Fuzzifying Images using Fuzzy Wavelet Denoising

Fuzzy connected filters were recently introduced as an extension of connected filters within the fuzzy set framework. They rely on the representation of the image gray levels by fuzzy quantities, which are suitable to represent imprecision usually contained in images. No robust construction method of these fuzzy images has been introduced so far. In this paper we propose a generic method to fuzzify a crisp image in order to explicitly take imprecision on grey levels into account. This method is based on the conversion of statistical noise present in an image, which cannot be directly represented by fuzzy sets, into a denoising imprecision. The detectability of constant gray level structures in these fuzzy images is also discussed.