Morphological filters: Statistics and further syntactic properties

Mathematical morphology has recently been introduced as a powerful tool for studying the geometrical properties of signals and systems. These techniques have been applied very successfully to the smoothing of noisy data. In this paper, we first derive some new mathematical morphology results for function and set processing (FSP) systems. Using these results we derive several statistical results for the (FSP) morphological filtering of random signals, by deriving probabilistic mappings between input and output signals. Finally, we introduce a two-dimensional filter for image restoration which has desirable structure preserving properties.