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Journal of Electronic Imaging

Equicontinuous random functions
Author(s): Jean C. Serra
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Paper Abstract

This paper proposes a class of random functions that models multidimensional scenes (microscopy, macroscopy, video sequences, etc.) in a particularly adequate way. In the triplet (Ω,σ,P) that defines a random function, the σ-algebra σ, here, is that introduced by G. Matheron in his theory of the upper (or lower) semi-continuous functions from a topological space E into R. On the other hand, the set Ω of the mathematical objects is the class Lφ of the equicontinuous functions of a given modulus, φ say, that map E, supposed to be metric, into R or (R)n. For a comprehensive member of metrics on R, class Lφ is a compact subset of the u.s.c. functions E→R, on which the topology reduces to that of the pointwise convergence. In addition, class Lφ is closed under the usual dilations, erosions and morphological filters, as well as for convolutions g such that ∫[g(dx)]=1. Examples of the soundness of the model are given.

Paper Details

Date Published: 1 January 1997
PDF: 9 pages
J. Electron. Imag. 6(1) doi: 10.1117/12.260395
Published in: Journal of Electronic Imaging Volume 6, Issue 1
Show Author Affiliations
Jean C. Serra, Ecole des Mines de Paris (France)

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