Fuzzy morphological polynomial image representation

  • Authors:

  • Chin-Pan Huang;Luis F. Chaparro

  • Affiliations:

  • Department of Computer and Communication Engineering, Ming Chuan University, Taoyuan, Taiwan;Department of Electrical and Computer Engineering, University of Pittsburgh, Pittsburgh, PA

  • Venue:
  • EURASIP Journal on Advances in Signal Processing - Special issue on time-frequency analysis and its applications to multimedia signals
  • Year:
  • 2010

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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.