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Building footprint extraction in remote sensing data benefits many important applications, such as urban planning and population estimation. Recently, rapid development of Convolutional Neural Networks (CNNs) and open-sourced high resolution satellite building image datasets have pushed the performance boundary further for automated building extractions. However, CNN approaches often generate imprecise building morphologies including noisy edges and round corners. In this paper, we leverage the performance of CNNs, and propose a module that uses prior knowledge of building corners to create angular and concise building polygons from CNN segmentation outputs. We describe a new transform, Relative Gradient Angle Transform (RGA Transform) that converts object contours from time vs. space to time vs. angle. We propose a new shape descriptor, Boundary Orientation Relation Set (BORS), to describe angle relationship between edges in RGA domain, such as orthogonality and parallelism. Finally, we develop an energy minimization framework that makes use of the angle relationship in BORS to straighten edges and reconstruct sharp corners, and the resulting corners create a polygon. Experimental results demonstrate that our method refines CNN output from a rounded approximation to a more clear-cut angular shape of the building footprint.