Linear Discrete Line Recognition and Reconstruction Based on a Generalized Preimage

  • Martine Dexet
  • Eric Andres
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4040)


A new efficient standard discrete line recognition method is presented. This algorithm incrementally computes in linear time all straight lines which cross a given set of pixels. Moreover, pixels can be considered in any order and do not need to be connected. A new invertible 2D discrete curve reconstruction algorithm based on the proposed recognition method completes this paper. This algorithm computes a polygonal line so that its standard digitization is equal to the discrete curve. These two methods are based on the definition of a new generalized preimage and the framework is the discrete analytical geometry.


Convex Polygon Recognition Algorithm Straight Line Segment Polygonal Line Standard Line 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Lorensen, W.E., Cline, H.E.: Marching cubes: a high resolution 3d surface construction algorithm. In: SIGGRAPH, Anaheim, USA. Computer Graphics (ACM), vol. 21, pp. 163–169 (1987)Google Scholar
  2. 2.
    Klette, R., Rosenfeld, A.: Digital straightness – a review. Discrete Applied Mathematics 139(1–3), 197–230 (2004)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Sivignon, I., Breton, R., Dupond, F., Andres, E.: Discrete analytical curve reconstruction without patches. Image and Vision Computing 23(2), 191–202 (2005)CrossRefGoogle Scholar
  4. 4.
    Debled-Rennesson, I., Reveillès, J.: A linear algorithm for segmentation of digital curves. International Journal of Pattern Recognition and Artificial Intelligence 9(6), 635–662 (1995)CrossRefGoogle Scholar
  5. 5.
    Dorst, L., Smeulders, A.W.M.: Discrete representation of straight lines. IEEE Transactions on Pattern Analysis and Machine Intelligence 6(4), 450–463 (1984)MATHCrossRefGoogle Scholar
  6. 6.
    Vittone, J., Chassery, J.M.: Recognition of digital naive planes and polyhedrization. In: Nyström, I., Sanniti di Baja, G., Borgefors, G. (eds.) DGCI 2000. LNCS, vol. 1953, pp. 296–307. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  7. 7.
    Cœurjolly, D.: Algorithmique et géométrie discrète pour la caractérisation des courbes et des surfaces. PhD thesis, Université Lumière Lyon 2, Lyon, France (2002)Google Scholar
  8. 8.
    Breton, R., Sivignon, I., Dupont, F., Andres, E.: Towards an invertible Euclidean reconstruction of a discrete object. In: Nyström, I., Sanniti di Baja, G., Svensson, S. (eds.) DGCI 2003. LNCS, vol. 2886, pp. 246–256. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. 9.
    Andres, E.: Discrete linear objects in dimension n: the standard model. Graphical Models 65, 92–111 (2003)MATHCrossRefGoogle Scholar
  10. 10.
    Maître, H.: Un panorama de la transformation de Hough – a review on Hough transform. Traitement du Signal 2(4), 305–317 (1985)MathSciNetGoogle Scholar
  11. 11.
    McIlroy, M.D.: A note on discrete representation of lines. AT&T Technical Journal 64(2), 481–490 (1985)Google Scholar
  12. 12.
    Dexet, M., Andres, E.: Hierarchical topological structure for the design of a discrete modeling tool. In: WSCG Full Papers Proceedings, Plzen, Czech Republic, pp. 1–8 (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Martine Dexet
    • 1
  • Eric Andres
    • 1
  1. 1.Laboratoire SICUniversité de PoitiersFuturoscope ChasseneuilFrance

Personalised recommendations