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Mathematical morphology and convolutions
Author(s) -
Mazille J. E.
Publication year - 1989
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1111/j.1365-2818.1989.tb02902.x
Subject(s) - mathematical morphology , structuring element , convolution (computer science) , thresholding , weighting , structuring , euclidean geometry , convolution theorem , set (abstract data type) , algorithm , computer science , mathematics , matrix (chemical analysis) , geometry , mathematical analysis , image processing , artificial intelligence , fourier transform , image (mathematics) , physics , fourier analysis , artificial neural network , programming language , finance , fractional fourier transform , economics , materials science , composite material , acoustics
SUMMARY The transforms of mathematical morphology may be generated by convolutions followed by thresholdings. Furthermore, the convolution‐thresholding pair may generalize mathematical morphology in three directions thanks to adjustments of the thresholding level, weighting of the coefficients of the convolution matrix and iterations. This leads to a wide set of non‐linear operators and structuring elements, including powerful directional transforms and an accurate iterative approach of a circular structuring element of any size and thus to a good approximation of the Euclidean distance.