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When using morphological features for the classification of high resolution hyperspectral images from urban areas, one should consider two important issues. The first one is that classical morphological openings and closings degrade the object boundaries and deform the object shapes. Morphological openings and closings by reconstruction can avoid this problem, but this process leads to some undesirable effects. Objects expected to disappear at a certain scale remain present when using morphological openings and closings by reconstruction. The second one is that the morphological profiles (MPs) with different structuring elements and a range of increasing sizes of morphological operators produce high-dimensional data. These high-dimensional data may contain redundant information and create a new challenge for conventional classification methods, especially for the classifiers which are not robust to the Hughes phenomenon. In this paper, we first investigate morphological profiles with partial reconstruction and directional MPs for the classification of high resolution hyperspectral images from urban areas. Secondly, we develop a semi-supervised feature extraction to reduce the dimensionality of the generated morphological profiles for the classification. Experimental results on real urban hyperspectral images demonstrate the efficiency of the considered techniques.