基于EM的直方图逼近及其应用

Histogram Approximation Based on Expectation Maximization Algorithm and Its Application

由于直方图一般是图像灰度或者其他分量的统计信息,因此分析图像的直方图是图像处理中的一个实用方法。直方图逼近是直方图分析方法之一,一般利用若干高斯分布函数来对直方图进行逼近。如何得到各个高斯分布函数的参数是问题的难点,解决此问题的一条途径把直方图逼近问题转化为统计学中的混合模型参数估计问题。文章首先采用EM(数学期望最大化)方法解决了这个问题,然后介绍了基于EM的直方图逼近方法在最优阈值化、直方图成份分析方面的应用。

Histogram is commonly the statistical information about gray level or other chromatic components of image. Analyzing the histogram of image is a useful method in image processing. Adopting several probability density functions （PDFs） with Gaussian distribution to approximate the histogram is one way for histogram analyzing. But how to acquire the parameters of these distributions remains a hard issue. This paper uses expectation maximization algorithm to estimate the parameters by converting histogram apporximation problem into Guassian mixture models problem in statistics, and then introduces its application in optimal thresholding and histogram component analysis.