Traditional kernel classifiers assume independence among the classification outputs. As a consequence, each misclassification receives the same weight in the loss function. Moreover, the kernel function only takes into account the similarity between input values and ignores possible relationships between the classes to be predicted. These assumptions are not consistent for most of real-life problems. In the particular case of remote sensing data, this is not a good assumption either. Segmentation of images acquired by airborne or satellite sensors is a very active field of research in which one tries to classify a pixel into a predefined set of classes of interest (e.g. water, grass, trees, etc.). In this situation, the classes share strong relationships, e.g. a tree is naturally (and spectrally) more similar to grass than to water. In this paper, we propose a first approach to remote sensing image classification using structured output learning. In our approach, the output space structure is encoded using a hierarchical tree, and these relations are added to the model in both the kernel and the loss function. The methodology gives rise to a set of new tools for structured classification, and generalizes the traditional non-structured classification methods. Comparison to standard SVM is done numerically, statistically and by visual inspection of the obtained classification maps. Good results are obtained in the challenging case of a multispectral image of very high spatial resolution acquired with QuickBird over a urban area.