Fuzzy logic and mathematical morphology: implementation by stack filters

Mathematical morphology has proven invaluable for signal/image processing. Fuzzy theory is enjoying great success in control and signal processing. We show that stack filters, which are already related to morphology, require slight modification to implement basic fuzzy operators. The article therefore provides a fast errorless method for implementation of basic fuzzy operations.

[1]  Sankar K. Pal,et al.  Fuzzy models for pattern recognition : methods that search for structures in data , 1992 .

[2]  Multiplies Sines.  A New Implementation of Generalized Order Statistic Filter by Threshold Decomposition , 1992 .

[3]  Jack Harris,et al.  FatBear: a nonarithmetic pico filter , 1993, Optics & Photonics.

[4]  Edward R. Dougherty,et al.  An introduction to morphological image processing , 1992 .

[5]  Edward J. Coyle,et al.  Threshold decomposition of multidimensional ranked order operations , 1985 .

[6]  Jaakko Astola,et al.  An Introduction to Nonlinear Image Processing , 1994 .

[7]  Edward J. Coyle,et al.  Stack filters , 1986, IEEE Trans. Acoust. Speech Signal Process..

[8]  J. Fitch,et al.  Median filtering by threshold decomposition , 1984 .

[9]  Jaakko Astola,et al.  Statistical properties of soft morphological filters , 1992, Electronic Imaging.

[10]  Michio Sugeno,et al.  Fuzzy systems theory and its applications , 1991 .

[11]  Petros Maragos,et al.  Morphological filters-Part II: Their relations to median, order-statistic, and stack filters , 1987, IEEE Trans. Acoust. Speech Signal Process..

[12]  Yong Hoon Lee,et al.  Threshold Boolean filters , 1994, IEEE Trans. Signal Process..

[13]  Tsu-Shuan Chang,et al.  A universal neural net with guaranteed convergence to zero system error , 1992, IEEE Trans. Signal Process..

[14]  David H. Eberly,et al.  The WMMR filters: a class of robust edge enhancers , 1993, IEEE Trans. Signal Process..