In this paper, a class of weighted vector directional filters (WVDFs) based on the selection of
the output sample from the multichannel input set is analyzed and optimized. The WVDF …

The LULU operators for sequences, that is Ln, Un and their compositions, are extended to
multidimensional arrays in a way which preserves their essential properties, eg, consistent …

For practical purposes median smoothers have often been considered the basic
components for the construction of simple non-linear smoothers for removing impulsive …

Flat morphological operators, also called stack filters, are the natural extension of increasing
set operators to grey-level images. The latter are usually modeled as functions E → T, where …

We consider morphological operations on images whose pixel values are considered as
labels without ordering between them, except for a least element⊥(meaning no label) and a …

Publisher Summary To many interested observers from fields near to image processing, the
need for mathematics of vision, as articulated by Meyer (1993), is convincing. This is …

The LULU operators, L n and U n, are smoothers, that is they smooth data received as a
signal. They are nonlinear and this nonlinearity makes them more robust but also more …

By a novel use of distributivity we obtain polynomial time algorithms to decide whether or not
a given min–max operator (stack filter) is idempotent or not. Several properties related to …

Stack filters are nonlinear filters used for image processing (examples: median filters, order
statistics). In the translation-invariant case a stack filter is determined by a positive Boolean …

This monograph details the author's most important contributions to the rapidly growing field
of nonlinear noise reduction in color images. Its content is structured into seven Chapters …