An Interval Type-2 Fuzzy Approach to Automatic PDF Generation for Histogram Specification

Image enhancement plays an important role in several application in the field of computer vision and image processing. Histogram specification (HS) is one of the most widely used techniques for contrast enhancement of an image, which requires an appropriate probability density function for the transformation. In this paper, we propose a fuzzy method to find a suitable PDF automatically for histogram specification using interval type - 2 (IT2) fuzzy approach, based on the fuzzy membership values obtained from the histogram of input image. The proposed algorithm works in 5 stages which includes - symmetric Gaussian fitting on the histogram, extraction of IT2 fuzzy membership functions (MFs) and therefore, footprint of uncertainty (FOU), obtaining membership value (MV), generating PDF and application of HS. We have proposed 4 different methods to find membership values - point-wise method, center of weight method, area method, and karnik-mendel (KM) method. The framework is sensitive to local variations in the histogram and chooses the best PDF so as to improve contrast enhancement. Experimental validity of the methods used is illustrated by qualitative and quantitative analysis on several images using the image quality index - Average Information Content (AIC) or Entropy, and by comparison with the commonly used algorithms such as Histogram Equalization (HE), Recursive Mean-Separate Histogram Equalization (RMSHE) and Brightness Preserving Fuzzy Histogram Equalization (BPFHE). It has been found out that on an average, our algorithm improves the AIC index by 11.5% as compared to the index obtained by histogram equalisation.