An overview of the relationship between approximation theory and filtration

This refereed conference paper gives the mathematical foundations and generic definition for filtration that goes beyond the
usual definition of linear filters and includes exotic filters such as: morphological filters, robust filter, segmentation filters and
other non-linear filters. The relationship between filtration and the established theory of approximation is established. It shows
that although both fields use the same kind of mathematical objects they are used in different ways with different criteria of fit.
The results from this paper formed the basis of a recently published International Standard on filtration: the ISO/TS 16610
series.