Advertisement

Surface reconstruction by layer peeling

Abstract

Given an input point cloud P in ℜ3, this paper proposes a novel algorithm to identify surface neighbors of each point pP respecting the underlying surface S and then to construct a piecewise linear surface for P. The algorithm utilizes the simple k-nearest neighborhood in constructing local surfaces. It makes use of two concepts: a local convexity criterion to extract a set of surface neighbors for each point, and a global projection test to determine an order for the reconstruction. Our algorithm not only produces a topologically correct surface for well-sampled point sets, but also adapts well to handle under-sampled point sets. Furthermore, the computational cost of the algorithm increases almost linearly in the size of the point cloud. It, thus, scales well to deal with large input point sets.

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 199

This is the net price. Taxes to be calculated in checkout.

References

  1. 1.

    Alexa, M., Adamsom, A.: On normals and projection operators for surfaces defined by point sets. In: Proceedings of 1st Symposium on Point Based Graphics, pp. 150–155 (2004)

  2. 2.

    Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., Silva, C.T.: Point set surfaces. In: Proceedings of IEEE Visualization, pp. 21–28 (2001)

  3. 3.

    Amenta, N., Bern, M.: Surface reconstruction by Voronoi filtering. In: Proceedings of 14th Annual Symposium on Computational Geometry, pp. 39–48 (1998)

  4. 4.

    Amenta, N., Choi, S., Dey, T.K., Leekha, N.: A simple algorithm for homeomorphic surface reconstruction. In: Proceedings of 16th Anuual Symposium on Computational Geometry, pp. 213–222 (2000)

  5. 5.

    Amenta, N., Choi, S., Kolluri, R.: The power crust. In: Proceedings of 6th ACM Symposium on Solid Modelling, pp. 249–260 (2001)

  6. 6.

    Amenta, N., Kil, Y.J.: Point-set surfaces. In: Proceedings of ACM SIGGRAPH, pp. 264–270 (2004)

  7. 7.

    Andersson, M., Giesen, J., Pauly, M., Speckmann, B.: Bounds on the k-nearest neighborhood for locally uniformly sampled surfaces. In: Proceedings of 1st Symposium on Point Based Graphics, pp. 167–171 (2004)

  8. 8.

    Arya, S., Mount, D.M., Natanyahu, N.S., Silverman, R., Wu, A.Y.: An optimal algorithm for approximate nearest searching in fixed dimension. J. ACM 45(6), 891–923 (1998)

  9. 9.

    Attali, D., Boissonnat, J.: A linear bound on the complexity of the Delaunay triangulation of points on polyhedral surfaces. In: Proceedings of 14th Annual Symposium on Computational Geometry, pp. 39–48 (1998)

  10. 10.

    Bern, M., Edelsbrunner, H., Eppstein, D., Mitchell, S., Tan, T.S.: Edge insertion for optimal triangulations. Discr. Comput. Geom. 10(1), 47–65 (1993)

  11. 11.

    Bernardini, F., Mittleman, J., Rushmeier, H., Silva, C., Taubin, G.: The ball-pivoting algorithm for surface reconstruction. IEEE Trans. Visual. Comput. Graph. 5(4), 349–359 (1999)

  12. 12.

    Carr, J.C., Beatson, R.K., Cherrie, J.B., Mitchell, T.J., Fright, W.R., McCallum, B.C., Evans, T.R.: Reconstruction and representation of 3D objects with radial basis functions. In: Proceedings of ACM SIGGRAPH, pp. 67–76 (2001)

  13. 13.

    Cheng, S.W., Dey, T.K., Edelsbrunner, H., Facello, M.A., Teng, S.H.: Sliver exudation. In: Proceedings of 15th Annual Symposium of Computational Geometry, pp. 1–13 (1999)

  14. 14.

    Dey, T.K., Giesen, J.: Detecting undersampling in surface reconstruction. In: Proceedings of 17th Annual Symposium of Computational Geometry, pp. 257–263 (2001)

  15. 15.

    Dey, T.K., Giesen, J., Goswami, S., Zhao, W.: Shape dimension and approximation from samples. Discr. Comput. Geom. 29, 419–434 (2003)

  16. 16.

    Dey, T.K., Goswami, S.: Tight cocone: A water-tight surface reconstructor. J. Comput. Inf. Sci. Engin. 3, 302–307 (2003)

  17. 17.

    Dey, T.K., Goswami, S.: Provable surface reconstruction from noisy samples. In: Proceedings of 20th Annual Symposium of Computational Geometry, pp. 330–339 (2004)

  18. 18.

    Funke, S., Ramos, E.A.: Smooth-surface reconstruction in near-linear time. In: Proceedings of Symposium on Discrete Algorithms, pp. 781–790 (2002)

  19. 19.

    Giesen, J., Wagner, U.: Shape dimension and intrinsic metric from samples of manifolds with high co-dimension. In: Proceedings of 19th Annual Symposium on Computational Geometry, pp. 329–337 (2003)

  20. 20.

    Gopi, M., Krishnan, S., Silva, C.T.: Surface reconstruction based on lower dimensional localized Delaunay triangulation. Comput. Graph. Forum (Eurographics) 19(3), C467–C478 (2000)

  21. 21.

    Hoppe, H., DeRose, T., Duchamp, T.: Surface reconstruction from unorganized points. In: Proceedings of ACM SIGGRAPH, pp. 71–78 (1992)

  22. 22.

    Levin, D.: Mesh-independent surface interpolation. In: Geometric Modelling for Scientific Visualization, pp. 37–49 (2003)

  23. 23.

    Linsen, L., Prautzsch, H.: Fan clouds – an alternative to meshes. In: Proceedings of Dagstuhl Seminar 02151 on Theoretical Foundations of Computer Vision – Geometry, Morphology and Computational Imaging (2003)

  24. 24.

    Mederos, B., Velho, L., de Figueiredo, L.H.: Smooth surface reconstruction from noisy clouds. In: Proceedings of Eurographics Symposium on Geometry Processing, pp. 53–62 (2005)

  25. 25.

    Mitra, N.J., Nguyen, A.: Estimating surface normals in noisy point cloud data. In: Proceedings of 19th Annual Symposium on Computational Geometry, pp. 322–328 (2003)

  26. 26.

    Mount, D.M., Arya, S.: ANN: A Library for Approximate Nearest Neighbor Searching. http://www.cs.umd.edu/∼mount/ANN/ (2005)

  27. 27.

    Ohtake, Y., Belyaev, A., Alexa, M., Turk, G., Seidel, H.P.: Multi-level partition of unity implicits. In: Proceedings of ACM SIGGRAPH, pp. 463–470 (2003)

  28. 28.

    Revelles, J., Urena, C., Lastra, M.: An efficient parametric algorithm for octree traversal. In: Proceedings of WSCG, pp. 212–219 (2000)

  29. 29.

    Scheidegger, C.E., Fleishman, S., Silva, C.T.: Triangulating point set surfaces with bounded error. In: Proceedings of Eurographics Symposium on Geometry Processing, pp. 63–72 (2005)

  30. 30.

    Xie, H., McDonnell, K.T., Qin, H.: Surface reconstruction of noisy and defective data sets. In: Proceedings of IEEE Visualization, pp. 259–266 (2004)

  31. 31.

    Zhao, H.K., Osher, S., Fedkiw, R.: Fast surface reconstruction using the level set method. In: Proceedings of IEEE Workshop on Variational and Level Set Methods, pp. 194–202 (2001)

Download references

Author information

Correspondence to Chi-Wan Lim.

Electronic Supplementary Material

Movie 1 23MB

Movie 1 23MB

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lim, C., Tan, T. Surface reconstruction by layer peeling. Visual Comput 22, 593–603 (2006) doi:10.1007/s00371-006-0048-9

Download citation

Keywords

  • Surface reconstruction
  • Mesh generation
  • Geometric modeling
  • Sampling
  • Scattered data