Advertisement

A New Approach to Analyse Neighbourhood Relations in 2D Polygonal Networks

  • Lourenço Bandeira
  • Pedro Pina
  • José Saraiva
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5197)

Abstract

A new algorithm to identify the neighbours of polygons on 4-connected raster images of 2D polygonal networks is presented in this paper. It is mainly based on mathematical morphology operators and can be indistinctively applied to networks of tri and tetravalent nature (with three and four edges at each vertex, respectively). The algorithm is tested on a varied set of polygonal terrains occurring on the surface of Mars and its computational performance compared to other approaches.

Keywords

Fast algorithm mathematical morphology topology Mars 

References

  1. 1.
    Aboav, D.A.: The arrangement of grains in a polycrystal. Metallography 3(4), 383–390 (1970)CrossRefGoogle Scholar
  2. 2.
    Aboav, D.A.: Arrangement of cells in a net. Metallography 13(1), 43–58 (1980)CrossRefGoogle Scholar
  3. 3.
    Lantuéjoul, C.: La squelettisation et son application aux mesures topologiques des mosaïques polycristallines. Thése de doctorat. ENSMP, Paris (1978)Google Scholar
  4. 4.
    Lewis, F.T.: The correlation between cell division and the shapes and sizes of prismatic cells in the epidermis of Cucumis. Anatomical Record 38(3), 341–376 (1928)CrossRefGoogle Scholar
  5. 5.
    Lewis, F.T.: A comparison between the mosaic of polygons in a film of artificial emulsion and the pattern of simple epithelium in surface view (cucumber epidermis and human amnion). Anatomical Record 50(3), 235–265 (1931)CrossRefGoogle Scholar
  6. 6.
    Mangold, N.: High latitude patterned grounds on Mars: Classification, distribution and climatic control. Icarus 174(2), 336–359 (2005)CrossRefGoogle Scholar
  7. 7.
    Pina, P., Fortes, M.A., Selmaoui, N.: Geometrical and topological characterization of cork cells by digital image analysis. In: Maragos, P., Schafer, R.W., Butt, M.A. (eds.) Mathematical Morphology and its Applications to Image and Signal Processing, pp. 458–466. Kluwer Academic Publishers, Boston (1996)Google Scholar
  8. 8.
    Pina, P., Saraiva, J., Bandeira, L., Barata, T.: Identification of martian polygonal patterns using the dynamics of watershed contours. In: Campilho, A., Kamel, M. (eds.) ICIAR 2006. LNCS, vol. 4142, pp. 691–699. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Vincent, L.: Graphs and mathematical morphology. Signal Processing 16(4), 365–388 (1989)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Weaire, D.: Some remarks on the arrangement of grains in a polycrystal. Metallography 7(2), 157–160 (1974)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Lourenço Bandeira
    • 1
  • Pedro Pina
    • 1
  • José Saraiva
    • 1
  1. 1.CERENA-Centro de Recursos Naturais e Ambiente, Instituto Superior TécnicoLisboaPortugal

Personalised recommendations