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We present a novel building segmentation system for densely built areas, containing thousands of buildings per square kilometer. We employ solely sparse LIDAR (Light/Laser Detection Ranging) 3D data, captured from an aerial platform, with resolution less than one point per square meter. The goal of our work is to create segmented and delineated buildings as well as structures on top of buildings without requiring scanning for the sides of buildings. Building segmentation is a critical component in many applications such as 3D visualization, robot navigation and cartography. LIDAR has emerged in recent years as a more robust alternative to 2D imagery because it acquires 3D structure directly, without the shortcomings of stereo in un- textured regions and at depth discontinuities. Our main technical contributions in this paper are: (i) a ground segmentation algorithm which can handle both rural regions, and heavily urbanized areas, where the ground is 20% or less of the data, (ii) a building segmentation technique, which is robust to buildings in close proximity to each other, sparse measurements and nearby structured vegetation clutter, and (Hi) an algorithm for estimating the orientation of a boundary contour of a building, based on minimizing the number of vertices in a rectilinear approximation to the building outline, which can cope with significant quantization noise in the outline measurements. We have applied the proposed building segmentation system to several urban regions with areas of hundreds of square kilometers each, obtaining average segmentation speeds of less than three minutes per km2 on a standard Pentium processor. Extensive qualitative results obtained by overlaying the 3D segmented regions onto 2D imagery indicate accurate performance of our system.