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On the Strong Property of Connected Open-Close and Close-Open Filters

  • Jose Crespo
  • Victor Maojo
  • José A. Sanandrés
  • Holger Billhardt
  • Alberto Muñoz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2301)

Abstract

This paper studies connectivity aspects that arise in image operators that process connected components of an input image. The focus is on morphological image analysis (i.e., on increasing image operators), and, in particular, on a robustness property satisfied by certain morphological filters that is denominated the strong-property. The behavior of alternating compositions of openings and closings will be investigated under certain assumptions, especially using a connected component preserving equation. A significant result is the finding that such an equation cannot guarantee the strong property of certain connected alternating filters. The class of openings and closings by reconstruction should therefore be defined to avoid such situations.

Keywords

Mathematical Morphology Image Operator Strong Property Central Pore Robustness Property 
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.

References

  1. 1.
    Serra, J.: Mathematical Morphology. Volume I. London: Academic Press (1982)zbMATHGoogle Scholar
  2. 2.
    Serra, J., ed.: Mathematical Morphology. Volume II: theoretical advances. London: Academic Press (1988)Google Scholar
  3. 3.
    Matheron, G.: Random Sets and Integral Geometry. New York: Wiley (1975)zbMATHGoogle Scholar
  4. 4.
    Heijmans, H.: Morphological Image Operators (Advances in Electronics and Electron Physics; Series Editor: P. Hawkes). Boston: Academic Press (1994)Google Scholar
  5. 5.
    Birkhoff, G.: Lattice Theory. American Mathematical Society, Providence (1984)Google Scholar
  6. 6.
    Maragos, P., Schafer, R.: Morphological filters—part I: Their set-theoretic analysis and relations to linear-shift-invariant filters. IEEE Trans. Acoust. Speech Signal Processing 35 (1987) 1153–1169CrossRefMathSciNetGoogle Scholar
  7. 7.
    Serra, J., Salembier, P.: Connected operators and pyramids. In: Proceedings of SPIE, Non-Linear Algebra and Morphological Image Processing, San Diego. Volume 2030. (1993) 65–76Google Scholar
  8. 8.
    Crespo, J., Serra, J., Schafer, R.: Image segmentation using connected filters. In Serra, J., Salembier, P., eds.: Workshop on Mathematical Morphology. (1993) 52–57Google Scholar
  9. 9.
    Crespo, J., Serra, J., Schafer, R.: Theoretical aspects of morphological filters by reconstruction. Signal Processing 47 (1995) 201–225CrossRefGoogle Scholar
  10. 10.
    Heijmans, H.: Connected morphological operators for binary images. Computer Vision and Image Understanding 73 (1999) 99–120zbMATHCrossRefGoogle Scholar
  11. 11.
    Crespo, J., Schafer, R., Serra, J., Gratin, C., Meyer, F.: The flat zone approach: A general low-level region merging segmentation method. Signal Processing 62 (1997) 37–60zbMATHCrossRefGoogle Scholar
  12. 12.
    Crespo, J., Maojo, V.: Shape preservation in morphological filtering and segmentation. In: XII Brazilian Symposium on Computer Graphics and Image Processing, IEEE Computer Society Press, SIBGRAPI 99. (1999) 247–256Google Scholar
  13. 13.
    Crespo, J., Schafer, R.: Locality and adjacency stability constraints for morphological connected operators. Journal of Mathematical Imaging and Vision 7 (1997) 85–102zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Matheron, G.: Filters and lattices. In Serra, J., ed.: Mathematical Morphology Volume II: theoretical advances. London: Academic Press (1988) 115–140Google Scholar
  15. 15.
    Salembier, P., Serra, J.: Flat zones filtering, connected operators, and filters by reconstruction. IEEE Transactions on Image Processing 4 (1995) 1153–1160CrossRefGoogle Scholar
  16. 16.
    Soille, P.: Morphological Image Analysis: Principles And Applications. Springer-Verlag Berlin, Heidelberg, New York (1999)zbMATHGoogle Scholar
  17. 17.
    Crespo, J., Maojo, V.: New results on the theory of morphological filters by reconstruction. Pattern Recognition 31 (1998) 419–429CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jose Crespo
    • 1
  • Victor Maojo
    • 1
  • José A. Sanandrés
    • 1
  • Holger Billhardt
    • 1
  • Alberto Muñoz
    • 2
  1. 1.Laboratorio de Inteligencia Artificial Facultad de InformáticaUniversidad Politécnica de MadridBoadilla del Monte (Madrid)Spain
  2. 2.Departamento de RadiodiagnósticoMadrid

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