Identifying rectangles in laser range data for urban scene reconstruction

In urban scenes, many of the surfaces are planar and bounded by simple shapes. In a laser scan of such a scene, these simple shapes can still be identified. We present a one-parameter algorithm that can identify point sets on a plane for which a rectangle is a fitting boundary. These rectangles have a guaranteed density: no large part of the rectangle is empty of points. We prove that our algorithm identifies all angles for which a rectangle fits the point set of size n in O(n logn) time. We experimentally evaluate our method on thirteen urban data sets. We also compare the rectangles found by our algorithm to the α-shape as a surface boundary. Figure 1: One of the regions used in the experiments. Each cluster has its own color and remaining unclustered points are black. A detail of this scene is shown in Figure 6.