  Digital dentistry has made significant advancements, yet numerous challenges
remain. This paper introduces the FDI 16 dataset, an extensive collection of
tooth meshes and point clouds. Additionally, we present a novel approach:
Variational FoldingNet (VF-Net), a fully probabilistic variational autoencoder
designed for point clouds. Notably, prior latent variable models for point
clouds lack a one-to-one correspondence between input and output points.
Instead, they rely on optimizing Chamfer distances, a metric that lacks a
normalized distributional counterpart, rendering it unsuitable for
probabilistic modeling. We replace the explicit minimization of Chamfer
distances with a suitable encoder, increasing computational efficiency while
simplifying the probabilistic extension. This allows for straightforward
application in various tasks, including mesh generation, shape completion, and
representation learning. Empirically, we provide evidence of lower
reconstruction error in dental reconstruction and interpolation, showcasing
state-of-the-art performance in dental sample generation while identifying
valuable latent representations.
