Equicontinuous random functions

Jean C. Serra

doi:10.1117/12.260395

1 January 1997 Equicontinuous random functions

Jean C. Serra

Author Affiliations +

Journal of Electronic Imaging, Vol. 6, Issue 1, (January 1997). https://doi.org/10.1117/12.260395

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 L_φ 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 L_φ 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 L_φ 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.

Citation Download Citation

Jean C. Serra "Equicontinuous random functions," Journal of Electronic Imaging 6(1), (1 January 1997). https://doi.org/10.1117/12.260395

Published: 1 January 1997

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