Advertisement

Simple Points and Generic Axiomatized Digital Surface-Structures

  • Sébastien Fourey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3322)

Abstract

We present a characterization of topology preservation within digital axiomatized digital surface structures (gads), a generic theoretical framework for digital topology introduced in [2]. This characterization is based on the digital fundamental group that has been classically used for that purpose. More briefly, we define here simple points within gads and give the meaning of the words: preserving the topology within gads.

Keywords

Simple Point Interior Vertex Unordered Pair Axiomatic Theory Adjacency Relation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bertrand, G.: Simple points, topological numbers and geodesic neighborhoods in cubics grids. Patterns Recognition Letters 15, 1003–1011 (1994)CrossRefGoogle Scholar
  2. 2.
    Fourey, S., Kong, T.Y., Herman, G.T.: Generic axiomatized digital surface-structures. Discrete Applied Mathematics 139, 65–93 (April 2004)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Fourey, S., Malgouyres, R.: Intersection number and topology preservation within digital surfaces. In: Proceedings of the Sixth International Workshop on Parallel Image Processing and Analysis (IWPIPA 1999), Madras, India, January 1999, pp. 138–158 (1999)Google Scholar
  4. 4.
    Fourey, S., Malgouyres, R.: Intersection number of paths lying on a digital surface and a new jordan theorem. In: Bertrand, G., Couprie, M., Perroton, L. (eds.) DGCI 1999. LNCS, vol. 1568, pp. 104–117. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  5. 5.
    Fourey, S., Malgouyres, R.: Intersection number and topology preservation within digital surfaces. Theoretical Computer Science 283(1), 109–150 (June 2002)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Fourey, S., Malgouyres, R.: A concise characterization of 3D simple points. Discrete Applied Mathematics 125(1), 59–80 (January 2003)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Herman, G.T.: Oriented surfaces in digital spaces. Graphical Models and Image Processing 55, 381–396 (1993)CrossRefGoogle Scholar
  8. 8.
    Herman, G.T.: Geometry of digital spaces. Birkhäuser, Basel (1998)zbMATHGoogle Scholar
  9. 9.
    Herman, G.T., Udupa, J.K.: Display of 3D discrete surfaces. In: Proceeddings of SPIE, vol. 283 (1983)Google Scholar
  10. 10.
    Khalimsky, E.D., Kopperman, R.D., Meyer, P.R.: Computer graphics and connected topologies on finite ordered sets. Topology and Its Applications 36, 1–17 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Kong, T.Y.: A digital fundamental group. Computers and Graphics 13, 159–166 (1989)CrossRefGoogle Scholar
  12. 12.
    Kong, T.Y.: On topology preservation in 2-d and 3-d thinning. International Journal of Pattern Recognition and Artificial Intelligence 9(5), 813–844 (1995)CrossRefGoogle Scholar
  13. 13.
    Kong, T.Y., Khalimsky, E.D.: Polyhedral analogs of locally finite topological spaces. In: Shortt, R.M. (ed.) General Topology and Applications: Proceedings of the 1988 Northeast Conference, pp. 153–164. Marcel Dekker, New York (1990)Google Scholar
  14. 14.
    Kong, T.Y., Roscoe, A.W., Rosenfeld, A.: Concepts of digital topology. Topology and Its Applications 46, 219–262 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Kong, T.Y., Rosenfeld, A.: Digital topology: introduction and survey. Computer Vision, Graphics and Image Processing 48, 357–393 (1989)CrossRefGoogle Scholar
  16. 16.
    Malgouyres, R., Lenoir, A.: Topology preservation within digital surfaces. Graphical Models (GMIP) 62, 71–84 (2000)CrossRefGoogle Scholar
  17. 17.
    Rosenfeld, A.: Connectivity in digital pictures. Journal of the Association for Computing Machinery 17, 146–160 (1970)zbMATHMathSciNetGoogle Scholar
  18. 18.
    Rosenfeld, A., Kong, T.Y., Nakamura, A.: Topology-preserving deformations of two-valued digital pictures. Graphical Models and Image Processing 60(1), 24–34 (January 1998)CrossRefGoogle Scholar
  19. 19.
    Rosenfeld, A., Kong, T.Y., Nakamura, A.: Topolgy-preserving deformations of two-valued digital pictures. Graphical Models and Image Processing 60(1), 24–34 (January 1998)CrossRefGoogle Scholar
  20. 20.
    Udupa, J.K.: Multidimensional digital boundaries. CVGIP: Graphical Models and Image Processing 56, 311–323 (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Sébastien Fourey
    • 1
  1. 1.GREYC Image – ENSICAENCaen cedexFrance

Personalised recommendations