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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Pauly, M., Gross, M., Kobbelt, L.: Efficient simplification of point-sampled surfaces. In: Proceedings of IEEE Visualization Conference (2002)
Wu, J., Kobbelt, L.P.: Optimized sub-sampling of point sets for surface splatting. In: Proceedings of Eurographics (2004)
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)
Linsen, L.: Point Cloud Representation. Universitat Karlsruhe, Germany (2001)
Dey, T.K., Giesen, J., Hudson, J.: Decimating samples for mesh simplification. In: Proceedings of Canadian Conference on Computational Geometry (2001)
Amenta, N., Choi, S., Dey, T., Leekha, N.; A simple algorithm for homeomorphic surface reconstruction. In: Proceedings of Symposium on Computational Geometry (2000)
Dey, T.K., Giesen, J., Hudson, J.: Sample shuffling for quality hierarchic surface meshing. In: Proceedings of 10th International Meshing Roundatble Conference (2001)
Alexa, M., Beh, J., Cohen-Or, D., Fleishman, S., Levin, D., Silva, C.: Point set surfaces. In: Proceedings of IEEE Visualization Conference (2001)
Garland, M., Heckbert, P.: Surface simplification using quadric error metrics. In: Proceedings of SIGGRAPH (1997)
Allègre, R., Chaine, R., Akkouche, S.: Convection-driven dynamic surface reconstruction. In: Proceedings of Shape Modeling International, IEEE Computer Society Press (2005)
Boissonnat, J.-D., Cazals, F.: Coarse-to-fine surface simplification with geometric guarantees. In: Proceedings of Eurographics (2001)
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)
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)
Boissonnat, J.-D., Oudot, S.: Provably good sampling and meshing of surfaces. Graph. Models Solid Model. Theory Appl. 67(5), 405–451 (2005)
Chew, L.P.: Guaranteed-quality mesh generation for curved surfaces. In: Proceedings of Symposium on Computational Geometry, San Diego, California, USA (1993)
Adamson, A., Alexa, M.: Approximating and intersecting surfaces from points. In: Proceedings of Symposium on Geometry Processing (2003)
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)
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)
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)
Shannon, C.E., Weaver, W.: The Mathematical Theory of Communication. University of Illinois Press, Urbana (1949)
Parzen, E.: On estimation of a probability density function and modes. Ann. Math. Stat. 33(3), 1065–1076 (1962)
Rosenblatt, M.: Remarks on some nonparametric estimates of a density function. Ann. Math. Stat. 27(3), 832–837 (1956)
Silverman, B.W.: Density Estimation for Statistics and Data Analysis, Published in Monographs on Statistics and Applied Probability. Chapman and Hall press, London (1986)
Muller, H., Petersen, A.: Density Estimation Including Examples. Wiley StatsRef: Statistics Reference Online, pp. 1–12 (2016)
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)
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)
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)
Guéziec, A.: Locally toleranced surface simplification. IEEE Trans. Vis. Comput. Graph. 5(2), 168–189 (1999)
Randolph, E.B.: PLTMG: A Software Package for Solving Elliptic Partial Differential Equations, La Jolla, California 92093-0112 (2016)
Acknowledgments
The Max Planck, Atene and Tennis shoe models used in this paper are the courtesy of AIM@SHAPE shape repository.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Mahdaoui, A., Bouazi, A., Marhraoui Hsaini, A., Sbai, E.H. (2018). Entropic Method for 3D Point Cloud Simplification. In: Ben Ahmed, M., Boudhir, A. (eds) Innovations in Smart Cities and Applications. SCAMS 2017. Lecture Notes in Networks and Systems, vol 37. Springer, Cham. https://doi.org/10.1007/978-3-319-74500-8_56
Download citation
DOI: https://doi.org/10.1007/978-3-319-74500-8_56
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-74499-5
Online ISBN: 978-3-319-74500-8
eBook Packages: EngineeringEngineering (R0)