[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Log in

A variational model for normal computation of point clouds

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

In this paper we present a novel model for computing the oriented normal field on a point cloud. Differently from previous two-stage approaches, our method integrates the unoriented normal estimation and the consistent normal orientation into one variational framework. The normal field with consistent orientation is obtained by minimizing a combination of the Dirichlet energy and the coupled-orthogonality deviation, which controls the normals perpendicular to and continuously varying on the underlying shape. The variational model leads to solving an eigenvalue problem. If unoriented normal field is provided, the model can be modified for consistent normal orientation. We also present experiments which demonstrate that our estimates of oriented normal vectors are accurate for smooth point clouds, and robust in the presence of noise, and reliable for surfaces with sharp features, e.g., corners, ridges, close-by sheets and thin structures.

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

Access this article

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

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

    Google Scholar 

  2. Alliez, P., Cohen-Steiner, D., Tong, Y., Desbrun, M.: Voronoi-based variational reconstruction of unoriented point sets. In: Proceedings of Symposium on Geometry and Processing 07 (2007)

    Google Scholar 

  3. Amenta, N., Bern, M.: Surface reconstruction by Voronoi filtering. In: SCG ’98: Proceedings of the Fourteenth Annual Symposium on Computational Geometry, pp. 39–48 (1998)

    Chapter  Google Scholar 

  4. Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15, 1373–1396 (2002)

    Article  Google Scholar 

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

    Chapter  Google Scholar 

  6. Dey, T., Li, G., Sun, J.: Normal estimation for point clouds: A comparison study for a Voronoi based method, pp. 39–46 (2005)

  7. Gross, M., Pfister, H.: Point-Based Graphics, The Morgan Kaufmann Series in Computer Graphics. Morgan Kaufmann, San Mateo (2007)

    Google Scholar 

  8. Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Surface reconstruction from unorganized points. In: Proceedings of SIGGRAPH’92, pp. 71–78 (1992)

    Google Scholar 

  9. Huang, H., Li, D., Zhang, H., Ascher, U., Cohen-Or, D.: Consolidation of unorganized point clouds for surface reconstruction. In: SIGGRAPH Asia ’09: ACM SIGGRAPH Asia 2009 Papers, pp. 1–7 (2009)

    Chapter  Google Scholar 

  10. Kazhdan, M., Bolitho, M., Hoppe, H.: Poisson surface reconstruction. In: SGP’06: Proceedings of the Fourth Eurographics Symposium on Geometry Processing, pp. 61–70 (2006)

    Google Scholar 

  11. Levin, D.: Mesh-independent surface interpolation. In: Brunnett, G., Hamann, B., Mueller, H. (eds.) Geometric Modeling for Scientific Visualization, pp. 37–49. Springer, Berlin (2003)

    Google Scholar 

  12. Li, B., Schnabel, R., Klein, R., Cheng, Z., Dang, G., Jin, S.: Robust normal estimation for point clouds with sharp features. Comput. Graph. 34(2), 94–106 (2010)

    Article  Google Scholar 

  13. Liu, S., Wang, C.C.L.: Technical section: Orienting unorganized points for surface reconstruction. Comput. Graph. 34(3), 209–218 (2010)

    Article  Google Scholar 

  14. Mitra, N.J., Nguyen, A., Guibas, L.: Estimating surface normals in noisy point cloud data. Int. J. Comput. Geom. Appl. 14, 261–276 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Mount, D.M., Arya, S.: Ann: A library for approximate nearest neighbor searching. http://www.cs.umd.edu/~mount/ann/. (2006)

  16. Ohtake, Y., Belyaev, A., Seidel, H.P.: 3D scattered data interpolation and approximation with multilevel compactly supported RBFs. Graph. Models 67(3), 150–165 (2005)

    Article  MATH  Google Scholar 

  17. OuYang, D., Feng, H.Y.: On the normal vector estimation for point cloud data from smooth surfaces. Comput. Aided Des. 37(10), 1071–1079 (2005)

    Article  Google Scholar 

  18. Pauly, M., Keiser, R., Kobbelt, L.P., Gross, M.: Shape modeling with point-sampled geometry. ACM Trans. Graph. 22(3), 641–650 (2003)

    Article  Google Scholar 

  19. Stewart, G.W.: Matrix Algorithms, Volume II: Eigensystems SIAM: Society for Industrial and Applied Mathematics, Philadelphia (2001)

    Book  Google Scholar 

  20. Sun, J., Smith, M., Smith, L., Farooq, A.: Examining the uncertainty of the recovered surface normal in three light photometric stereo. Image Vis. Comput. 25(7), 1073–1079 (2007)

    Article  Google Scholar 

  21. Yang, Z., Kim, T.W.: Moving parabolic approximation of point clouds. Comput. Aided Des. 39(12), 1091–1112 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhouwang Yang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, J., Yang, Z. & Chen, F. A variational model for normal computation of point clouds. Vis Comput 28, 163–174 (2012). https://doi.org/10.1007/s00371-011-0607-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-011-0607-6

Keywords

Navigation