Filtering

  • Pierre Soille

Abstract

In signal processing, a filter is usually defined as a linear, shift-invariant operation.

Keywords

Attenuation Convolution Deconvolution Acoustics Lester 

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Bibliographical notes and references

  1. Crespo, J. and Maojo, V. (1998), ‘New results on the theory of morphological filters by reconstruction’, Pattern Recognition 13 (4), 419–429.CrossRefGoogle Scholar
  2. Crespo, J., Serra, J. and Schafer, R. (1995), ‘Theoretical aspects of morphological filters by reconstruction’, Signal Processing 47, 201–225.CrossRefGoogle Scholar
  3. Harvey, N. and Marshall, S. (1996), ‘The use of genetic algorithms in morphological filter design’, Signal Processing: Image Communication 8 (1), 55–72.CrossRefGoogle Scholar
  4. Heijmans, H. (1996), ‘Self-dual morphological operators and filters’, Journal of Parallel and Distributed Computing 6, 15–36.MathSciNetGoogle Scholar
  5. Heijmans, H. (1997), ‘Composing morphological filters’, IEEE Transactions on Image Processing 6 (5), 713–724.CrossRefGoogle Scholar
  6. Jochems, T. (1994), Morphologie mathématique appliquée au contrôle industriel de pièces coulées, PhD thesis, Ecole des Mines de Paris.Google Scholar
  7. Jochems, T. and Préjean-Lefèvre, V. (1993), ‘Mathematische Morphologie in der Praxis: Konstruktion eines Algorithmus für die Erkennung von Produktionsfehlern in Turbinenschaufeln’, Vision 6 Voice Magazine 7 (1), 8–15.Google Scholar
  8. Kraft, P., Harvey, N. and Marshall, S. (1997), ‘Parallel genetic algorithms in the optimization of morphological filters: a general design tool’, Journal of Electronic Imaging 6 (4), 504–516.CrossRefGoogle Scholar
  9. Kramer, H. and Bruckner, J. (1975), ‘Iterations of non-linear transformations for enhancement on digital images’, Pattern Recognition 7, 53–58.MathSciNetMATHCrossRefGoogle Scholar
  10. Lester, J., Brenner, J. and Selles, W. (1980), ‘Local transforms for biomedical image analysis’, Computer Graphics and Image Processing 13, 17–30.CrossRefGoogle Scholar
  11. Maragos, P. and Schafer, R. (1987), ‘Morphological filters’, IEEE Transactions on Acoustics, Speech and Signal Processing 35 (8), 1153–1183.MathSciNetCrossRefGoogle Scholar
  12. Matheron, G. (1988), Filters and lattices, in J. Serra, ed., ‘Image analysis and mathematical morphology. Volume 2: theoretical advances’, Academic Press, chapter 6, pp. 115–140.Google Scholar
  13. Meyer, F. and Serra, J. (1989a), ‘Contrasts and activity lattice’, Signal Processing 16, 303–317.MathSciNetCrossRefGoogle Scholar
  14. Meyer, F. and Serra, J. (1989b), Filters: from theory to practice, in ‘Acta Stereologica’, Vol. 8/2, Freiburg im Breisgau, pp. 503–508.Google Scholar
  15. Peters, R. (1995), ‘A new algorithm for image noise reduction using mathematical morphology’, IEEE Transactions on Image Processing 4 (5), 554–567.CrossRefGoogle Scholar
  16. Salembier, P. (1992), ‘Structuring element adaptation for morphological filters’, Journal of Visual Communication and Image Representation 3 (2), 115–136.CrossRefGoogle Scholar
  17. Serra, J. (1988a), Alternating sequential filters, in J. Serra, ed., ‘Image analysis and mathematical morphology. Volume 2: theoretical advances’, Academic Press, chapter 10, pp. 203–214.Google Scholar
  18. Serra, J. (1988b), The centre and self-dual filtering, in J. Serra, ed., ‘Image analysis and mathematical morphology. Volume 2: theoretical advances’, Academic Press, chapter 8, pp. 159–180.Google Scholar
  19. Serra, J. (1988c), Introduction to morphological filters, in J. Serra, ed., ‘Image analysis and mathematical morphology. Volume 2: theoretical advances’, Academic Press, chapter 5, pp. 101–114.Google Scholar
  20. Serra, J. (1994), ‘Morphological filtering: an overview’, Signal Processing 38 (1), 311.CrossRefGoogle Scholar
  21. Serra, J. and Vincent, L. (1992), ‘An overview of morphological filtering’, Circuits Systems Signal Process 11 (1), 47–108.MathSciNetMATHCrossRefGoogle Scholar
  22. Sternberg, S. (1986), ‘Grayscale morphology’, Computer Graphics and Image Processing 35, 333–355.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Pierre Soille
    • 1
  1. 1.Silsoe Research InstituteSilsoe BedfordshireUK

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