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A framework to reconstruct 3D building rooftops from LiDAR data is proposed, in which the key contribution is a dynamic triangle - based method for precise rooftop detection. This framework consists of four steps: building point segmentation, coarse building rooftop detection, precise building rooftop determination, and 3D building rooftop reconstruction. The segmented LiDAR points belonging to each building are firstly derived. A triangle cluster - based normal analysis is then introduced to detect coarse building rooftops. A new dynamic triangle - based method is presented to determine precise rooftops by refining the coarse rooftops. Its main idea is a dynamic propagation strategy for new reliable triangle construction from an initial triangle network by reliability analysis of candidate points. 3D rooftop reconstruction can be carried out using the method proposed by this author. The experimental results illustrate that the proposed framework can derive the reliable and accurate 3D building rooftops.