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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Matheron representation theorem for gray-scale morphological filters
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by G. Crombez PDF
Proc. Amer. Math. Soc. 108 (1990), 795-799 Request permission

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
    G. Crombez, Group theoretical methods in gray-scale mathematical morphology, (preprint). C. R. Giardina and E. R. Dougherty, Morphological methods in image and signal processing, Prentice Hall, Englewood Cliffs, New Jersey, 1988.
  • G. Matheron, Random sets and integral geometry, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York-London-Sydney, 1975. With a foreword by Geoffrey S. Watson. MR 0385969
  • J. Serra, Image analysis and mathematical morphology, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1984. English version revised by Noel Cressie. MR 753649
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 108 (1990), 795-799
  • MSC: Primary 60D05; Secondary 68U10, 94A12
  • DOI: https://doi.org/10.1090/S0002-9939-1990-1000325-9
  • MathSciNet review: 1000325