Signal representation using fuzzy morphology and its applications
Luis F. Chaparro, Chin-Pan Huang · 1996
In this dissertation, new signal representations using fuzzy morphology are developed. We take advantage of the optimum fuzzy fitting and the efficient implementation of morphological operators to extract geometric information from the signal. The new signal representations provide results analogous to those given by the polynomial and the wavelet transforms. The fuzzy morphological polynomial (FMP) representation is based on fuzzy morphology and adaptive structuring functions. The geometrical decomposition is achieved by windowing and applying fuzzy morphological opening sequentially with each of the adaptive structuring elements aiming to fit the signal. The resulting representation is made to resemble an orthogonal expansion by constraining the results of opening to equal the adapted structuring functions. Properties of our geometrical decomposition are investigated and applied in calculating the adaptation parameters. Fuzzy morphological interpolation (FMI) algorithms are then developed. Based on this interpolation, the fuzzy morphological wavelet (FMW) representation, analogous to the wavelet transformation, is then obtained. The FMW allows perfect reconstruction, uses minimum and maximum operations instead of inner product or convolution. Properties of the FMI algorithm moreover permit us to develop fast pyramidal implementations for analysis and synthesis when the first and second order interpolators are used. We also extend our representations to two-dimensions. The representations are illustrated with one- and two-dimensional signals in data compression, fractal dimension estimation, and object recognition. The results show high performance and compare favorably with other commonly used methods.