Automatic segmentation of 3D tooth models into individual teeth is an important step in orthodontic CAD systems. 3D tooth segmentation is a mesh instance segmentation task. Complex geometric features on the surface of 3D tooth models often lead to failure of tooth boundary detection, so it is difficult to achieve automatic and accurate segmentation by traditional mesh segmentation methods. We propose a novel solution to address this problem. We map a 3D tooth model isomorphically to a 2D harmonic parameter space and convert it into an image. This allows us to use a CNN to learn a highly robust image segmentation model to achieve automated and accurate segmentation of 3D tooth models. Finally, we map the image segmentation mask back to the 3D tooth model and refine the segmentation result using an improved Fuzzy-Clustering-and-Cuts algorithm. Our method has been incorporated into an orthodontic CAD system, and performs well in practice.

将3D牙齿模型自动分割为单个牙齿是正畸CAD系统中的重要一步。3D牙齿分割是网格实例分割任务。3D牙齿模型表面上复杂的几何特征经常导致牙齿边界检测失败，因此很难通过传统的网格分割方法实现自动，准确的分割。我们提出一种新颖的解决方案来解决这个问题。我们将同构的3D牙齿模型映射到2D谐波参数空间，并将其转换为图像。这使我们能够使用CNN来学习高度鲁棒的图像分割模型，以实现3D牙齿模型的自动和准确分割。最后，我们将图像分割蒙版映射回3D牙齿模型，并使用改进的Fuzzy-Clustering-and-Cuts算法细化分割结果。