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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Matheron representation theorem for gray-scale morphological filters


Author: G. Crombez
Journal: Proc. Amer. Math. Soc. 108 (1990), 795-799
MSC: Primary 60D05; Secondary 68U10, 94A12
MathSciNet review: 1000325
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Abstract: We present a new proof of the Matheron representation theorem for gray-scale morphological filters, without using either the representation theorem for subsets of the plane or the umbra transform.


References [Enhancements On Off] (What's this?)

  • [1] G. Crombez, Group theoretical methods in gray-scale mathematical morphology, (preprint).
  • [2] C. R. Giardina and E. R. Dougherty, Morphological methods in image and signal processing, Prentice Hall, Englewood Cliffs, New Jersey, 1988.
  • [3] G. Matheron, Random sets and integral geometry, John Wiley\thinspace&\thinspace Sons, New York-London-Sydney, 1975. With a foreword by Geoffrey S. Watson; Wiley Series in Probability and Mathematical Statistics. MR 0385969 (52 #6828)
  • [4] J. Serra, Image analysis and mathematical morphology, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1984. English version revised by Noel Cressie. MR 753649 (87d:68106)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1000325-9
PII: S 0002-9939(1990)1000325-9
Keywords: Mathematical morphology, image analysis, translation invariant mapping
Article copyright: © Copyright 1990 American Mathematical Society