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


A new improved local Chan-Vese model
Proceedings of SPIE (March 03 2015)
Motion magnification using the Hermite transform
Proceedings of SPIE (December 21 2015)
Predictive motion estimation with global motion predictor
Proceedings of SPIE (January 17 2004)
VLSI Architectures For Image Filtering
Proceedings of SPIE (October 24 1988)
Nonseparable QMF Pyramids
Proceedings of SPIE (October 31 1989)
A new affine invariant method for image matching
Proceedings of SPIE (January 30 2012)
Nonlinear features in vernier acuity
Proceedings of SPIE (May 18 1999)

Back to Top