Digital dentistry has made significant advancements in recent years, yet numerous challenges remain to be addressed. In this study, we release a new extensive dataset of tooth meshes to encourage further research. Additionally, we propose Variational FoldingNet (VF-Net), which extends FoldingNet to enable probabilistic learning of point cloud representations. A key challenge in existing latent variable models for point clouds is the lack of a 1-to-1 mapping between input points and output points. Instead, they must rely on optimizing Chamfer distances, a metric that does not have a normalized distributional counterpart, preventing its usage in probabilistic models. We demonstrate that explicit minimization of Chamfer distances can be replaced by a suitable encoder, which allows us to increase computational efficiency while simplifying the probabilistic extension. Our experimental findings present empirical evidence demonstrating the superior performance of VF-Net over existing models in terms of dental scan reconstruction and extrapolation. Additionally, our investigation highlights the robustness of VF-Net's latent representations. These results underscore the promising prospects of VF-Net as an effective and reliable method for point cloud reconstruction and analysis.

翻译：数字牙科近年来取得了显著进展，但仍有诸多挑战亟待解决。本研究发布了一个新的大规模牙齿网格数据集，以推动进一步研究。此外，我们提出了变分FoldingNet（VF-Net），该方法扩展了FoldingNet，实现了点云表示的概率学习。现有点云潜变量模型面临的一个关键挑战是输入点与输出点之间缺乏一一对应映射，因此必须依赖优化Chamfer距离。然而，Chamfer距离作为一种度量指标，不存在归一化的分布对应形式，因而无法用于概率模型。我们证明，通过合适的编码器可以直接替代Chamfer距离的显式最小化，从而在简化概率扩展的同时提高计算效率。实验结果表明，在牙齿扫描重建和外推任务上，VF-Net的性能优于现有模型。此外，我们的研究还突出了VF-Net潜表示的鲁棒性。这些结果强调了VF-Net作为点云重建与分析的有效且可靠方法所具有的广阔前景。