Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Modeling Three-Dimensional Morse and Morse-Smale Complexes Read chapter Read first chapter

2013 | OriginalPaper | Chapter

13. Point Cloud Segmentation and Denoising via Constrained Nonlinear Least Squares Normal Estimates

Authors : Edward Castillo, Jian Liang, Hongkai Zhao

Published in: Innovations for Shape Analysis

Publisher: Springer Berlin Heidelberg

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We first introduce a surface normal estimation procedure for point clouds capable of handling geometric singularities in the data, such as edges and corners. Our formulation is based on recasting the popular Principal Component Analysis (PCA) method as a constrained nonlinear least squares (NLSQ) problem. In contrast to traditional PCA, the new formulation assigns appropriate weights to neighboring points automatically during the optimization process in order to minimize the contributions of points located across singularities. We extend this strategy to point cloud denoising by combining normal estimation, point projection, and declustering into one NLSQ formulation. Finally, we propose a point cloud segmentation technique based on surface normal estimates and local point connectivity. In addition to producing consistently oriented surface normals, the process segments the point cloud into disconnected components that can each be segmented further into piecewise smooth components as needed.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Group-Valued Regularization for Motion Segmentation of Articulated Shapes
next chapter Distance Images and the Enclosure Field: Applications in Intermediate-Level Computer and Biological Vision
Literature
1.
Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., Silva, C.T.: Computing and rendering point set surfaces. IEEE Trans. Vis. Comput. Graph. 9, 3–15 (2003)CrossRef
2.
Amenta, N., Bern, M.: Surface reconstruction by voronoi filtering. In: Proceedings of the Fourteenth Annual Symposium on Computational Geometry. ACM, New York (1998)
3.
Azariadis, P.: Parameterization of clouds of unorganized points using dynamic base surfaces. Comput. Aided Des. 36, 607–623 (2004)CrossRef
4.
Besl, P.J., Jain, R.C.: Segmentation through variable-order surface fitting. IEEE Trans. Pattern Anal. Mach. Intell. 10, 167–192 (1988)CrossRef
5.
Boissonnat, J.D., Cazals, F.: Smooth surface reconstruction via natural neighbor interpolation of distance functions. In: Proceedings of 16th Annual Symposium on Computational Geometry, pp. 223–232. ACM, New York (2000)
6.
Calderon, F., Ruiz, U., Rivera, M.: Surface-normal estimation with neighborhood reorganization for 3d reconstruction. In: Proceedings of the Congress on Pattern Recognition 12th Iberoamerican Conference on Progress in Pattern Recognition, Image Analysis and Applications, pp. 321–330. Springer, Berlin/Heidelberg (2007)
7.
Canny, J.: A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8, 679–698 (1986)CrossRef
8.
Demarsin, K., Vanderstraeten, D., Volodine, T., Roose, D.: Detection of closed sharp edges in point clouds using normal estimation and graph theory. Comput. Aided Des. 39, 276–283 (2007)CrossRef
9.
10.
Dey, T., Sun, J.: Normal and feature approximations from noisy point clouds. In: FSTTCS 2006: Foundations of Software Technology and Theoretical Computer Science, vol. 4337, pp. 21–32. Springer, Berlin/Heidelberg (2006)
11.
Dey, T.K., Li, G., Sun, J.: Normal estimation for point clouds: a comparison study for a voronoi based method. In: Proceedings Eurographics/IEEE VGTC Symposium Point-Based Graphics, vol. 0, pp. 39–46 (2005)CrossRef
12.
Fleishman, S., Drori, I., Cohen-or, D.: Bilateral mesh denoising. ACM Trans. Graph. 22, 950–953 (2003)CrossRef
13.
Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Surface reconstruction from unorganized points. In: Proceedings of ACM Siggraph, pp. 71–78. ACM, New York (1992)
14.
Hu, S., Wallner, J.: A second order algorithm for orthogonal projection onto curves and surfaces. Comput. Aided Graph. Des. 22(3), 251–260 (2005)MathSciNetMATHCrossRef
15.
Huang, J., Menq, C.-H.: Automatic data segmentation for geometric feature extraction from unorganized 3-D coordinate points. IEEE Trans. Robot. Autom. 17, 268–278 (2001)CrossRef
16.
Huang, H., Li, D., Zhang, H., Ascher, U., Cohen-Or, D.: Consolidation of unorganized point clouds for surface reconstruction. ACM Trans. Graph. 28, 176:1–176:7 (2009)
17.
Huber, P.J.: Robust Statistics. Wiley, New York (2004)
18.
Klasing, K., Althoff, D., Wollherr, D., Buss, M.: Comparison of surface normal estimation methods for range sensing applications. In: IEEE International Conference on Robotics and Automation, 2009. ICRA ’09. IEEE, Piscataway (2009)
19.
Lee, Y., Park, S., Jun, Y., Choi, W.C.: A robust approach to edge detection of scanned point data. Int. J. Adv. Manuf. Technol. 23, 263–271 (2004)CrossRef
20.
Leung, S., Zhao, H.: A grid based particle method for evolution of open curves and surfaces. J. Comput. Phys. 228, 2993–3024 (2009)MathSciNetMATHCrossRef
21.
Lipman, Y., Cohen-Or, D., Levin, D., Tal-Ezer, H.: Parameterization-free projection for geometry reconstruction. ACM Trans. Graph. 26, Article no 22 (2007)
22.
Liu, Y.S., Paul, J.C., Yong, J.H., Yu, P.Q., Zhang, H., Sun, J.G., Ramani, K.: Automatic least-squares projection of points onto point clouds with applications in reverse engineering. Comput. Aided Des. 38, 1251–1263 (2006)CrossRef
23.
Mitra, N., Nguyen, A., Guibas, L.: Estimating surface normals in noisy point cloud data. In: Spec. Issue Int. J. Comput. Geom. Appl. 14, 261–276 (2004)MathSciNetMATHCrossRef
24.
OuYang, D., Feng, H.-Y.: On the normal vector estimation for point cloud data from smooth surfaces. Comput. Aided Des. 37, 1071–1079 (2005)CrossRef
25.
Pauly, M., Gross, M., Kobbelt, L.P.: Efficient simplification of point-sampled surfaces. In: Proceedings of the conference on Visualization 2002. VIS 2002. IEEE Computer Society, Washington, DC (2002)
26.
Pauly, M., Keiser, R., Gross, M.: Multi-scale feature extraction on point-sampled surfaces. Comput. Graph. Forum 22, 281–289 (2003)CrossRef
27.
Pauly, M., Keiser, R., Kobbelt, L.P., Gross, M.: Shape modeling with point-sampled geometry. ACM Trans. Graph. 22, 641–650 (2003)CrossRef
28.
Rabbani, T., Van Den Heuvel, F., Vosselmann, G.: Segmentation of point clouds using smoothness constrain. ISPRS Comm. V Symp. Image Eng. Vis. Metrol. 36, 248–253 (2006)
29.
Schmaltz, C., Gwosdek, P., Bruhn, A., Weickert, J.: Electrostatic halftoning. Comput. Graph. Forum 29, 2313–2327 (2010)CrossRef
30.
Vosselman, G.: Advanced point cloud processing. In: Fritsch, D. (ed.) Photogrammetric Week ’09, pp. 137–146. Wichmann, Heidelberg (2009)
31.
Vosselman, G., Gorte, B., Rabbani, T., Sithole, G.: Recongnising structure in laser scanner point clouds. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci. 46, 33–38 (2004)
32.
Yang, M., Lee, E.: Segmentation of measured point data using parametric quadric surface approximation. Computer A 31, 449–457 (1999)MATHCrossRef
Metadata
Title
Point Cloud Segmentation and Denoising via Constrained Nonlinear Least Squares Normal Estimates
Authors
Edward Castillo
Jian Liang
Hongkai Zhao
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Innovations for Shape Analysis

Print ISBN: 978-3-642-34140-3

Electronic ISBN: 978-3-642-34141-0

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-34141-0_13

Premium Partner

    Image Credits