Regression Analysis Based Variance Estimation of Gaussian Distribution for Histogram Matching

Abstract

This paper describes an improved method of the variance estimation of Gaussian distribution for Histogram Matching based on Gaussian Distribution (HMGD). In our previous paper, focusing on the symmetry of the Gaussian function, we presented another method for the variance (or Gaussian width) estimation of Gaussian distribution in the original histogram. However, since the real shape of mountain like Gaussian function in the original image's histogram does not always show the good symmetry, the variance estimation method that we previously presented did not work so well as we expected. In this paper, we newly propose the improved estimation method using regression analysis, based on curvature computation for the cumulative histogram of original image's one. In the newly proposed method, first, we detect the histogram peak of original image's histogram by using curvature computation; next, we perform the regression analysis for the cumulative histogram, using an approximated function of the curvature that includes the variance parameter. Also in this paper, we show some experimental results by the estimation method.