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