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An important approach for image segmentation is clustering pixels based on their spectral properties. In particular, satellite images contain land cover types, some of which cover significantly large areas, while some (e.g., bridges and roads) occupy relatively much smaller regions. Automatically detecting regions or clusters of such widely varying sizes presents a challenging task. In this letter, a symmetry-based cluster validity index, named Sym-index (Symmetry distance-based index), is proposed. It is able to correctly indicate the presence of clusters of different sizes as long as they are internally symmetrical. A genetic-algorithm-based clustering technique that optimizes the Sym-index is used for image segmentation where the number of clusters is determined automatically. The superiority of the proposed index, as compared to other indices, is established for automatically segmenting the land cover types from SPOT and Indian Remote Sensing satellite images of two different cities in India.