Introduction to a simple yet effective Two-Dimensional Fuzzy Smoothing Filter

Annihilation or reduction of each kind of noise blended in correct data signals is a field that has attracted many researchers. It is a fact that fuzzy theory presents full capability in this field. Fuzzy filters are often strong in smoothing corrupted signals, whereas they have simple structures. In this paper, a new powerful yet simple fuzzy procedure is introduced for sharpness reduction in two-dimensional signals. It is indeed an extension of our previously published one-dimensional fuzzy smoothing filter. This procedure has been designed for annihilation of all unknown noises in two-dimensional corrupted signals, although works the best for impulse noise. The proposed method looks for \emph{sharp points} in the corrupted signal and then smoothes them out by \emph{sharing} their values with eight (or more) neighboring point values. Preservation of correct data in the corrupted signal is an important advantage of this method. To obtain experimental results of the proposed procedure, both color and black \& white images are used as the most common two-dimensional signals, and the results are compared with several other filters recently cited in the literature. Experimental results exhibit a high capability of our method in both numerical measures and visual inspection, preserving its simplicity. Finally, application of the proposed filter to socio-economic fields is presented using a demographic mixed data set to better illustrate original motivation for this idea.