Applications of the fuzzy metrics in image denoising and segmentation

In this paper, the problem of removing the image noise in color (RGB) images is addressed as well as the problem of the image segmentation. A new filter is created on the basis of the new fuzzy metric composed of two other fuzzy metrics with necessary characteristics for quality noise elimination in the image. In addition, the algorithm applied for image segmentation also uses the fuzzy metric, created of two other metrics that have the necessary characteristics for high-quality pixels segmentation, in the stage of deciding into which segment the pixel belongs. For this purpose, the concepts of fuzzy T-metrics and fuzzy S-metrics are presented, as well as numerous examples of fuzzy metrics used in applications. Also, the procedure for constructing new fuzzy metrics is introduced. Compared with the results obtained with the use of a VMF (vector median filter) the proposed method process is of higher sharpness level. Tests also showed better segmentation values using the fuzzy metric instead of the standard metric in the FCM algorithm