DETECTION AND RECONSTRUCTION OF FREE FORM SURFACES FROM AIRBORNE LASER SCANNING DATA Sagi Filin, Nizar Abo Akel, Yerach Doytsher Dept. of Transportation and Geo-Information Eng., Technion – Israel Institute of Technology, Haifa 32000, Israel {filin, anizar, doythser}@tx.technion.ac.il Commission III, WG 3 Keywords: LiDAR, City modeling, Building reconstruction, Free Form, Curved Surfaces. ABSTRACT: Building reconstruction from LiDAR data offers promising prospects for rapid generation of large-scale 3D models in an autonomous manner. Such reconstruction requires knowledge on a variety of parameters that refer to both the point cloud and the modeled building. The complexity of the reconstruction task has led many researchers to use external information, mostly in the form of detailed ground plans to localize the buildings and usually assume that buildings consist of only planar parts. These assumptions limit the reconstruction of complex buildings specifically when curved surfaces exist. We present in this paper a model that considers the point cloud as the only information source and analyzes the roof shapes. We extend the standard models to support free-form surfaces and reconstruct their shape. Since many of the buildings are still composed of planar faces, we maintain the planar based partitioning whenever possible but detect if non-planar surfaces exist and apply free-form surface models there. In such way, the standard models are extended to support general shape roofs without imposing an artificial model if not needed. In addition to the extension into non-planar roofs, our reconstruction involves the aggregation of the point set into individual faces, and learning the building shape from these aggregates. We show the effect of imposing geometric constraints on the reconstruction to generate realistic models of buildings. 1. INTRODUCTION Three-dimensional reconstruction of buildings becomes a fundamental part in a growing number of applications. Among the data sources available for such reconstruction, airborne laser scanning has emerged in recent years as a leading source for that purpose (see e.g., Brenner and Haala, 1998; Wang and Schenk, 2000; Brenner, 2000; Voegtle et al. 2005; Rottensteiner 2005), particularly due to the direct measurements of the surface topography both accurately and densely. Reconstruction of buildings from LiDAR data involves their detection in the point cloud, extraction of primitives that compose the building shape, and an agglomeration of the primitives into a geometric building structure. The detection will usually wear the form of object to background separation, e.g., via filtering, surface discontinuities analysis, segmentation, or with the support of external information, like ground plans (Vosselman and Dijkman, 2001; Haala et al. 2006). For the extraction of roof primitives, a segmentation of the data into planar faces will be applied in most cases. In Hoffman (2004) and Alharthy and Bethel (2004) a gradient based analysis is applied as a means to find roof planes. Voegtle et al. (2005) use classified data as an input, where the extraction of the roof planes is region growing based with a homogeneity predicate. Rottensteiner (2005) describes a roof delineation algorithm where the classified data is segmented in a similar fashion as in Voegtle et al. (2005). The boundaries of the detected planes are determined using the Voronoi diagram and the resulting edges are then grouped together into polyhedral models. The reconstruction of the roof model that follows, will usually involve modeling via geometrical representations such as, boundary representations, parametric models, or CSG trees. Despite the large body of research into building reconstruction, many challenges are still remaining. One such challenge concerns the general planar roof-face assumption that is common to almost all reconstruction models. While planar roof buildings are still the majority, buildings with general shape can be found in almost every scene. Using planar-based models for general curved or free-from surfaces, will lead to a wrong partitioning and a failure in the reconstruction process as the common outcome. Therefore, to increase the reliability of the building detection and modeling process, an extension of the reconstruction model to support a general shapes is a desired improvement. Nonetheless, as many of the buildings are still composed of planar faces, a planar based partitioning is an appealing concept to maintain whenever possible. An optimal reconstruction model will therefore not only involve finding a representation for curved surfaces but also deciding when planarity fails to hold and a more elaborate model is of need. To support any form of reconstruction that deviates from the planarity assumption, the utility of turning into a curved surface description should be weighted. In this paper, we address the problem of identifying curved roof faces when such exist. The motivation is limiting such detection only to those cases where non-planarity is needed while avoiding over-parameterization elsewhere. We then demonstrate the reconstruction of non- planar roofs structures using data with moderate point density (< 1 p/m 2 ). In the following Section we outline the roof face extraction model and then describe alternative methods for identifying deviations from planarity by looking into internal and external characteristics. We then study their applicability to the detection of curved segments and show the results of the surface reconstruction. 2. FEATURE EXTRCTION AND MODEL EVALUATION As noted, a reconstruction framework that assumes no prior information from external sources requires, i) the detection of buildings in the point cloud, ii) segmentation of the roof into faces and analysis of the results, and iii) geometric adjustment 119 IAPRS Volume XXXVI, Part 3 / W52, 2007