Fibonacci thresholding, signal representation and morphological filters

This paper presents a new weighted thresholding concept for the set-theoretical representation of signals and design of new morphological filters. Such representation maps many operations of nonbinary signal and image processing into simple operations over the binary signals and images. The weighted thresholding is invariant relative to the morphological transforms, including the basic ones, erosion and dilation. The main idea of using the weighted thresholding is the right choice of special levels of thresholding for signal and image processing. Fibonacci thresholding is defined and decomposition of the median filter in terms of such thresholding is described.