Skip to main content
Springer Nature Link
Log in

Surface Reconstruction from Point Clouds Using a Novel Variational Model

  • Conference paper
  • First Online:
Research and Development in Intelligent Systems XXXII (SGAI 2015)

Abstract

Multi-view reconstruction has been an active research topic in the computer vision community for decades. However, state of the art 3D reconstruction systems have lacked the speed, accuracy, and ease to use properties required by the industry. The work described in this paper is part of the effort to produce a multi-view reconstruction system for a UK company. A novel variational level set method is developed for reconstructing an accurate implicit surface for a set of unorganised points (point cloud). The variational model consists of three energy terms to ensure accurate and smooth surface reconstruction whilst preserving the fine details of the point cloud and increasing speed. The model also completely eliminated the need for reinitialisation associated with the level set method. Implementation details of the variational model using gradient descent optimisation are given, and the roles of its three energy terms are illustrated through numerical experiments. Experiments show that the proposed method outperformed the state of the art surface reconstruction approaches.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Edelsbrunner, H., Mücke, E.P.: Three-dimensional alpha shapes. ACM Trans. Gr. 13(1), 43–72 (1994)

    Article  MATH  Google Scholar 

  2. Amenta, N., Bern, M., Kamvysselis, M.: A new Voronoi-based surface reconstruction algorithm. In: Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques, pp. 415–421 (1998)

    Google Scholar 

  3. Boissonnat, J.D.: Geometric structures for three-dimensional shape representation. ACM Trans. Gr. 3(4), 266–286 (1984)

    Article  Google Scholar 

  4. Zhao, H.K., Osher, S., Merriman, B., Kan, M.: Implicit and nonparametric shape reconstruction from unorganized data using a variational level set method. Comput. Vis. Image Underst. 80(3), 295–314 (2000). Elsevier

    Article  MATH  Google Scholar 

  5. Zhao, H.K., Osher, S., Fedkiw, R.: Fast surface reconstruction using the level set method. In: Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision, 2001, pp. 194–201. IEEE (2001)

    Google Scholar 

  6. Ye, J., Bresson, X., Goldtein, T., Osher, S.: A fast variational method for surface reconstruction from sets of scattered points. CAM Report, 10(01) (2010)

    Google Scholar 

  7. Liang, J., Park, F., Zhao, H.K.: Robust and efficient implicit surface reconstruction for point clouds based on convexified image segmentation. J. Sci. Comput. 54(2–3), 577–602 (2013). Springer

    Article  MathSciNet  Google Scholar 

  8. Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79(1), 12–49 (1988). Elsevier

    Article  MathSciNet  MATH  Google Scholar 

  9. Li, C.M., Xu, C.Y., Gui, C.F., Fox, M.D.: Level set evolution without re-initialization: a new variational formulation. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005. CVPR 2005, 1, pp. 430–436. IEEE (2005)

    Google Scholar 

  10. Zhao, H.K.: A fast sweeping method for eikonal equations. Math. Comput. 74(250), 603–627 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kazhdan, M., Bolitho, M., Hoppe, H.: Poisson surface reconstruction. In: Proceedings of the fourth Eurographics symposium on Geometry processing (2006)

    Google Scholar 

  12. Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. Int. J. Comput. Vis. 22(1), 61–79 (1997). Springer

    Article  MATH  Google Scholar 

  13. Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenom. 60(1), 259–268 (1992). Elsevier

    Article  MathSciNet  MATH  Google Scholar 

  14. Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. Image Process. 10(2), 266–277 (2001). IEEE

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science, University of Nottingham, Nottingham, UK

    Jinming Duan, Ben Haines, Wil O. C. Ward & Li Bai

Authors
  1. Jinming Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ben Haines
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wil O. C. Ward
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Li Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jinming Duan .

Editor information

Editors and Affiliations

  1. School of Computing, University of Portsmouth, Portsmouth, United Kingdom

    Max Bramer

  2. School of Computing, Engineering and Mathematics, University of Brighton, Brighton, United Kingdom

    Miltos Petridis

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Duan, J., Haines, B., Ward, W.O.C., Bai, L. (2015). Surface Reconstruction from Point Clouds Using a Novel Variational Model. In: Bramer, M., Petridis, M. (eds) Research and Development in Intelligent Systems XXXII. SGAI 2015. Springer, Cham. https://doi.org/10.1007/978-3-319-25032-8_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-25032-8_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25030-4

  • Online ISBN: 978-3-319-25032-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics