The Important Properties and Applications of the Adaptive Weighted Fuzzy Mean Filter

The important properties and applications of the adaptive weighted fuzzy mean (AWFM) filter are presented in this paper. AWFM is an extension of the weighted fuzzy mean (WFM) filter to overcome the drawback of WFM in fine signal preservation. It not only preserves the high performance of WFM on heavy additive impulse noise, but also improves the efficiency of WFM on removing light additive impulse noise. Some deterministic and statistical properties of the AWFM filter are analyzed, and the main characteristic of the AWFM filter that maps the input signal space into a root signal space, where a root signal is an invariant signal to the filter, is also discussed. Compared with the other filters, AWFM exhibits better performance in the criteria of mean absolute error and mean square error. On the subjective evaluation of those filtered images, AWFM also results in a higher quality of global restoration.