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This paper presents a novel system for automatically updating land-cover maps by classifying remote sensing image time series. The proposed system assumes that a reliable training set is available only for one of the images (i.e., the source domain) in the time series, whereas it is not for another image to be classified (i.e., the target domain). To effectively classify the target domain the proposed system includes two steps: i) low-cost definition of the training set for the target domain; and ii) target domain classification according to the Bayesian cascade decision rule that exploits the temporal correlation between domains. In the proposed system, the low cost training set for the target domain is defined on the basis of transfer and active learning methods, which also use the temporal dependence information between the domains. Experimental results obtained on a time series of Landsat multispectral images show the effectiveness of the proposed technique.