We introduce GEM3D -- a new deep, topology-aware generative model of 3D shapes. The key ingredient of our method is a neural skeleton-based representation encoding information on both shape topology and geometry. Through a denoising diffusion probabilistic model, our method first generates skeleton-based representations following the Medial Axis Transform (MAT), then generates surfaces through a skeleton-driven neural implicit formulation. The neural implicit takes into account the topological and geometric information stored in the generated skeleton representations to yield surfaces that are more topologically and geometrically accurate compared to previous neural field formulations. We discuss applications of our method in shape synthesis and point cloud reconstruction tasks, and evaluate our method both qualitatively and quantitatively. We demonstrate significantly more faithful surface reconstruction and diverse shape generation results compared to the state-of-the-art, also involving challenging scenarios of reconstructing and synthesizing structurally complex, high-genus shape surfaces from Thingi10K and ShapeNet.

翻译：我们提出GEM3D——一种新颖的、具有拓扑感知能力的深度三维形状生成模型。该方法的核心是基于神经骨架的表示，该表示编码了形状拓扑与几何信息。通过去噪扩散概率模型，我们的方法首先生成基于中轴变换的骨架表示，随后通过骨架驱动的神经隐式公式生成表面。与先前的神经场方法相比，该神经隐式公式充分利用生成骨架表示中存储的拓扑和几何信息，从而生成在拓扑与几何上更为精确的表面。我们讨论了该方法在形状合成与点云重建任务中的应用，并进行了定性与定量评估。实验结果表明，与现有最先进技术相比，我们在结构复杂、高亏格形状表面（源于Thingi10K与ShapeNet数据集）的重建与合成等挑战性场景中，实现了显著更优的表面重建保真度与形状生成多样性。