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This paper presents a solution framework for the segmentation and reconstruction of polyhedral building roofs from aerial LIght Detection And Ranging (lidar) point clouds. The eigenanalysis is first carried out for each roof point of a building within its Voronoi neighborhood. Such analysis not only yields the surface normal for each lidar point but also separates the lidar points into planar and nonplanar ones. In the second step, the surface normals of all planar points are clustered with the fuzzy k-means method. To optimize this clustering process, a potential-based approach is used to estimate the number of clusters, while considering both geometry and topology for the cluster similarity. The final step of segmentation separates the parallel and coplanar segments based on their distances and connectivity, respectively. Building reconstruction starts with forming an adjacency matrix that represents the connectivity of the segmented planar segments. A roof interior vertex is determined by intersecting all planar segments that meet at one point, whereas constraints in the form of vertical walls or boundary are applied to determine the vertices on the building outline. Finally, an extended boundary regularization approach is developed based on multiple parallel and perpendicular line pairs to achieve topologically consistent and geometrically correct building models. This paper describes the detail principles and implementation steps for the aforementioned solution framework. Results of a number of buildings with diverse roof complexities are presented and evaluated.