We present PolyGNN, a polyhedron-based graph neural network for 3D building reconstruction from point clouds. PolyGNN learns to assemble primitives obtained by polyhedral decomposition via graph node classification, achieving a watertight, compact, and weakly semantic reconstruction. To effectively represent arbitrary-shaped polyhedra in the neural network, we propose three different sampling strategies to select representative points as polyhedron-wise queries, enabling efficient occupancy inference. Furthermore, we incorporate the inter-polyhedron adjacency to enhance the classification of the graph nodes. We also observe that existing city-building models are abstractions of the underlying instances. To address this abstraction gap and provide a fair evaluation of the proposed method, we develop our method on a large-scale synthetic dataset covering 500k+ buildings with well-defined ground truths of polyhedral class labels. We further conduct a transferability analysis across cities and on real-world point clouds. Both qualitative and quantitative results demonstrate the effectiveness of our method, particularly its efficiency for large-scale reconstructions. The source code and data of our work are available at https://github.com/chenzhaiyu/polygnn.

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