Geometric Feature Estimators for Noisy Discrete Surfaces

  • L. Provot
  • I. Debled-Rennesson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4992)


We present in this paper robust geometric feature estimators on the border of a possibly noisy discrete object. We introduce the notion of patch centered at a point of this border. Thanks to a width parameter, attached to a patch, the noise on the border of the discrete object can be considered, and an extended flat neighborhood of a border point is computed. Stable geometric features are then extracted around this point. A normal vector estimator is proposed as well as a detector of convex and concave parts on the border of a discrete object.


Normal Vector Patch Area Discrete Object Convex Part Discrete Surface 
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  1. 1.
    Yagel, R., Cohen, D., Kaufman, A.E.: Normal estimation in 3d discrete space. The Visual Computer 8(5&6), 278–291 (1992)CrossRefGoogle Scholar
  2. 2.
    Thürmer, G., Wüthrich, C.A.: Normal computation for discrete surfaces in 3d space. Computer Graphics Forum 16(3), 15–26 (1997)CrossRefGoogle Scholar
  3. 3.
    Lenoir, A.: Fast estimation of mean curvature on the surface of a 3d discrete object. In: Ahronovitz, E. (ed.) DGCI 1997. LNCS, vol. 1347, pp. 175–186. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  4. 4.
    Papier, L., Françon, J.: Évaluation de la normale au bord d’un objet discret 3d. Revue internationale de CFAO et d’Infographie 13(2), 205–226 (1998)Google Scholar
  5. 5.
    Tellier, P., Debled-Rennesson, I.: 3d discrete normal vectors. In: Bertrand, G., Couprie, M., Perroton, L. (eds.) DGCI 1999. LNCS, vol. 1568, pp. 447–457. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  6. 6.
    Coeurjolly, D., Flin, F., Teytaud, O., Tougne, L.: Multigrid Convergence and Surface Area Estimation. In: Asano, T., Klette, R., Ronse, C. (eds.) Geometry, Morphology, and Computational Imaging. LNCS, vol. 2616, pp. 101–119. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Hermann, S., Klette, R.: Multigrid analysis of curvature estimators. In: Proceedings of Image and Vision Computing New Zealand, pp. 108–112 (2003)Google Scholar
  8. 8.
    Veelaert, P.: Uncertain geometry in computer vision. In: Andrès, É., Damiand, G., Lienhardt, P. (eds.) DGCI 2005. LNCS, vol. 3429, pp. 359–370. Springer, Heidelberg (2005)Google Scholar
  9. 9.
    Debled-Rennesson, I., Rémy, J.L., Rouyer-Degli, J.: Linear segmentation of discrete curves into fuzzy segments. Discrete Applied Math. 151, 122–137 (2005)CrossRefzbMATHGoogle Scholar
  10. 10.
    Debled-Rennesson, I., Feschet, F., Rouyer-Degli, J.: Optimal blurred segments decomposition of noisy shapes in linear time. Computers & Graphics 30(1), 30–36 (2006)CrossRefGoogle Scholar
  11. 11.
    Provot, L., Buzer, L., Debled-Rennesson, I.: Recognition of blurred pieces of discrete planes. In: Kuba, A., Nyúl, L.G., Palágyi, K. (eds.) DGCI 2006. LNCS, vol. 4245, pp. 65–76. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Nguyen, T.P., Debled-Rennesson, I.: Curvature estimation in noisy curves. In: Kropatsch, W.G., Kampel, M., Hanbury, A. (eds.) CAIP 2007. LNCS, vol. 4673, pp. 474–481. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Lenoir, A., Malgouyres, R., Revenu, M.: Fast computation of the normal vector field of the surface of a 3-d discrete object. In: Miguet, S., Ubéda, S., Montanvert, A. (eds.) DGCI 1996. LNCS, vol. 1176, pp. 101–112. Springer, Heidelberg (1996)Google Scholar
  14. 14.
    Thiel, E., Montanvert, A.: Chamfer masks: discrete distance functions, geometrical properties and optimization. In: 11th ICPR, The Hague, The Netherlands, vol. 3, pp. 244–247 (1992)Google Scholar
  15. 15.
    Borgefors, G.: On digital distance transforms in three dimensions. Computer Vision and Image Understanding 64(3), 368–376 (1996)CrossRefGoogle Scholar
  16. 16.
    Verwer, B., Verbeek, P., Dekker, S.: An efficient uniform cost algorithm applied to distance transforms. IEEE Transactions on Pattern Analysis and Machine Intelligence 11(4), 425–429 (1989)CrossRefGoogle Scholar
  17. 17.
    Coeurjolly, D.: Visibility in discrete geometry: An application to discrete geodesic paths. In: Braquelaire, A., Lachaud, J.-O., Vialard, A. (eds.) DGCI 2002. LNCS, vol. 2301, pp. 326–337. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  18. 18.
    Provot, L., Debled-Rennesson, I.: Segmentation of noisy discrete surfaces. In: 12th International Workshop on Combinatorial Image Analysis, Buffalo, NY, USA, vol. 4958, pp. 160–171 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • L. Provot
    • 1
  • I. Debled-Rennesson
    • 1
  1. 1.LORIA NancyVandœuvre-lès-Nancy CedexFrance

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