ToothAxis: Generalizable Tooth Axis Estimation Network from CBCT or IOS Models

Tooth axes, indicating the orientation of teeth, are crucial in orthodontics and dental implants. The precise and automated estimation of tooth axes in 3D dental models is of significant importance. In clinical settings, Cone-beam computed tomography (CBCT) images and intraoral scanning (IOS) models are the two primary forms of digital data, providing 3D volumetric and surface information of the oral cavity, respectively. However, the detection of tooth axes remains largely manual annotation due to the complexities associated with geometric definitions and the variations among different tooth types and individuals. In this paper, we propose a novel two-stage network, named ToothAxis, for tooth axis estimation using either CBCT or IOS models. Given that IOS models only capture the tooth crown surface and lack information about the tooth roots, we initially employ an implicit-function tooth completion module for 3D tooth completion in the first stage. Subsequently, with the 3D tooth models segmented from CBCT images or completed from IOS models, a point-wise offset-based module is proposed in the second stage to accurately estimate the tooth axes. This design aims to encode tooth orientation into a dense representation, which is better suited for sparse information regression tasks, such as tooth axis estimation. Additionally, we incorporate a class-specific feature attention module to integrate global context representation, thereby enhancing robustness in managing diverse tooth shapes. We evaluated ToothAxis on a dataset obtained from real-world dental clinics, comprising 529 tooth models with corresponding CBCT images and paired IOS models. Finally, the ToothAxis achieves angle errors of LA ($2.921^{\circ }$), PSA ($4.801^{\circ }$), and LSA ($5.074^{\circ }$) on tooth models extracted from CBCT images, and LA ($5.326^{\circ }$), PSA ($6.360^{\circ }$), and LSA ($6.520^{\circ }$) on partial crowns extracted from IOS models. Extensive evaluations, ablation studies, and comparative analyses demonstrate that our method achieves accurate tooth axis estimations and surpasses state-of-the-art approaches.