Fibonacci thresholding: signal representation and morphological filters

Abstract

A new weighted thresholding concept is presented, which is used for the set-theoretical representation of signals, the producing new signals containing a large number of key features that are in the original signals and the design new morphological filters. Such representation maps many operations of non binary signal and image processing to the union of the simple operations over the binary signals and images. The weighted thresholding is invariant under the morphological transformations, including the basic ones, erosion and dilation. The main idea of using the weighted thresholding is in the choice of the special level of thresholding on which we can concentrate all our attention for the future processing. Together with arithmetical thresholding the so-called Fibonacci levels are chosen because of many interesting properties; one of them is the effective decomposition of the median filter. Experimental results show that the Fibonacci thresholding is much promised and can be used for many applications, including the image enhancement, segmentation, and edge detection.

On a Lexical Vector in Teaching English Grammar

“…For positive numbers 𝑎 and 𝑏, this ratio equals to 𝛷 = 𝑏/𝑎 = (𝑏 + 𝑎)/𝑏, if 𝑏 > 𝑎. The number 𝛷 was found in proportions of parts in construction of Egyptian pyramids [3], in arts [4]- [6], in fashion [7], in medicine [8,9], face detection [10], image enhancement [11,12], and many applications in engineering.…”