An application of fuzzy relations to image enhancement

Abstract

When images are converted from one form to another they are subject to nonlinear transformations that reduce the output quality. This paper presents an image enhancement technique based on fuzzy relations that can be applied to improve the appearance of these images.

A grey-scale image I with M rows and N columns is viewed as a weighted relation from a set X with M elements into a set Y with N elements with g(x, y) representing the grey-value at location (x, y) in I. An appropriate choice of two thresholds corresponding to pixels close to black and white pixels is made which partitions the image into crisp and fuzzy pixels. The fuzzy pixels correspond to pixels which are either black or white with a certain degree of membership between 0 and 1. The original image is transformed into an enhanced image by forming its dual complement. This is achieved by first constructing fuzzy sets σ_x and σ_y on X and Y respectively and applying these fuzzy sets to manipulate only the fuzzy pixels in I. After the entire transformation, the maximally fuzzy pixels, that is, pixels with membership value equal to $\text{1}\text{2}$, get enhanced towards either black or white, depending on the neighborhood pixels of the segment to which they belong. The performance of the proposed technique is demonstrated on several images. Enhanced images obtained using other techniques are also presented for comparison.