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Received：05 March 2017，
Revised：2017-9-19，
Published：16 January 2018
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目的
2
从3维牙颌模型上分割出单颗牙齿是计算机辅助正畸系统的重要步骤。由于3维测量分辨率和网格重建精度的有限性，三角网格牙颌模型上牙龈和牙缝边界往往融合在一起，使得单颗牙齿的自动分割变得极为困难。传统方法容易导致分割线断裂、分支干扰等问题，且手工交互较多，为此提出一种新颖的基于路径规划技术的单颗牙齿自动分割方法。
方法
2
为避免在探测边界时牙龈和牙缝相互干扰，采用牙龈路径和牙缝路径分开规划策略。首先基于离散曲率分析和一种双重路径规划法搜索牙龈分割路径，并基于搜索到的牙龈路径利用图像形态学和B样条拟合技术构建牙弓曲线；然后综合牙龈路径和牙弓曲线的形态特征探测牙龈路径上的牙缝凹点以划界每颗牙齿的牙龈边界轮廓，并通过匹配和搜索牙龈边界轮廓上颊舌侧凹点间的最优路径确定齿间牙缝边界路径；最后细化整个路径以获取每颗牙齿精确的封闭分割轮廓。
结果
2
对不同畸形程度的患者牙颌模型进行分割实验，结果表明，本文方法对于严重畸形的牙齿能够产生正确的分割结果，而且简单快速，整个分割过程基本能够控制在20 s以内。和现有方法相比，本文方法具有较少的人工干预和参数调整，除了在个别牙齿边界较为模糊的位置需要手动调整外，大部分情况都是自动的。
结论
2
提出的路径规划方法具有强大的抗干扰能力，能够有效克服牙缝牙沟等分支干扰以及分割线断裂等问题，最大程度地减少人工干预，适用于各类畸形牙患者模型的牙齿分割。
Objective
2
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
2
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
2
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
2
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.
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