No abstract

Image filtering, which removes or reduces noises from the contaminated images, is an important task in image processing. This paper presents a novel approach to the problem of noise reduction for gray-scale images. The proposed technique is able to remove the noise component, while adapting itself to the local noise intensity. In this way, the proposed algorithm can be considered as a modification of the median filter driven by fuzzy membership functions. Experimental results are compared to static median filter by numerical measures and visual inspection. As was expected, the new filter shows better performances.

The fuzzy topological space was introduced by Dip in 1999 depending on the notion of fuzzy spaces. Dip’s approach helps to rectify the deviation in some definitions of fuzzy subsets in fuzzy topological spaces. In this paper, further definitions, and theorems on fuzzy topological space fill the lack in Dip’s article. Different types of fuzzy topological space on fuzzy space are presented such as co-finite, co-countable, right and left ray, and usual fuzzy topology. Furthermore, boundary, exterior, and isolated points of fuzzy sets are investigated and illustrated based on fuzzy spaces. Finally, separation axioms are studied on fuzzy spaces