Achieving meticulous segmentation of tooth point clouds from intra-oral scans stands as an indispensable prerequisite for various orthodontic applications. Given the labor-intensive nature of dental annotation, a significant amount of data remains unlabeled, driving increasing interest in semi-supervised approaches. One primary challenge of existing semi-supervised medical segmentation methods lies in noisy pseudo labels generated for unlabeled data. To address this challenge, we propose GeoT, the first framework that employs instance-dependent transition matrix (IDTM) to explicitly model noise in pseudo labels for semi-supervised dental segmentation. Specifically, to handle the extensive solution space of IDTM arising from tens of thousands of dental points, we introduce tooth geometric priors through two key components: point-level geometric regularization (PLGR) to enhance consistency between point adjacency relationships in 3D and IDTM spaces, and class-level geometric smoothing (CLGS) to leverage the fixed spatial distribution of tooth categories for optimal IDTM estimation. Extensive experiments performed on the public Teeth3DS dataset and private dataset demonstrate that our method can make full utilization of unlabeled data to facilitate segmentation, achieving performance comparable to fully supervised methods with only $20\%$ of the labeled data.

翻译：实现口腔内扫描牙齿点云的精细分割是各类正畸应用不可或缺的前提。鉴于牙科标注工作的高度密集性，大量数据仍处于未标注状态，这推动了对半监督方法的日益关注。现有半监督医学分割方法的一个主要挑战在于为未标注数据生成的伪标签存在噪声。为解决此问题，我们提出了GeoT，这是首个采用实例依赖转移矩阵（IDTM）来显式建模半监督牙科分割中伪标签噪声的框架。具体而言，为处理由数万个牙科点产生的IDTM巨大解空间，我们通过两个关键组件引入牙齿几何先验知识：点级几何正则化（PLGR）以增强三维空间与IDTM空间中点邻接关系的一致性，以及类级几何平滑（CLGS）以利用牙齿类别固定的空间分布实现最优IDTM估计。在公开数据集Teeth3DS及私有数据集上进行的大量实验表明，我们的方法能充分利用未标注数据提升分割性能，仅需$20\%$的标注数据即可达到与全监督方法相当的性能水平。