A 3D Curvilinear Skeletonization Algorithm with Application to Path Tracing

  • John Chaussard
  • Laurent Noël
  • Venceslas Biri
  • Michel Couprie
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7749)

Abstract

We present a novel 3D curvilinear skeletonization algorithm which produces filtered skeletons without needing any user input, thanks to a new parallel algorithm based on the cubical complex framework. These skeletons are used in a modified path tracing algorithm in order to produce less noisy images in less time than the classical approach.

References

  1. 1.
    Bertrand, G.: On critical kernels. Comptes Rendus de l’Académie des Sciences, Série Mathématiques I(345), 363–367 (2007)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bertrand, G., Couprie, M.: A New 3D Parallel Thinning Scheme Based on Critical Kernels. In: Kuba, A., Nyúl, L.G., Palágyi, K. (eds.) DGCI 2006. LNCS, vol. 4245, pp. 580–591. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Chaussard, J.: Topological tools for discrete shape analysis. Ph.D. thesis, Université Paris-Est (December 2010)Google Scholar
  4. 4.
    Chaussard, J., Couprie, M.: Surface Thinning in 3D Cubical Complexes. In: Wiederhold, P., Barneva, R.P. (eds.) IWCIA 2009. LNCS, vol. 5852, pp. 135–148. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Chaussard, J., Couprie, M., Talbot, H.: Robust skeletonization using the discrete lambda-medial axis. Pattern Recognition Letters (2010) (in press)Google Scholar
  6. 6.
    Couprie, M., Coeurjolly, D., Zrour, R.: Discrete bisector function and euclidean skeleton in 2D and 3D. Image and Vision Computing 25(10), 1543–1556 (2007)CrossRefGoogle Scholar
  7. 7.
    Hesselink, W.H., Roerdink, J.B.T.M.: Euclidean skeletons of digital image and volume data in linear time by the integer medial axis transform. IEEE Transactions on Pattern Analysis and Machine Intelligence 30(12), 2204–2217 (2008)CrossRefGoogle Scholar
  8. 8.
    Kajiya, T.: The Rendering Equation. Computer Graphics (ACM SIGGRAPH 1986 Proceedings) 20(4), 143–150 (1986)CrossRefGoogle Scholar
  9. 9.
    Lafortune, E.P., Willems, Y.D.: Bi-directional path tracing. In: Proceedings of the 3rd International Conference on Computational Graphics and Visualization Techniques, pp. 145–153 (1993)Google Scholar
  10. 10.
    Liu, L., Chambers, E.W., Letscher, D., Ju, T.: A simple and robust thinning algorithm on cell complexes. Computer Graphics Forum (Proceedings of Pacific Graphics 2010) (2010)Google Scholar
  11. 11.
    Matheron, G.: Eléments pour une Théorie des Milieux Poreux (1967)Google Scholar
  12. 12.
    Palágyi, K.: A Subiteration-Based Surface-Thinning Algorithm with a Period of Three. In: Hamprecht, F.A., Schnörr, C., Jähne, B. (eds.) DAGM 2007. LNCS, vol. 4713, pp. 294–303. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • John Chaussard
    • 1
  • Laurent Noël
    • 2
  • Venceslas Biri
    • 2
  • Michel Couprie
    • 2
  1. 1.Sorbonne Paris Cité, LAGA, CNRS(UMR 7539)Université Paris 13VilletaneuseFrance
  2. 2.LIGM, A3SI-ESIEEUniversité Paris EstNoisy le Grand CedexFrance

Personalised recommendations