Detailed geometric models of the real world are in increasing demand. LiDAR data is appropriate to reconstruct such models. For urban reconstruction, it works well to reconstruct the individual surfaces of the scene and connect them to form the scene geometry. There are various methods for reconstructing the free-form shape of a point sample on a single surface. However, these methods do not take the context of the surface into account. We present the generalized and guided α-shape: two extensions of the well known α-shape. The generalized α-shape handles lines (generalized points) as if they are infinite collections of points. The guided α-shape handles lines (guides) as indicators for preferred locations for the boundary of the shape. The guided α-shape uses (parts of) these lines as boundary where the points suggest that this is appropriate. We prove that, for an input of n points and m guides, both the generalized and guided α-shape can be constructed in O((n + m) log(n + m)) time. We apply guided α-shapes to urban reconstruction from LiDAR, where neighboring surfaces can be connected conveniently along their intersection lines into adjacent surfaces of a 3D model. We analyze guided α-shapes of both synthetic and real data and show they are consistently better than α-shapes for this application.
The demand for large geometric models is increasing, especially of urban environments. This has resulted in production of massive point cloud data from images or LiDAR. Visualization and further processing generally require a detailed, yet concise representation of the scene's surfaces. Related work generally either approximates the data with the risk of over-smoothing, or interpolates the data with excessive detail. Many surfaces in urban scenes can be modeled more concisely by planar approximations. In earlier work, we presented a method for efficiently computing planar polygons approximating a point set. Here, we present a method that combines these polygons into a watertight model. In regions where no polygons were detected, the shape is closed with free-form meshes based on visibility information. To achieve this, we divide 3-space into inside and outside volumes by combining a constrained Delaunay tetrahedralization with a graph-cut. We compare our method with related work on several large urban LiDAR data sets. We construct similar shapes with a third fewer triangles to model the scenes. Additionally, our results are more visually pleasing and closer to a human modeler's description of urban scenes using simple boxes.
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