Image Processing on Fuzzy Near Sets

Fuzzy image processing involves various fuzzy approaches. These fuzzy approaches help in understanding and processing of images as fuzzy sets. Mathematical morphology is used for analysing the shapes and forms of the objects in images. In morphological methods structuring elements are applied to an input image which creates an output image of the same size. The size and shape of the neighbourhood is chosen in such a way that a morphological operation relating to different shapes in the input image is constructed. In this paper the pixel values of an image are converted to fuzzy near membership values and the corresponding image is found. Using the fuzzy near membership image, gray and binary images are formed using MATLAB. Mathematical morphology operations dilation, erosion, opening and closing for different structuring elements such as line, square, diamond, sphere, disk, cube, neighbourhood, octagon and rectangle are performed for fuzzy membership and binary images. Taking dilation and opening as upper approximations, erosion and closing as lower approximations, the exact measures are calculated for different structuring elements and the corresponding images formed. It is found that the exact measure for the structuring element neighbourhood of fuzzy near membership and binary images are exactly equal. The corresponding images are also exactly similar.