Morphological pseudoconvolutions: One-parameter families of derived filters with increased invariant classes
Academic Article
Overview
Identity
Additional Document Info
Other
View All
Overview
abstract
The present paper introduces a digital gray-scale morphological filtering technique that is based on postfiltering a given filter so the invariant class of the new filter is larger than the invariant class of the original filter. More specifically, the invariant class of the new filter contains the original invariant class together with all signals whose variation is below a chosen threshold. The postfiltering includes a single erosion and a single dilation by a one-parameter structuring element, the choice of parameter determining the resulting invariant class. While the methodology is quite general, the two applications considered pertain to moving averages with nonnegative weights and moving medians, both of which are morphological filters. Both suppress noise in a signal and each possesses specific advantages and disadvantages. In brief, means tend to give better noise suppression while blurring edges, whereas medians preserve edges, while at the same time flattening small background variation in the underlying signal. The new one-parameter family of filters derived from moving averages are called pseudomeans. The filters derived from medians are called pseudomedians. Both preserve uncorrupted low background variation, as well as steps. Because they preserve small variation while at the same time behaving like the original filters, both filters are especially effective when the noise occurs in bursts, rather than uniformly across the signal. 1992 Birkhuser.
