Regularisation of 3D Signed Distance Fields

  • Rasmus R. Paulsen
  • Jakob Andreas Bærentzen
  • Rasmus Larsen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5575)


Signed 3D distance fields are used a in a variety of domains. From shape modelling to surface registration. They are typically computed based on sampled point sets. If the input point set contains holes, the behaviour of the zero-level surface of the distance field is not well defined. In this paper, a novel regularisation approach is described. It is based on an energy formulation, where both local smoothness and data fidelity are included. The minimisation of the global energy is shown to be the solution of a large set of linear equations. The solution to the linear system is found by sparse Cholesky factorisation. It is demonstrated that the zero-level surface will act as a membrane after the proposed regularisation. This effectively closes holes in a predictable way. Finally, the performance of the method is tested with a set of synthetic point clouds of increasing complexity.


Input Point Voxel Volume Print Circuit Board Assembly Unorganised Point Voxel Centre 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Bærentzen, J.A., Aanæs, H.: Computing discrete signed distance fields from triangle meshes. Technical report, Informatics and Mathematical Modelling, Technical University of Denmark, DTU, Richard Petersens Plads, Building 321, DK-2800 Kgs, Lyngby (2002)Google Scholar
  2. 2.
    Bærentzen, J.A., Christensen, N.J.: Volume sculpting using the level-set method. In: International Conference on Shape Modeling and Applications, pp. 175–182 (2002)Google Scholar
  3. 3.
    Besag, J.: On the statistical analysis of dirty pictures. Journal of the Royal Statistical Society, Series B 48(3), 259–302 (1986)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Bloomenthal, J.: An implicit surface polygonizer. In: Graphics Gems IV, pp. 324–349 (1994)Google Scholar
  5. 5.
    Botsch, M., Bommes, D., Kobbelt, L.: Efficient Linear System Solvers for Mesh Processing. In: Martin, R., Bez, H.E., Sabin, M.A. (eds.) IMA 2005. LNCS, vol. 3604, pp. 62–83. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Botsch, M., Sorkine, O.: On Linear Variational Surface Deformation Methods. IEEE Transactions on Visualization and Computer Graphics, 213–230 (2008)Google Scholar
  7. 7.
    Burke, E.K., Cowling, P.I., Keuthen, R.: New models and heuristics for component placement in printed circuit board assembly. In: Proc. Information Intelligence and Systems, pp. 133–140 (1999)Google Scholar
  8. 8.
    Curless, B., Levoy, M.: A volumetric method for building complex models from range images. In: Proceedings of ACM SIGGRAPH, pp. 303–312 (1996)Google Scholar
  9. 9.
    Darkner, S., Vester-Christensen, M., Larsen, R., Nielsen, C., Paulsen, R.R.: Automated 3D Rigid Registration of Open 2D Manifolds. In: MICCAI 2006 Workshop From Statistical Atlases to Personalized Models (2006)Google Scholar
  10. 10.
    Davis, T.A., Hager, W.W.: Row modifications of a sparse cholesky factorization. SIAM Journal on Matrix Analysis and Applications 26(3), 621–639 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Golub, G.H., Van Loan, C.F.: Matrix Computations. Johns Hopkins University Press (1996)Google Scholar
  12. 12.
    Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Surface reconstruction from unorganized points. In: ACM SIGGRAPH, pp. 71–78 (1992)Google Scholar
  13. 13.
    Jakobsen, B., Bærentzen, J.A., Christensen, N.J.: Variational volumetric surface reconstruction from unorganized points. In: IEEE/EG International Symposium on Volume Graphics (September 2007)Google Scholar
  14. 14.
    Jones, M.W., Bærentzen, J.A., Sramek, M.: 3D Distance Fields: A Survey of Techniques and Applications. IEEE Transactions On Visualization and Computer Graphics 12(4), 518–599 (2006)CrossRefGoogle Scholar
  15. 15.
    Leventon, M.E., Grimson, W.E.L., Faugeras, O.: Statistical shape influence in geodesic active contours. In: IEEE Conference on Computer Vision and Pattern Recognition, 2000, vol. 1 (2000)Google Scholar
  16. 16.
    Lorensen, W.E., Cline, H.E.: Marching cubes: A high resolution 3D surface construction algorithm. Computer Graphics (SIGGRAPH 1987 Proceedings) 21(4), 163–169 (1987)Google Scholar
  17. 17.
    Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical recipes in C: the art of scientific computing. Cambridge University Press, Cambridge (2002)zbMATHGoogle Scholar
  18. 18.
    Schneider, R., Kobbelt, L.: Geometric fairing of irregular meshes for free-form surface design. Computer Aided Geometric Design 18(4), 359–379 (2001)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Rasmus R. Paulsen
    • 1
  • Jakob Andreas Bærentzen
    • 1
  • Rasmus Larsen
    • 1
  1. 1.Informatics and Mathematical ModellingTechnical University of DenmarkKgs. LyngbyDenmark

Personalised recommendations