Fuzzy Integral Filters: Properties and Parallel Implementation

Fuzzy integrals as image filters provide a standard representational form which generalize linear filters such as the averaging filter, morphological filters such as flat dilations and erosions, and order statistic filters such as the median filter. However, fuzzy integral filters are computationally intensive. Computing the output value obtained by fuzzy integral filtering at a point involves sorting all the pixels in a neighborhood of the point according to their values and then computing ordered weighted sum or maximum with respect to an appropriate fuzzy measure. In this paper we discuss some properties of fuzzy integral filters and describe a method for enhancing the processing elements of single instruction, multiple data (SIMD) mesh computers with comparators and counters to efficiently implement fuzzy integral filters.

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