marching cubes. In Proc. Visualization’03, Seattle, USA, 2003, pp.59–66.

  16. Floater M S. Parametric tilings and scattered data approximation. Int. J. Shape Modeling, 1998, 4: 165–182.

    Article  Google Scholar 

  17. Nielson G M, Zhang L, Lee K. Lifting curve parameterization methods to isosurfaces. Computer Aided Geometric Design, 2004, 21: 751–766.

    Article  MATH  MathSciNet  Google Scholar 

  18. Gu X, Wang Y, Chan T F, Thompson P M, Yau S-T. Genus zero surface conformal mapping and its applications to brain surface mapping. IEEE Trans. Med. Imaging, 2004, 23(9): 949–958.

    Article  Google Scholar 

  19. Hong W, Gu X, Qiu F, Jin M, Kaufman A E. Conformal virtual colon flattening. In Proc. Symposium on Solid and Physical Modeling, Wales, UK, June 6–8, 2006, pp.85–93.

  20. Warfield S K, Kaus M, Jolesz F A, Kikinis R. Adaptive, template moderated, spatially varying statistical classification. Med Image Anal, 2000, 4(1): 43–55.

    Article  Google Scholar 

  21. Nielson G M, Graf G, Huang A, Phliepp M, Holmes R. Shrouds: Optimal separating surface for enumerated volumes. In Proc. VisSym’03, Grenoble, France, Eurographics Association, 2003, pp.75–84.

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Authors and Affiliations

  1. Arizona State University, Tempe, AZ, U.S.A.

    Gregory M. Nielson

  2. Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Li-Yan Zhang

  3. Handong Global University, Pohang, Kyungbuk, Korea

    Kun Lee

  4. National Central University, Taipei, Taiwan, China

    Adam Huang

Authors
  1. Gregory M. Nielson
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  2. Li-Yan Zhang
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  3. Kun Lee
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  4. Adam Huang
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Corresponding author

Correspondence to Gregory M. Nielson.

Additional information

This work is supported by the US Army Research Office under contract W911NF-05-1-0301 and the US National Science Foundation.

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Nielson, G.M., Zhang, LY., Lee, K. et al. Spherical Parameterization of Marching Cubes IsoSurfaces Based upon Nearest Neighbor Coordinates. J. Comput. Sci. Technol. 24, 30–38 (2009). https://doi.org/10.1007/s11390-009-9201-z

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  • DOI: https://doi.org/10.1007/s11390-009-9201-z

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