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Very high resolution satellite images provide valuable information to researchers. Among these, urban-area boundaries and building locations play crucial roles. For a human expert, manually extracting this valuable information is tedious. One possible solution to extract this information is using automated techniques. Unfortunately, the solution is not straightforward if standard image processing and pattern recognition techniques are used. Therefore, to detect the urban area and buildings in satellite images, we propose the use of scale invariant feature transform (SIFT) and graph theoretical tools. SIFT keypoints are powerful in detecting objects under various imaging conditions. However, SIFT is not sufficient for detecting urban areas and buildings alone. Therefore, we formalize the problem in terms of graph theory. In forming the graph, we represent each keypoint as a vertex of the graph. The unary and binary relationships between these vertices (such as spatial distance and intensity values) lead to the edges of the graph. Based on this formalism, we extract the urban area using a novel multiple subgraph matching method. Then, we extract separate buildings in the urban area using a novel graph cut method. We form a diverse and representative test set using panchromatic 1-m-resolution Ikonos imagery. By extensive testings, we report very promising results on automatically detecting urban areas and buildings.