Conditional Copulas for Change Detection in Heterogeneous Remote Sensing Images

A new preprocessing technique is presented in this paper to automatically highlight changes in multitemporal strongly heterogeneous remotely sensed images. The proposed technique is devoted to the case where the two acquisitions, before and after a given event, are significantly different, due, for instance, to different sensors, acquisition modalities, or climatic conditions. In a previous study, it was proven that the local statistics of the images acquired at the two dates could be used to extract a relevant change indicator. Nevertheless, this measure is valid when the two observations have been derived from similar acquisitions. When the acquisition modalities differ, local statistics tend to be too different from one image to the other one to be relevant in highlighting the ground evolution without mixing with the changes at ground. The technique proposed in this paper to overcome this limitation is based on the assumption that some dependence indeed exists between the two images in unchanged areas. This dependence is modeled by quantile regression applied according to the copula theory and used to perform an estimation of the local statistics that would have been observed if the acquisition conditions of the first image had been similar to the ones of the second image. The method yields an estimate of the local statistics of the first image through the point of view of the second one. Then, usual Kullback-Leibler-based comparisons of those statistics are applied to define a change measure, which may be analyzed (e.g., by thresholding) in order to detect changes. Experimental results are shown to validate the proposed method by using a pair of Synthetic Aperture Radar (SAR) images onboard European Remote Sensing (ERS) Satellite images and a pair of optical-SAR images (from the High Resolution Visible (HRV) sensor onboard Satellite Pour l´Observation de la Terre (SPOT) satellite and from ERS-SAR) acquired before and after a flood.