# ToothForge: Automatic Dental Shape Generation using Synchronized Spectral Embeddings

arXiv: https://arxiv.org/abs/2506.02702 · HTML: https://mlsanity.com/paper/2506.02702/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 29 references that are in the map.
- First posted on arXiv 3 Jun 2025.

## Builds on (most cited first, 13 of 13)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [Volumetric and Multi-View CNNs for Object Classification on 3D Data](https://mlsanity.com/paper/1604.03265/) (2016)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [Subdivision-Based Mesh Convolution Networks](https://mlsanity.com/paper/2106.02285/) (2021)
- [Point2SSM: Learning Morphological Variations of Anatomies from Point Cloud](https://mlsanity.com/paper/2305.14486/) (2023)
- [From Mesh Completion to AI Designed Crown](https://mlsanity.com/paper/2501.04914/) (2025)
- [Enhancing Image Classification in Small and Unbalanced Datasets through Synthetic Data Augmentation](https://mlsanity.com/paper/2409.10286/) (2024)

## Built on by (most cited first, 3 of 3)

- [From Synthetic Data to Real Restorations: Diffusion Model for Patient-specific Dental Crown Completion](https://mlsanity.com/paper/2603.26588/) (2026)
- [Deep Spectral Models for Robust Dental Shape Generation](https://mlsanity.com/paper/2606.31293/) (2026)
- [SCALP: Semi-Supervised Statistical Shape Modeling from Imperfect 3D Photogrammetry via Landmark-Anchored Spectral Warp](https://mlsanity.com/paper/2608.00187/) (2026)

## Abstract (arXiv)

We introduce ToothForge, a spectral approach for automatically generating novel 3D teeth, effectively addressing the sparsity of dental shape datasets. By operating in the spectral domain, our method enables compact machine learning modeling, allowing the generation of high-resolution tooth meshes in milliseconds. However, generating shape spectra comes with the instability of the decomposed harmonics. To address this, we propose modeling the latent manifold on synchronized frequential embeddings. Spectra of all data samples are aligned to a common basis prior to the training procedure, effectively eliminating biases introduced by the decomposition instability. Furthermore, synchronized modeling removes the limiting factor imposed by previous methods, which require all shapes to share a common fixed connectivity. Using a private dataset of real dental crowns, we observe a greater reconstruction quality of the synthetized shapes, exceeding those of models trained on unaligned embeddings. We also explore additional applications of spectral analysis in digital dentistry, such as shape compression and interpolation. ToothForge facilitates a range of approaches at the intersection of spectral analysis and machine learning, with fewer restrictions on mesh structure. This makes it applicable for shape analysis not only in dentistry, but also in broader medical applications, where guaranteeing consistent connectivity across shapes from various clinics is unrealistic. The code is available at https://github.com/tiborkubik/toothForge.