Sufficient Conditions for General 2D Operators to Preserve Topology

  • Péter Kardos
  • Kálmán Palágyi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8466)


An important requirement for various applications of binary image processing is to preserve topology. This issue has been earlier studied for two special types of image operators, namely, reductions and additions, and there have been some sufficient conditions proposed for them. In this paper, as an extension of those earlier results, we give novel sufficient criteria for general operators working on 2D pictures.


Digital Topology Binary Operators Topology Preservation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hall, R.W.: Parallel connectivity–preserving thinning algorithm. In: Kong, T.Y., Rosenfeld, A. (eds.) Topological Algorithms for Digital Image Processing, Machine Intelligence and Pattern Recognition, vol. 19, pp. 145–179. Elsevier Science (1996)Google Scholar
  2. 2.
    Hall, R.W., Kong, T.Y., Rosenfeld, A.: Shrinking binary images. In: Kong, T.Y., Rosenfeld, A. (eds.) Topological Algorithms for Digital Image Processing, Machine Intelligence and Pattern Recognition, vol. 19, pp. 31–98. Elsevier Science (1996)Google Scholar
  3. 3.
    Herman, G.T.: Geometry of digital spaces. Birkhäuser, Boston (1998)Google Scholar
  4. 4.
    Kong, T.Y.: Minimal non-simple and minimal non-cosimple sets in binary images on cell complexes. In: Kuba, A., Nyúl, L.G., Palágyi, K. (eds.) DGCI 2006. LNCS, vol. 4245, pp. 169–188. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Kong, T.Y.: On topology preservation in 2-d and 3-d thinning. International Journal of Pattern Recognition and Artificial Intelligence 9, 813–844 (1995)CrossRefGoogle Scholar
  6. 6.
    Kong, T.Y., Rosenfeld, A.: Digital topology: Introduction and survey. Computer Vision, Graphics, and Image Processing 48, 357–393 (1989)CrossRefGoogle Scholar
  7. 7.
    Lam, L., Lee, S.-W., Suen, C.Y.: Thinning methodologies – A comprehensive survey. IEEE Trans. Pattern Analysis and Machine Intelligence 14, 869–885 (1992)CrossRefGoogle Scholar
  8. 8.
    Kardos, P., Palágyi, K.: Sufficient conditions for topology preserving additions and general operators. In: Proc. 14th Int. Conf. Computer Graphics and Imaging, CGIM 2013, pp. 107–114. IASTED ACTA Press (2013)Google Scholar
  9. 9.
    Ma, C.M.: On topology preservation in 3D thinning. CVGIP: Image Understanding 59, 328–339 (1994)CrossRefGoogle Scholar
  10. 10.
    Marchand-Maillet, S., Sharaiha, Y.M.: Binary digital image processing – A discrete approach. Academic Press (2000)Google Scholar
  11. 11.
    Németh, G., Kardos, P., Palágyi, K.: 2D parallel thinning and shrinking based on sufficient conditions for topology preservation. Acta Cybernetica 20, 125–144 (2011)zbMATHGoogle Scholar
  12. 12.
    Németh, G., Kardos, P., Palágyi, K.: Thinning combined with iteration-by-iteration smoothing for 3D binary images. Graphical Models 73, 335–345 (2011)CrossRefGoogle Scholar
  13. 13.
    Palágyi, K., Németh, G., Kardos, P.: Topology Preserving Parallel 3D Thinning Algorithms. In: Brimkov, V.E., Barneva, R.P. (eds.) Digital Geometry Algorithms. Theoretical Foundations and Applications to Computational Imaging, pp. 165–188. Springer (2012)Google Scholar
  14. 14.
    Ronse, C.: Minimal test patterns for connectivity preservation in parallel thinning algorithms for binary digital images. Discrete Applied Mathematics 21, 67–79 (1988)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Rosenfeld, A.: Arcs and curves in digital pictures. Journal of the ACM 20(1), 81–87 (1973)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Rosenfeld, A.: Digital topology. The American Mathematical Monthly 86(8), 621–630 (1979)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Serra, J.: Image Analysis and Mathematical Morphology. Academic Press (1982)Google Scholar
  18. 18.
    Suen, C.Y., Wang, P.S.P.: Thinning Methodologies for Pattern Recognition. Series in Machine Perception and Artificial Intelligence, vol. 8. World Scientific, Singapore (1994)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Péter Kardos
    • 1
  • Kálmán Palágyi
    • 1
  1. 1.Department of Image Processing and Computer GraphicsUniversity of SzegedHungary

Personalised recommendations