Copula-based Stochastic Kernels for Abrupt Change Detection

This paper shows how to obtain a binary change map from similarity measures of the local statistics of images before and after a disaster. The decision process is achieved by the use of a zz-SVM in which a stochastic kernel has been defined. Stochastic kernel includes two similarity measures, based on the local statistics, to detect changes from the images: 1) A distance between maginal probability density functions (pdfs) and 2) the mutual information between the two observations. Distance between marginal pdfs is evaluated by using a series expansion of the Kullbak-Leibler distance. It is achieved by estimating cumulants up to order 4 from a sliding window of fixed size. Mutual information is estimated through a parametric model that is issued from the copulas theory. It is based on rank statistics and yields an analytic expression, that depends on the parameter of the copula only, to be evaluated to obtain the mutual information. Preliminary results are shown on a pair of Radarsat images acquire before and after a lava flow. A ground truth allows to show the accuracy of the stochastic kernels and the SVM decision.