Adaptively Adjusting Marching Cubes Output to Fit A Trilinear Reconstruction Filter

  • Fabio Allamandri
  • Paolo Cignoni
  • Claudio Montani
  • Roberto Scopigno
Part of the Eurographics book series (EUROGRAPH)


The paper focuses on the improvement of the quality of isosurfaces fitted on volume datasets with respect to standard MC solutions. The new solution presented improves the precision in the reconstruction process using an approach based on mesh refinement and driven by the evaluation of the trilinear reconstruction filter. The iso-surface reconstruction process is adaptive, to ensure that the complexity of the fitted mesh will not become excessive. The proposed approach has been tested on many datasets; we discuss the precision of the obtained meshs and report data on fitted meshes complexity and processing times.


Splitting Point Reconstruction Filter Volume Dataset Interpolation Filter Marching Cube 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. L. Bajaj, V. Pascucci, D. R. Schikore. Fast isocontouring for improved interactivity. In 1996 IEEE Volume Visualization Symp., pages 39–46.Google Scholar
  2. 2.
    P. Cignoni, P. Marino, C. Montani, E. Puppo, R. Scopigno. Speeding up isosurface extraction using interval trees. IEEE Trans, on Visualization and Comp. Graph., 3 (2): 158–170, 1997.CrossRefGoogle Scholar
  3. 3.
    P. Cignoni, C. Rocchini, R. Scopigno. Metro: measuring error on simplified surfaces. Technical Report B4-01-01-96, I.E.I. - C.N.R., Pisa, Italy, January 1996.Google Scholar
  4. 4.
    M. J. Dürst. Letters: Additional reference to “Marching Cubes. ACM Computer Graphics, 22 (4): 72–73, 1988.Google Scholar
  5. 5.
    T. Fruhauf. Ray casting opaque isosurfaces in nonregularly gridded CFD data. In P.Zanarini R. Scateni, J. J. van Wijk, editor, Visualization in Scientific Computing, pages 45–57. Springer, Wien, 1995.Google Scholar
  6. 6.
    Mark Hall and Joe Warren. Adaptive polygonalization of implicitly defined surfaces. IEEE CGA, 10 (11): 33–42, 1990.Google Scholar
  7. 7.
    B. Hamann, I. J. Trotts, G. E. Farin. On approximating contours of the piece- wise trilinear interpolant using triangular rational-quadratic Bézier patches. IEEE ToVCG, 3 (3): 215–227, 1997.Google Scholar
  8. 8.
    L. Hong, S. Muraki, A. Kaufman, D. Bartz, T. He. Virtual voyage: Interactive navigation in the human colon. In SIGGRAPH 97 Conference Proceedings, pages 27–34.Google Scholar
  9. 9.
    L. Kobbelt. Discrete fairing. In Proceedings of the Seventh IMA Conference on the Mathematics of Surfaces, pages 101–131, 1997.Google Scholar
  10. 10.
    Y. Livnat, H. V. Shen, C. R. Johnson. A near optimal isosurface extraction algorithm for structured and unstructured grids. IEEE Trans, on Vis. and Comp. Graph., 2 (1): 73–84, 1996.CrossRefGoogle Scholar
  11. 11.
    W. E. Lorensen, H. E. Cline. Marching cubes: A high resolution 3D surface construction algorithm. In Computer Graphics (SIGGRAPH ‘87 Proceedings), 21(4):163–170, 1987.CrossRefGoogle Scholar
  12. 12.
    S. Marschner, R. Lobb. An evaluation of reconstruction filters for volume rendering. In IEEE Visualization ‘94, pages 100–107, 1994.CrossRefGoogle Scholar
  13. 13.
    T. Möller, R. Machiraju, K. Mueller, R. Yagel. Classification and local error estimation of interpolation and derivative filters for volume rendering. In Proceedings 1996 Symp. on Volume Visualization (Oct. 28–29), pages 71–78, 1996.CrossRefGoogle Scholar
  14. 14.
    T. Möller, R. Machiraju, K. Mueller, R. Yagel. A comparison of normal estimation schemes. In IEEE Visualization ‘97, 1997.Google Scholar
  15. 15.
    C. Montani, R. Scateni, R. Scopigno. A modified look-up table for implicit disambiguation of Marching Cubes. The Visual Computer, 10 (6): 353–355, 1994.CrossRefGoogle Scholar
  16. 16.
    B. K. Natarajan. On generating topologically consistent isosurfaces from uniform samples. Visual Computer, 11 (1): 52–62, 1994.CrossRefGoogle Scholar
  17. 17.
    Peter J. Neugebauer, Konrad Klein. Adaptive triangulation of objects reconstructed from multiple range images. In IEEE Visualization ‘97 - Late-Breaking Hot Topics Session, October 1997.Google Scholar
  18. 18.
    G. M. Nielson, B. Hamann. The asymptotic decider: removing the ambiguity in marching cubes. In Visualization ‘91, pages 83–91, 1991.CrossRefGoogle Scholar
  19. 19.
    A. Puig, D. Tost, I. Navazo. Interactive cerebral blood vessels exploration system. In IEEE Visualization ‘97, October 1997.Google Scholar
  20. 20.
    L. A. Sadarjoen, F. H. Post. Deformable surface techniques for field visualization. Computer Graphics Forum, 16 (3): 109–116, 1997.CrossRefGoogle Scholar
  21. 21.
    L. Velho. Simple and efficient polygonalization of implicit surfaces. Journal of Graphics Tools, 1 (2): 5–24, 1996.Google Scholar
  22. 22.
    J. Wilhelms, A. van Gelder. Topological considerations in isosurface generation. ACM Computer Graphics, 24 (5): 79–86, Nov 1990.CrossRefGoogle Scholar
  23. 23.
    Jane Wilhelms, Allen van Gelder. Octrees for faster isosurface generation. ACM ToG, 11 (3): 201–227, July 1992.MATHGoogle Scholar

Copyright information

© Springer-Verlag/Wien 1998

Authors and Affiliations

  • Fabio Allamandri
    • 1
  • Paolo Cignoni
    • 1
  • Claudio Montani
    • 1
  • Roberto Scopigno
    • 1
  1. 1.Istituto di Elaborazione dell’Informazione Consiglio Nazionale delle RicerchePisaItaly

Personalised recommendations