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

TL;DR

This paper introduces a novel interval type-2 fuzzy method for automatically generating probability density functions to enhance image contrast through histogram specification, improving image quality metrics over existing methods.

Contribution

It proposes a new fuzzy approach for automatic PDF generation in histogram specification using interval type-2 fuzzy sets, with four methods for membership value calculation.

Findings

Improves image contrast as measured by AIC index by 11.5% over histogram equalization.

Sensitive to local histogram variations, leading to better contrast enhancement.

Outperforms existing algorithms like HE, RMSHE, and BPFHE in qualitative and quantitative analyses.

Abstract

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.