While it is reasonable to assume that the noise characteristics are known sufficiently such that they can be modelled analytically and estimated from the difference image, we have no information concerning the intensities of the regions of change. Likewise, we know little about the magnitudes of the difference map intensities produced by change, except that we would generally expect them to be significantly larger than zero. Since this provides little help for threshold selection we do not try to analyse difference map intensities, but consider the original (pre-differenced) images instead. Change occurs when corresponding pixels in the two images have significantly different intensities, but it is difficult to quantify what is meant by significant. One solution is to consider in addition to each individual pixel all the intensities in a surrounding window. Comparing two windows is a more tractable task since there are many techniques available for comparing two distributions, and this is the approach taken by Jain and Nagel [ 9 ] and Hsu et al. [ 7 ]. In contrast to them we shall use a non-parametric method so that no assumptions about the intensity distributions need to be made. One of the most popular is the Kolmogorov-Smirnov test which was used for change detection in satellite imagery by Eghbali [ 4 ]. It has the nice property that it is invariant to image scaling or offsets. As an alternative we have also experimented with the Cramér-von Mises test which is often more powerful than the Kolmogorov-Smirnov test [ 22 ]. Rather than testing the maximum value of the difference between the two cumulative distributions it uses instead the summed squared differences. Thresholding is performed by accepting as motion only those pixels whose distributions are dissimilar, i.e. their test statistic is above the critical value for a selected significance value (e.g. 5%).
Following Eghbali we normalise the data to reduce sensitivity to large scale variations between the images. Each window is rescaled and offset so that it has zero mean and unit standard deviation.
Paul L Rosin