Boundary Filtering in Surface Reconstruction

  • Michal Varnuška
  • Ivana Kolingerová
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3044)


One of the methods for 3D data model acquisition is the real object digitization followed by the surface reconstruction. Many algorithms have been developed during past years, each of them with its own advantages and disadvantages. We use for the reconstruction a CRUST algorithm by Nina Amenta, which selects surface triangles from the Delaunay tetrahedronization using information from the dual Voronoi diagram. Unfortunately, these candidate surface triangles do not form a manifold, so it is necessary to perform some other steps for manifold extraction. In this paper we present some improvements and observations for this step.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Amenta, N., Bern, M., Eppstein, D.: The CRUST and b-skeleton: combinatorical surface reconstruction. Graph. Models and Image Processing, 125-135 (1998)Google Scholar
  2. 2.
    Dey, T.K., Kumar, P.: A simple provable algorithm for curve reconstruction. In: Proc. ACMSIAM Sympos. Discr. Algorithms, pp. 893–894 (1999)Google Scholar
  3. 3.
    Attali, D.: R-regular shape reconstruction from unorganized points. In: Proc. of 13th ACM Sympos. of Discr. Algorithms, pp. 248–253 (1997)Google Scholar
  4. 4.
    Mencl, R., Müller, H.: Interpolation and approximation of surfaces from three-dimensional scattered data points. In: Eurographics (1998)Google Scholar
  5. 5.
    Miller, J.V., Breen, D.E., Lorenzem, W.E., O’Bara, R.M., Wozny, M.J.: Geometrically deformed models: A Method for extracting closed geometric models from volume data. In: Proc. SIGGRAPH, pp. 217–226 (1991)Google Scholar
  6. 6.
    Muraki, S.: Volumetric shape description of range data using “Blobby model”. Comp. Graphics, 217–226 (1991)Google Scholar
  7. 7.
    Boissonat, J.D.: Geometric structures for three-dimensional shape representation. ACM Trans. Graphics 3, 266–286 (1984)CrossRefGoogle Scholar
  8. 8.
    Mencl, R.: A graph based approach to surface reconstruction. Comp. Graph. forum, EUROGRAPHICS 1995 14(3), 445–456 (1995)CrossRefGoogle Scholar
  9. 9.
    Mencl, R., Müller, H.: Graph based surface reconstruction using structures in scattered point sets. In: Proc. CGI, pp. 298–311 (1998)Google Scholar
  10. 10.
    Hoppe, H., DeRose, T., Duchamp, T., Halstead, M., Jin, H., McDonald, J., Schweitzer, J., Stuetzle, W.: Piecewise smooth surface reconstruction. In: SIGGRAPH 1994, pp. 295–302 (1994)Google Scholar
  11. 11.
    Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Surface reconstruction from unorganized points. Computer Graphics 26(2), 71–78 (1992)CrossRefGoogle Scholar
  12. 12.
    Curless, B., Levoy, M.: A volumetric method for building complex models from range images. In: SIGGRAPH, pp. 302–312 (1996)Google Scholar
  13. 13.
    Levoy, M.: The Digital Michelangelo project: 3D scanning of large statues. In: Proceedings of the 27th annual ACM conference on Comp. Graphics, pp. 131–144Google Scholar
  14. 14.
    Algorri, M.E., Schmitt, F.: Surface reconstruction from unstructured 3D data. Computer Graphic Forum, 47–60 (1996)Google Scholar
  15. 15.
    Edelsbrunner, H., Mücke, E.P.: Three-dimensional alpha shapes. ACM Trans. Graphics 13, 43–72 (1994)MATHCrossRefGoogle Scholar
  16. 16.
    Edelsbrunner, H.: Weighted alpha shapes. Technical report UIUCDCS-R92-1760, DCS University of Illinois at Urbana-Champaign, Urbana, Illinois (1992)Google Scholar
  17. 17.
    Bernardini, F., Bajaj, C.: A triangulation based. Sampling and reconstruction manifolds using a-shapes. In: 9th Canad. Conf. on Comput. Geometry, pp. 193–168 (1997)Google Scholar
  18. 18.
    Bernardini, F., Mittleman, J., Rushmeier, H., Silva, C., Taubin, G.: The ball pivoting algorithm for surface reconstruction. IEEE Trans. on Vis. and Comp. Graphics 5(4), 349–359 (1999)CrossRefGoogle Scholar
  19. 19.
    Amenta, N., Bern, M., Kamvysselis, M.: A new Voronoi-based surface reconstruction algorithm. In: SIGGRAPH, pp. 415–421 (1998)Google Scholar
  20. 20.
    Amenta, N., Bern, M.: Surface reconstruction by Voronoi filtering. Discr. and Comput. Geometry 22(4), 481–504 (1999)MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Amenta, N., Choi, S., Dey, T.K., Leekha, N.: A simple algorithm for homeomorphic surface reconstruction. In: 16th. Sympos. Comput. Geometry, pp. 213–222 (2000)Google Scholar
  22. 22.
    Dey, T.K., Giesen, J., Hudson, J.: Delaunay Based Shape Reconstruction from Large Data. In: Proc. IEEE Sympos. in Parallel and Large Data Visualization and Graphics, pp. 19–27 (2001)Google Scholar
  23. 23.
    Dey, T.K., Giesen, J., Leekha, N., Wenger, R.: Detecting boundaries for surface reconstruction using co-cones. Intl. J. Computer Graphics & CAD/CAM 16, 141–159 (2001)Google Scholar
  24. 24.
    Dey, T.K., Giesen, J.: Detecting undersampling in surface reconstruction. In: Proc. of 17th ACM Sympos. Comput. Geometry, pp. 257–263 (2001)Google Scholar
  25. 25.
    Amenta, Choi, S., Kolluri, R.: The Power Crust. In: Proc. of 6th ACM Sympos. on Solid Modeling (2001)Google Scholar
  26. 26.
    Dey, T.K., Goswami, S.: Tight Cocone: A water-tight surface reconstructor. In: Proc. 8th ACM Sympos. Solid Modeling application (2003), pp. 127–134 (2003), [27]Google Scholar
  27. 27.
    Varnuška, M., Kolingerová, I.: Improvements to surface reconstruction by CRUST algorithm. In SCCG 2003, Budmerice, Slovakia, pp. 101–109 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Michal Varnuška
    • 1
  • Ivana Kolingerová
    • 1
  1. 1.Centre of Computer Graphics and Data Visualization Department of Computer Science and EngineeringUniversity of West BohemiaPilsenCzech Republic

Personalised recommendations