Original Articles

Fully Trend Preserving Operators

Published in: Quaestiones Mathematicae
Volume 27 , issue 3 , 2004 , pages: 217–229

DOI: 10.2989/16073600409486096

Author(s): C.H. Rohwer

Keywords: LULU-OPERATORS , MATHEMATICAL MORPHOLOGY , LOCAL MONOTONICITY , VARIATION PRESERVATION , FULL TREND PRESERVATION , SMOOTHING , NON-LINEAR MULTIRESOLUTION DECOMPOSITION

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Abstract

The concept of fully trend preserving (ftp) operators on sequences was introduced to prove variation preservation on the outputs of LULU-separators. It turns out that this property is central in further analysis of compositions of LULU-smoothers, and other smoothers. Several important results follow, amongst them the co-idempotence of a large class of smoothers. This has been an unresolved problem up to now.

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