Entropic Method for 3D Point Cloud Simplification

  • Abdelaaziz Mahdaoui
  • A. Bouazi
  • A. Marhraoui Hsaini
  • E. H. Sbai
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 37)

Abstract

To represent the surface of complex objects, the samples resulting from their digitization can contain a very large number of points. Simplification techniques analyse the relevance of the data. These simplification techniques provide models with fewer points than the original ones. Whereas reconstruction of a surface, with simplified point cloud, must be close to the original. In this article, we develop a method of simplification based on the concept of entropy, which is a mathematical function that intuitively corresponds to the amount of information this allows considering only relevant points.

Keywords

Simplification Entropy 3D point cloud Density estimator Mesh quality Compactness 

Notes

Acknowledgments

The Max Planck, Atene and Tennis shoe models used in this paper are the courtesy of AIM@SHAPE shape repository.

References

  1. 1.
    Pauly, M., Gross, M., Kobbelt, L.: Efficient simplification of point-sampled surfaces. In: Proceedings of IEEE Visualization Conference (2002)Google Scholar
  2. 2.
    Wu, J., Kobbelt, L.P.: Optimized sub-sampling of point sets for surface splatting. In: Proceedings of Eurographics (2004)Google Scholar
  3. 3.
    Ohtake, Y., Belyaev, A.G., Seidel, H.-P.: An integrating approach to meshing scattered point data. In: Proceedings of Symposium on Solid and Physical Modeling (2005)Google Scholar
  4. 4.
    Linsen, L.: Point Cloud Representation. Universitat Karlsruhe, Germany (2001)Google Scholar
  5. 5.
    Dey, T.K., Giesen, J., Hudson, J.: Decimating samples for mesh simplification. In: Proceedings of Canadian Conference on Computational Geometry (2001)Google Scholar
  6. 6.
    Amenta, N., Choi, S., Dey, T., Leekha, N.; A simple algorithm for homeomorphic surface reconstruction. In: Proceedings of Symposium on Computational Geometry (2000)Google Scholar
  7. 7.
    Dey, T.K., Giesen, J., Hudson, J.: Sample shuffling for quality hierarchic surface meshing. In: Proceedings of 10th International Meshing Roundatble Conference (2001)Google Scholar
  8. 8.
    Alexa, M., Beh, J., Cohen-Or, D., Fleishman, S., Levin, D., Silva, C.: Point set surfaces. In: Proceedings of IEEE Visualization Conference (2001)Google Scholar
  9. 9.
    Garland, M., Heckbert, P.: Surface simplification using quadric error metrics. In: Proceedings of SIGGRAPH (1997)Google Scholar
  10. 10.
    Allègre, R., Chaine, R., Akkouche, S.: Convection-driven dynamic surface reconstruction. In: Proceedings of Shape Modeling International, IEEE Computer Society Press (2005)Google Scholar
  11. 11.
    Boissonnat, J.-D., Cazals, F.: Coarse-to-fine surface simplification with geometric guarantees. In: Proceedings of Eurographics (2001)Google Scholar
  12. 12.
    Boissonnat, J., Oudot, S.: Provably good surface sampling and approximation. In: SGP 2003 Proceedings of the 2003 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, Aachen, Germany (2003)Google Scholar
  13. 13.
    Boissonnat, J.-D., Oudot, S.: An effective condition for sampling surfaces with guarantees. In: SM 2004 Proceedings of the Ninth ACM Symposium on Solid Modeling and Applications, Genoa, Italy (2004)Google Scholar
  14. 14.
    Boissonnat, J.-D., Oudot, S.: Provably good sampling and meshing of surfaces. Graph. Models Solid Model. Theory Appl. 67(5), 405–451 (2005)CrossRefMATHGoogle Scholar
  15. 15.
    Chew, L.P.: Guaranteed-quality mesh generation for curved surfaces. In: Proceedings of Symposium on Computational Geometry, San Diego, California, USA (1993)Google Scholar
  16. 16.
    Adamson, A., Alexa, M.: Approximating and intersecting surfaces from points. In: Proceedings of Symposium on Geometry Processing (2003)Google Scholar
  17. 17.
    Pauly, M., Gross, M.: Spectral processing of point-sampled geometry. In: SIGGRAPH 2001 Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, New York, NY, USA (2001)Google Scholar
  18. 18.
    Witkin, A.P., Heckbert, P.S.: Using particles to sample and control implicit surfaces. In: SIGGRAPH 1994 Proceedings of the 21st Annual Conference on Computer Graphics and Interactive Techniques, New York, NY, USA (1994)Google Scholar
  19. 19.
    Wang, J., Li, X., Ni, J.: Probability density function estimation based on representative data samples. In: Communication Technology and Application (ICCTA 2011), IET International Conference, Beijing, China (2011)Google Scholar
  20. 20.
    Shannon, C.E., Weaver, W.: The Mathematical Theory of Communication. University of Illinois Press, Urbana (1949)MATHGoogle Scholar
  21. 21.
    Parzen, E.: On estimation of a probability density function and modes. Ann. Math. Stat. 33(3), 1065–1076 (1962)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Rosenblatt, M.: Remarks on some nonparametric estimates of a density function. Ann. Math. Stat. 27(3), 832–837 (1956)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Silverman, B.W.: Density Estimation for Statistics and Data Analysis, Published in Monographs on Statistics and Applied Probability. Chapman and Hall press, London (1986)Google Scholar
  24. 24.
    Muller, H., Petersen, A.: Density Estimation Including Examples. Wiley StatsRef: Statistics Reference Online, pp. 1–12 (2016)Google Scholar
  25. 25.
    Bernardini, F., Mittleman, J., Rushmeier, H., Silva, C., Taubin, G.: The ball-pivoting algorithm for surface reconstruction. IEEE Trans. Vis. Comput. Graph. 5(4), 349–359 (1999)CrossRefGoogle Scholar
  26. 26.
    Mahdaoui, A., Bouazi, A., Hsaini, A.M., Sbai, E.: Comparative study of combinatorial 3D reconstruction algorithms. Int. J. Eng. Trends Technol. 48(5), 247–251 (2017)CrossRefGoogle Scholar
  27. 27.
    Marhraoui Hsaini, A., Bouazi, A., Mahdaoui, A., Sbai, E.H.: Reconstruction and adjustment of surfaces from a 3-D point cloud. Int. J. Comput. Trends Technol. (IJCTT) 37(2), 105–109 (2016)CrossRefGoogle Scholar
  28. 28.
    Guéziec, A.: Locally toleranced surface simplification. IEEE Trans. Vis. Comput. Graph. 5(2), 168–189 (1999)CrossRefGoogle Scholar
  29. 29.
    Randolph, E.B.: PLTMG: A Software Package for Solving Elliptic Partial Differential Equations, La Jolla, California 92093-0112 (2016)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of Physics, Faculty of ScienceMoulay Ismail UniversityMeknesMorocco
  2. 2.Ecole Supérieure de TechnologieMoulay Ismail UniversityMeknesMorocco

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