Variational Autoencoding of Dental Point Clouds

TL;DR

This paper addresses the challenge of probabilistic 3D modeling for dental point clouds by introducing VF-Net, a fully probabilistic variational autoencoder that establishes a one-to-one correspondence between input and output points through per-point encodings projected onto a learnable 2D plane $\mathcal{G}=[-1,1]^2$. By replacing Chamfer-distance–based reconstruction with a likelihood-based objective and a normalizing-flow prior over the latent, VF-Net enables tractable probabilistic evaluation and efficient mesh generation, shape completion, and representation learning. The approach yields a new dataset (FDI 16) of 7,732 dental tooth meshes/point clouds and demonstrates state-of-the-art generative performance and lower reconstruction errors on dental data, along with robust latent representations and interpolation capabilities. The work offers practical impact for digital dentistry, including edge-deployable mesh generation and reliable shape completion, while acknowledging ethical considerations around potential misuse of realistic synthetic dental data.

Abstract

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 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

Figures (13)

• Figure 1: VF-Net teeth samples, generated by our probabilistic variational autoencoder for point clouds. Note the wide variety in the samples which retain anatomical details in its cusps/fissure composition.
• Figure 2: VF-Net is a variational autoencoder with a normalizing flow prior over the shape latent. Individual points are projected to 2D space, establishing a one-to-one connection and facilitating mesh generation and shape completion. The decoder follows FoldingNet’s with added residual connections, while the variance network consists of 3 folding modules as introduced in FoldingNet.
• Figure 3: Top: Mesh data samples from our released FDI 16 dataset and their corresponding VF-Net reconstructions. Note the large variety in health conditions between the teeth.
• Figure 4: FoldingNet's mesh reconstructions have gaps and highly distorted facets. Conversely, VF-Net's mesh facets are even more regular than the input point cloud, and points in the reconstruction are placed closely resembling its input.
• Figure 5: Intra-point cloud relative predicted variance (red is high, green is low). Notably, the carabelli cusp and aligner attachment areas exhibit high variance, two features only present in a subset of individuals.