Abstract
A novel signal representation using fuzzy mathematical morphology is developed. We take advantage of the optimum fuzzy fitting and the efficient implementation of morphological operators to extract geometric information from signals. The new representation provides results analogous to those given by the polynomial transform. Geometrical decomposition of a signal is achieved by windowing and applying sequentially fuzzy morphological opening with structuring functions. The resulting representation is made to resemble an orthogonal expansion by constraining the results of opening to equate adapted structuring functions. Properties of the geometric decomposition are considered and used to calculate the adaptation parameters. Our procedure provides an efficient and flexible representation which can be efficiently implemented in parallel. The application of the representation is illustrated in data compression and fractal dimension estimation temporal signals and images.
Highlights
Signal representation is an area of great interest in the signal and image processing
In developing the Fuzzy Morphological Polynomial (FMP) representation [12], we take the advantage of polynomial transform idea [5, 6], the morphological decomposition recursive procedures [8,9,10] and using multiple structuring functions [11] overcoming some of the problems mentioned before
An amplitude index (AI) of a geometrical structuring function μki,j (m, n) of size M × N is defined by the summation of amplitude at every pixel as AI i, j =
Summary
Signal representation is an area of great interest in the signal and image processing. We propose fuzzy mathematical morphology [7] to represent one- and two-dimensional signals. Similar to morphological operator, are nonlinear but well suited for efficient implementation in parallel They allow to extract geometrical information in signals by appropriate transformations. In developing the Fuzzy Morphological Polynomial (FMP) representation [12], we take the advantage of polynomial transform idea [5, 6], the morphological decomposition recursive procedures [8,9,10] and using multiple structuring functions [11] overcoming some of the problems mentioned before. As developed in [13], is based on the concept of fitting a structuring element to the signal. We develop the one-dimensional FMP representation based on a recursive geometric decomposition for a given signal membership function. Some of the results in this paper were presented before in [12]
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