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A general problem of supervised remotely sensed image classification assumes prior knowledge to be available for all the thematic classes that are present in the considered dataset. However, the ground-truth map representing that prior knowledge usually does not really describe all the land-cover typologies in the image, and the generation of a complete training set often represents a time-consuming, difficult and expensive task. This problem affects the performances of supervised classifiers, which erroneously assign each sample drawn from an unknown class to one of the known classes. In the present paper, a classification strategy is described that allows the identification of samples drawn from unknown classes through the application of a suitable Bayesian decision rule. The proposed approach is based on support vector machines (SVMs) for the estimation of probability density functions and on a recursive procedure to generate prior probability estimates for known and unknown classes. In the experiments, both a synthetic dataset and two real datasets were used.