Automatic extraction of building roofs from remote sensing data is important for many applications including 3D city modeling, urban planning, disaster management, and simulations. In this paper, we propose an automatic workflow for roof reconstruction by polygonal models from classified high-density LIDAR data. Roof planes are initially delineated by a segmentation algorithm combining a robust Hough-based normal estimator and a region growing strategy. Then, each roof is modeled by a 2D α-shape mesh which is used to discover not only building outline but also all ridges defined by intersecting roof planes, without any geometrical calculations. The mesh directly encodes the topological relations between neighboring planes which allows us to build the final polygonal model straightforwardly. This topological approach makes our solution more simple and robust than existing methods which mostly extract the intersection lines by means of geometrical computations. Experimental results show that the proposed workflow offers a high success rate for extraction at plane level (94% completeness, 92.7% correctness, 90.8% quality) when LIDAR point density is sufficiently high.