A Theoretical Framework for Change Detection Based on a Compound Multiclass Statistical Model of the Difference Image

The change detection (CD) problem is very important in the remote sensing domain. The advent of a new generation of multispectral (MS) sensors has given rise to new challenges in the development of automatic CD techniques. In particular, typical approaches to CD are not able to well model and properly exploit the increased radiometric resolution characterizing new data as this results in a higher sensitivity to the number of natural classes that can be statistically modeled in the images. In this paper, we introduce a theoretical framework for the description of the statistical distribution of the difference image as a compound model where each class is determined by temporally correlated class transitions in the bitemporal images. The potential of the proposed framework is demonstrated on the very common problem of binary CD based on setting a threshold on the magnitude of the difference image. Here, under some simplifying assumptions, a multiclass distribution of the magnitude feature is derived and an unsupervised method based on the expectation–maximization algorithm and Bayes decision is proposed. Its effectiveness is demonstrated on a large variety of data sets from different MS sensors. In particular, experimental tests confirm that: 1) the fitting of the magnitude distribution significantly improves if compared with already existing models and 2) the overall CD error is close to the optimal value.