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This paper introduces a novel system for automatic detection and height estimation of buildings with polygonal shape roofs in singular satellite images. The system is capable of detecting multiple flat polygonal buildings with no angular constraints or shape priors. The proposed approach employs image primitives such as lines, and line intersections, and examines their relationships with each other using a graph-based search to establish a set of rooftop hypotheses. The height (mean height from rooftop edges to the ground) of each rooftop hypothesis is estimated using shadows and acquisition geometry. The potential ambiguities in identification of shadows in an image and the uncertainty in identifying true shadows of a building have motivated for a fuzzy logic-based approach that estimates buildings heights according to the strength of shadows and the overlap between identified shadows in the image and expected shadows according to the building profile. To reduce the time complexity of the implemented system, a maximum number of eight sides for polygonal rooftops is assumed. Promising experimental results verify the effectiveness of the presented system with overall mean shape accuracy of 94% and mean height error of 0.53 m on QuickBird satellite (0.6 m/pixel) imageries.