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This paper presents a novel protocol for the accuracy assessment of the thematic maps obtained by the classification of very high resolution images. As the thematic accuracy alone is not sufficient to adequately characterize the geometrical properties of high-resolution classification maps, we propose a protocol that is based on the analysis of two families of indices: 1) the traditional thematic accuracy indices and 2) a set of novel geometric indices that model different geometric properties of the objects recognized in the map. In this context, we present a set of indices that characterize five different types of geometric errors in the classification map: 1) oversegmentation; 2) undersegmentation; 3) edge location; 4) shape distortion; and 5) fragmentation. Moreover, we propose a new approach for tuning the free parameters of supervised classifiers on the basis of a multiobjective criterion function that aims at selecting the parameter values that result in the classification map that jointly optimize thematic and geometric error indices. Experimental results obtained on QuickBird images show the effectiveness of the proposed protocol in selecting classification maps characterized by a better tradeoff between thematic and geometric accuracies than standard procedures based only on thematic accuracy measures. In addition, results obtained with support vector machine classifiers confirm the effectiveness of the proposed multiobjective technique for the selection of free-parameter values for the classification algorithm.