Neighborhood Base Matched Morphological Filters: Cross-fertilization with Linear Lowpass Filtering

The manuscript introduces Neighborhood Base Matched Morphological Filters (NBM-MF) by fusion of linear lowpass filtering process into the mathematical morphology structure of the operators. This internal cross-fertilization is gained via the deployment of a dynamic structuring element that adaptively matches itself to the neighborhood base of the signal/image. The neighborhood base is indeed the base-line/base-surface of the signal/image approximated by linear lowpass filtering called hereafter 'base'. This cross-fertilization enables NBM-MF for modifying geometrical features of the signal/image more adaptively to the local geometry, and thereof having stronger filtering efficiency and less side effects of disturbing the original structure of the signal/image. The morphological smoothing is deployed for the efficiency evaluation of NBM-MF compared to the classical MF. Using three different numerical evaluation criteria, the morphological smoothing of signals with different noise and different base structure approves the higher efficiency of NBM-MF with respect to the classical one.