Objective

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Segmentation of individual tooth from 3D dental meshes is an important process in computer-aided orthodontic system. However

gingival margin and tooth interstices usually overlap or fuse due to limited measuring resolution and mesh-triangulating precision

which causes the automatic segmentation of teeth directly from 3D dental models into individual tooth objects to be extraordinarily difficult

especially when dealing with models with severe malocclusion problems. Traditional approaches easily lead to boundary breaks

branch interferences

and manual interactions. Therefore

a novel and automatic tooth segmentation method based on path planning is proposed in this study. As path-planning method can provide mathematically piecewise optimal boundaries while greatly reducing sensitivity to local noise and intervening structures

such as tooth interstices and fossae; it can reduce user interaction and repair time to a great extent.

Method

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The proposed strategy avoids the limitations of previous methods by initially searching gingiva-teeth boundary paths and then tooth-tooth interstitial boundary paths to avoid interference between gingiva and interstice in the course of detecting boundaries. Dental differential characteristics

image morphology

and B-spline-fitting technology are also employed to ensure stability and accuracy. The feature region of interest between gingiva and teeth is firstly extracted using a discrete curvature analysis. The optimal gingiva-teeth boundary paths are detected based on this feature region by using a novel double-path-planning algorithm. The algorithm initially searches the gingiva-teeth paths on the basis of the vertex distance information of the feature region to ensure that the paths avoid the branching points at tooth interstices. Accurate gingiva-teeth paths are then searched by formulating the neighborhood set of initial gingiva-teeth paths

their vertex distance and curvature information to ensure that the paths adhere to the high-curvature locations between gingiva and teeth. Afterward

the searched gingiva-teeth paths are projected on the occlusal plane to form a gingiva-teeth path binary image

and the dental arch curve is automatically constructed using image morphology and a B-spline-extended-fitting technology. The interstitial concave corners on the gingiva-teeth paths are detected and deleted by combining the normal vectors and curvature characteristics of the gingiva-teeth boundary paths and the ones of the dental arch curve to demarcate the gingival boundary of each individual tooth. The tooth-tooth interstitial boundary paths are then obtained by searching the optimal paths from the endpoints on the lingual side of the gingival boundary of each tooth to their corresponding ones on the buccal side. The tooth-tooth interstitial paths and the gingiva-teeth paths constitute the closed boundary of each individual tooth. These path boundaries can be further refined by using a simple yet efficient method based on bipartition and path searching.

Result

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Experiments on numerous dental models of patients with different levels of crowding problems are conducted to verify the efficiency and accuracy of the proposed method. The segmentation performance

time consumption

and user interaction of the proposed method are analyzed and compared with those of other published approaches. Results demonstrate that although some models include considerable noise and intervened branches

such as tooth fossae and grooves

the proposed method can easily remove these interference structures and produce good segmentation results even for severely deformed teeth and complex tooth arrangements. Besides

the proposed method involves fewer user interactions and parameter adjustments. And the procedures are automatic

except from setting the default curvature threshold for some models. In special cases where the tooth boundary is ambiguous

additional interactions are needed to repair undetected regions within this system interface manually. However

all these interactions are simple and time saving. The time consumption in manually repairing few missing or unwanted boundaries is generally less than 10 s. The key procedures (i.e.

the gingiva-teeth path planning and the tooth-tooth interstitial path planning) only take less than 1 s

which greatly reduce the searching time compared with that of other methods. The most time-consuming operations are feature region extraction (5~6 s) and path refining (4~5 s). Along with the entire program execution time

the entire execution in each segmentation experiment can be finished in less than 20 s.

Conclusion

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This study proposes a novel automated approach for segmenting individual tooth from dental meshes based on path planning. The approach utilizes the strong anti-interference and anti-fracture capabilities of path planning to avoid local noise

intervening structures

and boundary breaks. The proposed method can effectively overcome the interferences of interstice and fossa and the difficulty of path walking around tooth interstice branches by combining multiple-path planning

image morphology

and B-spline-fitting technology. Therefore

good results can be obtained even in the presence of distorted tooth shapes and complex tooth arrangements. Furthermore

the method is fast and effective and involves fewer user interactions and parameter adjustments compared with published approaches. The experimental results demonstrate that the proposed approach can address different levels of crowding problems. Therefore

this approach can be applied to clinical orthodontic planning treatments to improve their accuracy and efficiency. The limitation of the approach is that in cases where the convex and concave features of the gingival boundary is not distinct

the method may require user interactions to guarantee accurate results. However

all required interactions are simple and time saving. In the future

additional prior knowledge and artificial intelligence will be fused into the proposed framework to further enhance its efficiency and robustness.