Receptive Fields for Generalized Map Pyramids: The Notion of Generalized Orbit

  • Carine Grasset-Simon
  • Guillaume Damiand
  • Pascal Lienhardt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3429)


A pyramid of n-dimensional generalized maps is a hierarchical data structure. It can be used, for instance, in order to represent an irregular pyramid of n-dimensional images. A pyramid of generalized maps can be built by successively removing and/or contracting cells of any dimension. In this paper, we define generalized orbits, which extend the classical notion of receptive fields. Generalized orbits allow to establish the correspondence between a cell of a pyramid level and the set of cells of previous levels, the removal or contraction of which have led to the creation of this cell. In order to define generalized orbits, we extend, for generalized map pyramids, the notion of connecting walk defined by Brun and Kropatsch.


Irregular pyramids generalized maps generalized map pyramids connecting walks generalized orbits 


  1. 1.
    Burt, P., Hong, T., Rosenfeld, A.: Segmentation and estimation of image region properties through cooperative hierarchical computation. IEEE Transactions on Systems, Man and Cybernetics 11, 802–809 (1981)CrossRefGoogle Scholar
  2. 2.
    Meer, P.: Stochastic image pyramids. Computer Vision, Graphics and Image Processing 45, 269–294 (1989)CrossRefGoogle Scholar
  3. 3.
    Montanvert, A., Meer, P., Rosenfeld, A.: Hierarchical image analysis using irregular tessellations. IEEE Transactions on Pattern Analysis and Machine Intelligence 13, 307–316 (1991)CrossRefGoogle Scholar
  4. 4.
    Jolion, J.M., Montanvert, A.: The adaptive pyramid: A framework for 2d image analysis. Computer Vision, Graphics and Image Processing 55, 339–348 (1992)zbMATHGoogle Scholar
  5. 5.
    Kropatsch, W.: Building irregular pyramids by dual-graph contraction. Vision, Image and Signal Processing 142, 366–374 (1995)CrossRefGoogle Scholar
  6. 6.
    Brun, L., Kropatsch, W.: Irregular pyramids with combinatorial maps. In: Amin, A., Pudil, P., Ferri, F., Iñesta, J.M. (eds.) SPR 2000 and SSPR 2000. LNCS, vol. 1876, pp. 256–265. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  7. 7.
    Brun, L., Kropatsch, W.G.: Introduction to combinatorial pyramids. In: Bertrand, G., Imiya, A., Klette, R. (eds.) Digital and Image Geometry. LNCS, vol. 2243, pp. 108–127. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Brun, L., Kropatsch, W.G.: Combinatorial pyramids. In: Suvisoft (ed.) IEEE International conference on Image Processing (ICIP), Barcelona, September 2003, vol. II, pp. 33–37 (2003)Google Scholar
  9. 9.
    Brun, L., Kropatsch, W.G.: Contraction kernels and combinatorial maps. Pattern Recognition Letters 24, 1051–1057 (2003)zbMATHCrossRefGoogle Scholar
  10. 10.
    Grasset-Simon, C., Damiand, G., Lienhardt, P.: Pyramids of n-dimensional generalized map. Technical Report 2, SIC, Université de Poitiers (2004)Google Scholar
  11. 11.
    Lienhardt, P.: N-dimensional generalized combinatorial maps and cellular quasi-manifolds. International Journal of Computational Geometry and Applications, 275–324 (1994)Google Scholar
  12. 12.
    Brun, L., Kropatsch, W.G.: Receptive fields within the combinatorial pyramid framework. In: Braquelaire, A., Lachaud, J.-O., Vialard, A. (eds.) DGCI 2002. LNCS, vol. 2301, pp. 92–101. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  13. 13.
    Damiand, G., Lienhardt, P.: Removal and contraction for n-dimensional generalized maps. In: Nyström, I., Sanniti di Baja, G., Svensson, S. (eds.) DGCI 2003. LNCS, vol. 2886, pp. 408–419. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. 14.
    Lienhardt, P.: Subdivisions of n-dimensional spaces and n-dimensional generalized maps. In: Proceedings of the fifth annual Symposium on Computational Geometry, Saarbruchen, West Germany, pp. 228–236 (1989)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Carine Grasset-Simon
    • 1
  • Guillaume Damiand
    • 1
  • Pascal Lienhardt
    • 1
  1. 1.SIC, FRE-CNRS 2731Université de Poitiers, bât. SP2MIFuturoscope ChasseneuilFrance

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