44-Issue 7

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TopoGen: Topology-Aware 3D Generation with Persistence Points
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Hu, Jiangbei; Fei, Ben; Xu, Baixin; Hou, Fei; Wang, Shengfa; Lei, Na; Yang, Weidong; Qian, Chen; He, Ying; Christie, Marc; Pietroni, Nico; Wang, Yu-Shuen
Topological properties play a crucial role in the analysis, reconstruction, and generation of 3D shapes. Yet, most existing research focuses primarily on geometric features, due to the lack of effective representations for topology. In this paper, we introduce TopoGen, a method that extracts both discrete and continuous topological descriptors-Betti numbers and persistence points-using persistent homology. These features provide robust characterizations of 3D shapes in terms of their topology. We incorporate them as conditional guidance in generative models for 3D shape synthesis, enabling topology-aware generation from diverse inputs such as sparse and partial point clouds, as well as sketches. Furthermore, by modifying persistence points, we can explicitly control and alter the topology of generated shapes. Experimental results demonstrate that TopoGen enhances both diversity and controllability in 3D generation by embedding global topological structure into the synthesis process.