Surface Reconstruction with Smart Growing Cells

  • Hendrik Annuth
  • Christian-A. Bohn
Part of the Studies in Computational Intelligence book series (SCI, volume 321)

Abstract

We propose Growing Cells Meshing (GCM) - a reconstruction algorithm which creates triangle meshes from clouds of arbitrary point samples registered on object surfaces. GCM is different to classical approaches in the way that it uses an artificial neural network together with an iterative learning technique to represent the triangle mesh. Based on the Growing Cell Structures (GCS) approach [3] we introduce the Smart Growing Cells (SGC) network as extension to fulfill the requirements of surface reconstruction. Our method profits from the well-know benefits entailed by neural networks, like autonomy, robustness, scalability, the ability of retrieving information from very complex data, and adaptability. On the downside, typical drawbacks like undesirable smoothing of information, inability to exactly model detailed, discontinuous data, or a vast amount of computing resources at big network sizes are overcome for the application of surface reconstruction. The GCM approach creates high-quality triangulations of billions of points in few minutes. It perfectly covers any amount and distribution of samples, holes, and inconsistent data. It discovers and represents edges, manages clusters of input sample points, and it is capable of dynamically adapting to incremental sample data.

Keywords

Surface Reconstruction Reference Vector Discontinuity Modeling Vertex Valence Edge Collapse 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Álvarez, R., Noguera, J.V., Tortosa, L., Zamora, A.: A mesh optimization algorithm based on neural networks. Inf. Sci. 177(23), 5347–5364 (2007)CrossRefGoogle Scholar
  2. 2.
    Edelsbrunner, H., Mcke, E.P.: Three-dimensional alpha shapes (1994)Google Scholar
  3. 3.
    Fritzke, B.: Growing cell structures - a self-organizing network for unsupervised and supervised learning. Neural Networks 7, 1441–1460 (1993)CrossRefGoogle Scholar
  4. 4.
    Fritzke, B.: A growing neural gas network learns topologies. In: Tesauro, G., Touretzky, D.S., Leen, T.K. (eds.) Advances in Neural Information Processing Systems 7, pp. 625–632. MIT Press, Cambridge (1995)Google Scholar
  5. 5.
    Hoffmann, M., Vrady, L.: Free-form surfaces for scattered data by neural networks. Journal for Geometry and Graphics 2, 1–6 (1998)MATHMathSciNetGoogle Scholar
  6. 6.
    Hoppe, H.: Poisson surface reconstruction and its applications. In: SPM 2008: Proceedings of the 2008 ACM symposium on Solid and physical modeling, p. 10. ACM, New York (2008)CrossRefGoogle Scholar
  7. 7.
    Hoppe, H., Derose, T., Duchamp, T., Halstead, M., Jin, H., McDonald, J., Schweitzer, J., Stuetzle, W.: Piecewise smooth surface reconstruction, pp. 295–302 (1994)Google Scholar
  8. 8.
    Hoppe, H., DeRose, T., Duchamp, T., McDonald, J.A., Stuetzle, W.: Surface reconstruction from unorganized points. In: Thomas, J.J. (ed.) SIGGRAPH 1992, pp. 71–78. ACM, New York (1992)CrossRefGoogle Scholar
  9. 9.
    Huang, Q.-X., Adams, B., Wand, M.: Bayesian surface reconstruction via iterative scan alignment to an optimized prototype. In: SGP 2007: Proceedings of the fifth Eurographics symposium on Geometry processing, pp. 213–223. Eurographics Association, Aire-la-Ville, Switzerland (2007)Google Scholar
  10. 10.
    Ivrissimtzis, I., Jeong, W.K., Lee, S., Lee, Y., Seidel, H.P.: Neural meshes: surface reconstruction with a learning algorithm. Research Report MPI-I-2004-4-005, Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany (2004)Google Scholar
  11. 11.
    Ivrissimtzis, I., Jeong, W.K., Seidel, H.P.: Neural meshes: Statistical learning methods in surface reconstruction. Tech. Rep. MPI-I-2003-4-007, Max-Planck-Institut fr Informatik, Saarbrücken (2003)Google Scholar
  12. 12.
    Ivrissimtzis, I., Lee, Y., Lee, S., Jeong, W.-K., Seidel, H.-P.: Neural mesh ensembles. In: 3DPVT 2004: Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium, pp. 308–315. IEEE Computer Society, Washington (2004)CrossRefGoogle Scholar
  13. 13.
    Ivrissimtzis, I.P., Jeong, W.K., Seidel, H.P.: Using growing cell structures for surface reconstruction. In: SMI 2003: Proceedings of the Shape Modeling International 2003, p. 78. IEEE Computer Society, Washington (2003)CrossRefGoogle Scholar
  14. 14.
    Kohonen, T.: Self-Organized Formation of Topologically Correct Feature Maps. Biological Cybernetics 43, 59–69 (1982)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Kolluri, R., Shewchuk, J.R., O’Brien, J.F.: Spectral surface reconstruction from noisy point clouds. In: SGP 2004: Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, pp. 11–21. ACM, New York (2004)CrossRefGoogle Scholar
  16. 16.
    Mari, J.F., Saito, J.H., Poli, G., Zorzan, M.R., Levada, A.L.M.: Improving the neural meshes algorithm for 3d surface reconstruction with edge swap operations. In: SAC 2008, pp. 1236–1240. ACM, New York (2008)CrossRefGoogle Scholar
  17. 17.
    Muraki, S.: Volumetric shape description of range data using “blobby model”. In: SIGGRAPH 1991: Proceedings of the 18th annual conference on Computer graphics and interactive techniques, pp. 227–235. ACM, New York (1991)CrossRefGoogle Scholar
  18. 18.
    Storvik, G.: Bayesian surface reconstruction from noisy images. In: Interface 1996 (1996)Google Scholar
  19. 19.
    Taubin, G.: A signal processing approach to fair surface design. In: SIGGRAPH, pp. 351–358 (1995)Google Scholar
  20. 20.
    Tournois, J., Wormser, C., Alliez, P., Desbrun, M.: Interleaving delaunay refinement and optimization for practical isotropic tetrahedron mesh generation. In: SIGGRAPH 2009: ACM SIGGRAPH 2009 papers, pp. 1–9. ACM, New York (2009)CrossRefGoogle Scholar
  21. 21.
    Vrady, L., Hoffmann, M., Kovcs, E.: Improved free-form modelling of scattered data by dynamic neural networks. Journal for Geometry and Graphics 3, 177–183 (1999)Google Scholar
  22. 22.
    Yoon, M., Lee, Y., Lee, S., Ivrissimtzis, I., Seidel, H.P.: Surface and normal ensembles for surface reconstruction. Comput. Aided Des. 39(5), 408–420 (2007)CrossRefGoogle Scholar
  23. 23.
    Yu, Y.: Surface reconstruction from unorganized points using self-organizing neural networks. In: IEEE Visualization 1999, Conference Proceedings, pp. 61–64 (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Hendrik Annuth
    • 1
  • Christian-A. Bohn
    • 1
  1. 1.Wedel University of Applied SciencesWedel, FRG

Personalised recommendations