Fuzzy Metrics and Its Applications in Image Processing

This paper is a review of recent research, in which fuzzy metrics and their applications in image processing are studied. The notions of the fuzzy T-metric and the fuzzy S-metric are presented, after which, examples of known fuzzy metrics are provided, along with theorems that enable algorithms to develop new metrics. Two applications of fuzzy metrics in image processing are illustrated: Image filtering and Copy-move forgery detection. Image filtering reduces the amount of noise, while maintaining satisfactory image quality. The aim was to improve the sharpness and quality of the image, measured by the image quality indices UIQI and CPBD. It is illustrated that the image filtered with this modified algorithm has better quality and greater sharpness than images filtered with the median filter. The fuzzy metric parameters that produce images with the best quality and sharpness are determined experimentally. The digital image falsification obtained by copying and pasting part of the original image into another part of the same image is also considered. Copy-move forgery detection (CMFD) is one of the methods used to detect such forgeries in images. A cluster algorithm that successfully solves this problem is presented.