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Roofless buildings are encountered in case of conflicts and disasters as well as construction sites. A methodology for characterizing and counting roofless buildings in very high resolution optical images is presented. Using morphological transform to extract specific image components, the proposed method spatially aggregates them in a fuzzy logic framework. The result is a map of roofless building membership. This membership map is then used with partial ground truth to estimate the total number of roofless buildings. Finally, the methods are validated with a WorldView panchromatic image, where the membership map and the counting estimate show good accuracies.