An O(K)-time implementation of fuzzy integral filters on an enhanced mesh processor array

Fuzzy integrals as image filters, even with respect to a restrictive fuzzy measure, generalize linear filters such as the averaging filter, morphological filters such as the dilation and the erosion, and order statistic filters such as the median filter. Fuzzy integral filters use fuzzy measures to model ambiguity about each pixel in its neighborhood to enhance an image. However, fuzzy integral filters are computationally intensive. For each pixel, a fuzzy integral filter first sorts all the pixels in its neighborhood according to their values and then takes the ordered weighted sum or maximum with respect to an appropriate fuzzy measure. For an n×n image and a √K×√K(=K) neighborhood, the filter with respect to a fuzzy measure that only depends on set cardinalities takes O(n² K log K) time, if implemented on a serial computer. Even combining the moving window technique with a balanced search tree data structure, we can only reduce the time to O(n² K). To achieve real-time filtering performance, we need to employ parallel processing techniques. The SIMD mesh architecture is considered as a natural parallel architecture for image processing, since it directly mirrors image data structures and can be efficiently implemented in hardware. However, fuzzy integral filters require more parallelism within processing elements (PEs) for fast determination of the order statistics of pixels. In this paper, we consider enhancing the PEs of an SIMD mesh computer with comparators and counters to efficiently implement fuzzy integral filters. For the neighborhood of K pixels, we augment the K registers of each PE with K comparators and K counters to speed the sorting process. For an n×n image on an n×n enhanced mesh computer, a fuzzy integral filter of size K with respect to a fuzzy measure that only depends on set cardinalities takes O(K) time, which is optimal