Fuzzy integrals as a generalized class of order filters

Michel Grabisch

doi:10.1117/12.196709

30 December 1994 Fuzzy integrals as a generalized class of order filters

Michel Grabisch

Proceedings Volume 2315, Image and Signal Processing for Remote Sensing; (1994) https://doi.org/10.1117/12.196709
Event: Satellite Remote Sensing, 1994, Rome, Italy

Abstract

We introduce a new large class of filters similar to order filters, namely fuzzy integrals. Fuzzy integrals are a generalization of Lebesgue integral, and are defined with respect to a nonadditive measure. Fuzzy integrals can also be viewed as function processing filters, and appear to include a large class of known filters. We show that fuzzy integrals includes as particular case all linear filters, all order filters, and thus rank filters, the median, erosion, and dilation, whose properties of noise filtering are well known. In a second part, we give more insight into properties related to morphological filters, in an attempt to generalize results known for rank filters. Considering a gray level image as a fuzzy set, we extend the usual definition of dual filters with respect to complementation to any function processing filter. Based on this, we show that the dual of a fuzzy integral filter is the fuzzy integral filter with respect to the dual measure.

Citation Download Citation

Michel Grabisch "Fuzzy integrals as a generalized class of order filters", Proc. SPIE 2315, Image and Signal Processing for Remote Sensing, (30 December 1994); https://doi.org/10.1117/12.196709

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