This paper focuses on the application of Extreme Learning Machines (ELM) to the classification of remote sensing hyperspectral data. The specific aim of the work is to obtain accurate thematic maps of soybean crops, which have proven to be difficult to identify by automated procedures. The classification process carried out is as follows: First, spectral data is transformed into a hyper-spherical representation. Second, a robust image gradient is computed over the hyper-spherical representation allowing an image segmentation that identifies major crop plots. Third, feature selection is achieved by a greedy wrapper approach. Finally, a classifier is trained and tested on the selected image pixel features. The classifiers used for feature selection and final classification are Single Layer Feedforward Networks (SLFN) trained with either the ELM or the incremental OP-ELM. Original image pixel features are computed following a Functional Data Analysis (FDA) characterization of the spectral data. Conventional ELM training of the SLFN improves over the classification performance of state of the art algorithms reported in the literature dealing with the data treated in this paper. Moreover, SLFN-ELM uses less features than the referred algorithms. OP-ELM is able to find competitive results using the FDA features from a single spectral band.