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Extended Attribute Profiles (EAPs), which are obtained by applying morphological attribute filters to an image in a multilevel architecture, can be used for the characterization of the spatial characteristics of objects in a scene. EAPs have proved to be discriminant features when considered for thematic classification in remote sensing applications especially when dealing with very high resolution images. Altimeter data (such as LiDAR) can provide important information, which being complementary to the spectral one can be valuable for a better characterization of the surveyed scene. In this paper, we propose a technique performing a classification of the features extracted with EAPs computed on both optical and LiDAR images, leading to a fusion of the spectral, spatial and elevation data. The experiments were carried out on LiDAR data along either with a hyperspectral and a multispectral image acquired on a rural and urban area of the city of Trento (Italy), respectively. The classification accuracies obtained pointed out the effectiveness of the features extracted by EAPs on both optical and LiDAR data for classification.