Equicontinuous functions: a model for mathematical morphology (Invited Paper)

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Abstract
The classes of the equicontinuous functions from a metric space E into an ecart lattice T offer a remarkably consistent theoretical framework to morphological operations. It is proved that in the case of robust lattices, they are closed under sup and inf, with exceptional properties of continuity in addition. Special attention is paid to the cases when T is totally ordered (e.g., R or Z), and to the (finite or not) products of this case, i.e., to multispectral and/or motion images modelling.

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