基于EM和BIC的直方图拟合方法应用于遥感变化检测阈值确定

Determination of Threshold in Change Detection Based on Histogram Approximation Using Expectation Maximization Algorithm and Bayes Information Criterion

利用遥感图像进行变化检测时,确定"差异图像"上各变化类型的阈值非常关键。本文引入图像直方图拟合方法来确定变化阈值。首先通过基于变化向量分析方法,得到变化强度图像,然后假设该变化强度图像中的像元值符合混合高斯分布模型,利用期望最大(EM)算法和贝叶斯信息准则(BIC)求出最佳的混合高斯分布模型,拟合此时的图像直方图,最后利用贝叶斯判别准则确定出各变化类型的变化阈值。试验证明,这种方法是一种较为有效的自动确定变化阈值的方法。

One of the key issues of land use/cover change detection using remote sensing images is the threshold determination.This paper introduces the histogram approximation method based on Expectation Maximization(EM) algorithm and Bayes Information Criterion(BIC) into unsupervised change detection.EM algorithm is an iterative algorithm that has many advantages in estimating the statistical values.BIC is always used for evaluating a statistical model on the aspects of accuracy and complexity.'Difference image' is acquired by applying the change vector analysis(CVA) technique,which can magnify the difference between the two-temporal images.The probability distribution function(PDF) of its histogram can be modeled as a mixture of M Gaussian distributions.Different values of M will get different models.The best one will make the value of BIC minimum.According to this criterion,the statistical values of the mixture Gaussian distributions can be estimated using the EM algorithm and BIC.Then the threshold of the change detection will be obtained by finding the intersection point of two neighbor Gaussian distributions.M Gaussian distributions will gain M points that are the M thresholds.M is regarded as the number of the changed types.The estimated values including means and variations and the prior distributions of every Gaussian distribution have definite physical meanings.The means indicate the values of images of those changed types based on which difference image can be classified quickly.The variations illustrate the difference in one changed types,and the percentage of every change types can be given by the prior distributions of every Gaussian distribution.The traditional methods of change detection by remote sensing based on EM algorithm is often assuming the difference image containing two types of pixels.Which are changed pixels and unchanged pixels.But when there are more than one changed types and the difference images' histogram becomes complex,this method is proved not accurate.To compare these two methods and validate this method,this paper chose the area around the Miyun Reservoir as the experiment area.There are more than one types changed including water,bare land and vegetation and so on,so this area is representative for change detection study.The experiment data is 2001 TM image and 2004 ETM+ image.The difference image's histogram is modeled by 4 Gaussian distribution,according to the models the difference image is classified 4 types.Then the difference image is processed by traditional method of change detection based on EM algorithm.The entropy is introduced to evaluate the two experimental results,which is usually used to evaluate the uncertainty of one pixel belonging to one classification.Its advantage is that it can make the pixels' uncertainty visible in the image.Results show that the histogram approximation based on EM and BIC method is credible and effective in change detection from the remote sensing images,especially when the changed types are more complex.