Topology of a Smile: Persistent Homology in Dental Imaging

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.

Modern deep learning architectures have demonstrated strong performance in dental CBCT segmentation. One remaining crucial challenge is accurate tooth labeling in cases with missing or malpositioned teeth, which are highly relevant for dental practice. Transformer-based architectures should in theory be able to resolve such ambiguities using global anatomical context. However, due to the high resolution of CBCT volumes and the wide spatial distribution of teeth within volumes, dense patch-based volumetric processing faces an inherent trade-off. Computational costs limit the number of patches that can be used in self-attention and thus, one can either increase the extent of the context captured in self-attention or capture fine-grained structural details by using small patches, but not both. In this work, we present Teeth2Point, an efficient point-based transformer framework for dental CBCT semantic segmentation that can avoid this trade-off. Teeth2Point first localizes volumetric regions of interest (ROIs) surrounding teeth using a convolutional model, then converts ROIs into point tokens using adaptive sampling. A transformer model predicts accurate segmentations using the point tokens, which allow capturing global context while retaining high resolution. The transformer is first pretrained using self-supervised learning (SSL), in the style of DINO but using domain-specific augmentation strategies, followed by supervised finetuning. The SSL pretraining, which includes random token masking, provides robustness to complex anatomical variations. Compared with the strongest two-stage baseline, Teeth2Point improves abnormal-case performance by 1.44 DSC points on average across four datasets; relative to the first-stage nnU-Net, the gain is 1.9 points.

With the rapid advancement of artificial intelligence, intelligent dentistry for clinical diagnosis and treatment has become increasingly promising. As the primary clinical dentistry task, tooth structure segmentation for Cone-Beam Computed Tomography (CBCT) has made significant progress in recent years. However, challenges arise from the obtainment difficulty of full-annotated data, and the acquisition variability of multi-source data across different institutions, which have caused low-quality utilization, voxel-level inconsistency, and domain-specific disparity in CBCT slices. Thus, the rational and efficient utilization of multi-source and unlabeled data represents a pivotal problem. In this paper, we propose SemiTooth, a generalizable semi-supervised framework for multi-source tooth segmentation. Specifically, we first compile MS3Toothset, Multi-Source Semi-Supervised Tooth DataSet for clinical dental CBCT, which contains data from three sources with different-level annotations. Then, we design a multi-teacher and multi-student framework, i.e., SemiTooth, which promotes semi-supervised learning for multi-source data. SemiTooth employs distinct student networks that learn from unlabeled data with different sources, supervised by its respective teachers. Furthermore, a Stricter Weighted-Confidence Constraint is introduced for multiple teachers to improve the multi-source accuracy.Extensive experiments are conducted on MS3Toothset to verify the feasibility and superiority of the SemiTooth framework, which achieves SOTA performance on the semi-supervised and multi-source tooth segmentation scenario.