Membership function construction for interval-valued fuzzy sets with application to Gaussian noise reduction

Models based on interval-valued fuzzy sets make it possible to manage numerical and spatial uncertainty in grey-scale values of image pixels. In a recent paper, we proposed a method that links the ultrafuzziness index (that makes it possible to take into account some uncertainty, like noise, and inherent to image capture) with impulse noise removal. However, computing with interval-valued fuzzy sets requires assigning their membership functions (MFs). The present article proposes a novel method for the generation of membership functions, based on image histogram, to remedy that drawback and it complements our previous study. The performance of the method is evaluated by applying this technique to the particular case of Gaussian noise detection and reduction, which remains a crucial issue for image processing. Experimental results have demonstrated that the proposed method leads to interval-valued fuzzy filters that are comparable with some well-known conventional and fuzzy filters, especially in the case of iterative filtering methods. Image details are preserved while reducing Gaussian noise, and the link between image noise and interval-valued fuzzy sets is thus verified. The main advantage of the proposed technique is to use basic image information, namely an image histogram, which is easy to obtain.