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——一种全新的、具有拓扑感知能力的深度三维形状生成模型。该方法的核心是一种基于神经骨架的表征方式，可同时编码形状拓扑与几何信息。通过去噪扩散概率模型，我们的方法首先依据中轴变换（Medial Axis Transform, MAT）生成基于骨架的表征，随后通过骨架驱动的神经隐式公式生成曲面。该神经隐式函数充分利用生成骨架表征中存储的拓扑与几何信息，与先前的神经场公式相比，能够生成拓扑与几何精度更高的曲面。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，与现有最优方法相比，我们的方法在曲面重建保真度与形状生成多样性方面均具有显著优势，尤其适用于从Thingi10K和ShapeNet数据集中重建与合成结构复杂、高亏格形状曲面的挑战性场景。