3D tooth segmentation is a challenging fundamental problem in computer-aided design (CAD) systems for orthodontic treatment planning. Existing methods of tooth segmentation cannot meet the requirements for both efficiency and accuracy. This paper presents a coarse-to-fine 3D tooth segmentation algorithm, called C2F-3DToothSeg, to improve tooth segmentation. The algorithm consists of two steps: extraction of the coarse gum line and optimization of this line. A concavity-sensitive harmonic field is searched in a local region of entire dental meshes to produce a series of isolines. The best isoline is selected as the coarse gum line, which is then optimized by a heuristic feature line extraction scheme to yield an accurate gum line. Extensive visual and numerical experiments demonstrate that our C2F-3DToothSeg has better overall performance in accuracy and efficiency compared to other existing methods directly applicable in orthodontic CAD systems. A point on the tooth surface is loosely found to locate the center zone of each individual tooth via a simple intuitive single click of the operation. The experiments also show that our method is robust to different complex dental models; for example, it copes with bulge bubbles, decay and cavity issues, and dental accessories.

3D 牙齿分割是用于正畸治疗计划的计算机辅助设计 (CAD) 系统中一个具有挑战性的基本问题。现有的牙齿分割方法不能同时满足效率和准确性的要求。本文提出了一种从粗到细的 3D 牙齿分割算法，称为 C2F-3DToothSeg，以改进牙齿分割。该算法包括两个步骤：粗牙龈线的提取和该线的优化。在整个牙网的局部区域中搜索对凹度敏感的谐波场以产生一系列等值线。选择最佳等值线作为粗牙龈线，然后通过启发式特征线提取方案对其进行优化以产生准确的牙龈线。大量的视觉和数值实验表明，与直接适用于正畸 CAD 系统的其他现有方法相比，我们的 C2F-3DToothSeg 在准确性和效率方面具有更好的整体性能。通过简单直观的单击操作，可以松散地找到牙齿表面上的一个点来定位每个牙齿的中心区域。实验还表明，我们的方法对不同的复杂牙科模型具有鲁棒性；例如，它可以处理膨胀气泡、腐烂和蛀牙问题以及牙科配件。实验还表明，我们的方法对不同的复杂牙科模型具有鲁棒性；例如，它可以处理膨胀气泡、腐烂和蛀牙问题以及牙科配件。实验还表明，我们的方法对不同的复杂牙科模型具有鲁棒性；例如，它可以处理膨胀气泡、腐烂和蛀牙问题以及牙科配件。