Uncorrelated versus independent elliptically-contoured distributions for anomalous change detection in hyperspectral imagery

The detection of actual changes in a pair of images is confounded by the inadvertent but pervasive differences that inevitably arise whenever two pictures are taken of the same scene, but at different times and under different conditions. These differences include effects due to illumination, calibration, misregistration, etc. If the actual changes are assumed to be rare, then one can “learn” what the pervasive differences are, and can identify the deviations from this pattern as the anomalous changes. A recently proposed framework for anomalous change detection recasts the problem as one of binary classification between pixel pairs in the data and pixel pairs that are independently chosen from the two images. When an elliptically-contoured (EC) distribution is assumed for the data, then analytical expressions can be derived for the measure of anomalousness of change. However, these expression are only available for a limited class of EC distributions. By replacing independent pixel pairs with uncorrelated pixel pairs, an approximate solution can be found for a much broader class of EC distributions. The performance of this approximation is investigated analytically and empirically, and includes experiments comparing the detection of real changes in real data.