# B-Spline Embedded Structure Learning for 3D Tooth Segmentation

arXiv: https://arxiv.org/abs/2608.17291 · HTML: https://mlsanity.com/paper/2608.17291/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 18 references that are in the map.
- First posted on arXiv 18 Aug 2026.

## Builds on (most cited first, 8 of 8)

- [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)
- [Seed1.8 Model Card: Towards Generalized Real-World Agency](https://mlsanity.com/paper/2603.20633/) (2026)
- [Two-Stage Mesh Deep Learning for Automated Tooth Segmentation and Landmark Localization on 3D Intraoral Scans](https://mlsanity.com/paper/2109.11941/) (2021)
- [Learning Context-aware Classifier for Semantic Segmentation](https://mlsanity.com/paper/2303.11633/) (2023)
- [DArch: Dental Arch Prior-assisted 3D Tooth Instance Segmentation](https://mlsanity.com/paper/2204.11911/) (2022)
- [TSegAgent: Zero-Shot Tooth Segmentation via Geometry-Aware Vision-Language Agents](https://mlsanity.com/paper/2603.19684/) (2026)

## Abstract (arXiv)

Accurate 3D tooth segmentation forms the cornerstone of digital dentistry, yet it remains a formidable challenge due to the inherent intricacy of real-world dentitions, such as crowding, misaligned teeth and high morphological similarity between adjacent teeth. To resolve this, we present B-Spline Embedded Structure Learning, a novel framework that distills the inherent sequential arrangement of teeth into a continuous structural constraint to regularize representation space. Our approach parameterizes the global dental topology by fitting a parametric B-spline trajectory to tooth centers, assigning each point a continuous structural embedding that forces the shared backbone to capture global arch organization. To fully exploit these embedded priors, we introduce a Structure-Aware Dynamic Classifier (SADC) to substitute rigid static templates with adaptive, case-calibrated decision boundaries. SADC regularizes dynamic prototype pooling via a localized Gaussian proximity gate and contextually co-evolves them through an attention block modeling spatial relations and bilateral symmetries across teeth. Extensive evaluations on the 3DTeethSeg22 benchmark demonstrate that our method establishes a new state-of-the-art accuracy with exceptional structural robustness and efficiency in computational overhead, markedly enhancing the model's capacity to handle complex dental configurations.