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This letter presents unsupervised hyperspectral-image classification based on fuzzy-clustering algorithms that spatially exploit membership relations. Not only is the conventional fuzzy c-means approach used to demonstrate the advantage of using membership relations but also Gustafson-Kessel clustering, which uses an adaptive distance norm, is, for the first time, used for the segmentation of hyperspectral images. A novel approach to include spatial information in the segmentation process is achieved by making use of spatial relations of fuzzy-membership functions among neighbor pixels. Two- and three-dimensional Gaussian filtering of fuzzy-membership degrees is utilized for this purpose. A novel phase-correlation-based similarity measure is used to further enhance the performance of the proposed approach by taking spatial relations into account for pixels with similar spectral characteristics only. It is shown that the proposed approach provides superior clustering performance for hyperspectral images.