Fuzzy LUM filters [image denoising/enhancement applications]

Fuzzy ranks are a component of fuzzy ordering theory developed to incorporate sample spread information into sample ranking. In this paper, the well-known lower-upper-middle (LUM) filters are generalized by utilizing the fuzzy ranks, which is called fuzzy LUM (F-LUM) filters. We develop the statistical and deterministic properties of the F-LUM filters and present their performance in image denoising and enhancing applications. As shown by the experimental results, the F-LUM filters inherit the simplicity and versatility of the LUM filters such that they can perform signal smoothing, sharpening and outlier rejection using a single filter structure, while having great improvement in detail preservation and robustness to noise.