三维数字化牙齿模型被广泛的应用于口腔正畸领域，特别是三维数字化成像在口腔正畸诊断、治疗和疗效预测中发挥的作用。牙齿的好坏会影响一个人的气质和形象，如今不同年龄阶段的人都会存在牙齿方面的疾病或者问题。因此，利用计算机技术辅助诊断牙齿疾病，发展计算机辅助模拟矫正系统，对牙齿矫正具有重要意义。由于目前的牙齿三维模型都是口腔扫描得来的，只有牙冠和牙龈表面部分，缺少牙根部分数据，不利于牙齿模拟仿真。为了帮助医生进行虚拟牙齿矫正，本文通过研究牙冠模型边缘特点，将牙冠模型进行平滑处理，去除边缘噪点，可以更好的进行牙齿三维仿真。并针对如何基于三维牙冠数据模型建立完整的牙齿模型进行了研究，主要研究内容如下：

（1）针对三维牙冠模型边缘存在噪点的问题，本文提出了一种基于噪点分类的牙冠边缘平滑处理方法。该方法首先依据牙冠边缘特点，经拟合分析提出将噪点分为边界线中的噪点和拟合曲线中的噪点两种。然后，利用高斯曲率进行噪点识别。最后，使用改进的拉普拉斯算子和最小二乘拟合方法分别对这两种噪点进行去除，输出去噪后的三维牙冠模型。实验结果证明，该方法针对于牙冠边缘的平滑处理效果从噪点去除率、面片填充率、面片删除率三个方面，和传统的拉普拉斯相比，噪点去除率提升了86.0%，面片填充概率增大约为两倍，删除面片的概率基本一致。和最小二乘拟合方法相比，噪点去除率提升了75.9%，面片填充率减少22.61%，删除面片也减少22.14%。

（2）由于口腔扫描的牙颌三维模型缺少牙根数据，而完整的三维牙齿模型关系到医生排牙、种植、正畸和生物力学分析的结果。因此，本文提出了基于牙冠特征的牙齿根部模拟仿真方法。该方法首先将牙齿根部分为单牙根和多牙根分别进行仿真，将单牙根和多牙根牙齿进行分段，并对每个分段设计不同仿真方案。然后，针对多牙根仿真，根据多牙根的支根空间分布情况和空间曲线交汇特点，提出了一种基于几何特征的多牙根的支根选择方法和一种改进快速交点选择的曲线融合方法。根据牙根的数目进行支根选择，完成牙根模拟仿真。最后，利用机器学习的方法学习真实牙冠模型表面的特征，进行根部的风格迁移，使得牙齿仿真效果更加接近于真实牙齿。该方法从冠根比和粗糙度两个方面进行了单牙根和多牙根仿真处理前后的对比，对风格迁移前后效果进行了对比。实验结果表明，本文构造的牙根模型已经非常接近真实牙齿。

Three-dimensional digital tooth models are widely used in the field of orthodontics, especially the role of three-dimensional digital imaging in the diagnosis, treatment and curative effect prediction of orthodontics. The quality of teeth will affect a person's temperament and image. Nowadays, people of different ages will have dental diseases or problems. Therefore, the use of computer technology to assist in the diagnosis of dental diseases and the development of computer-assisted simulation correction systems are of great significance to orthodontics. As the current 3D models of teeth are obtained from oral scans, only the crown and gingival surface are part of the tooth, and the root part of the data is lacking, which is not conducive to tooth simulation. In order to help doctors perform virtual orthodontics, this thesis studies the edge characteristics of the crown model, smoothes the crown model, removes edge noise, and can better perform 3D simulation of teeth. And research on how to build a complete tooth model based on the three-dimensional crown data model, the main research contents are as follows:

(1) Aiming at the problem of noise points on the edges of 3D dental crown models, this thesis proposed a method for smoothing the edges of teeth based on noise points classification. Firstly, according to the characteristics of the edge of the tooth crown, this method proposed to divide the noise into two types: the noise in the boundary line and the noise in the fitting curve. Then, the Gaussian curvature was used for noise recognition. Finally, the improved Laplacian operator and the least square fitting method were used to remove these two noise points, and the denoised three-dimensional crown model is output. The experimental results show that the method is aimed at the smoothing effect of the crown edge in terms of noise removal rate, patch filling rate, and patch deletion rate. Compared with the traditional Laplacian, the noise removal rate is increased by 86.0%. , The probability of patch filling increases approximately twice, and the probability of deleting patches is basically the same. Compared with the least squares fitting method, the noise removal rate is increased by 75.9%, the patch filling rate is reduced by 22.61%, and the deleted patch is also reduced by 22.14%.

(2) Because the three-dimensional dental model of the oral scan lacks root data, the complete three-dimensional tooth model is related to the results of the doctor's tooth arrangement, implantation, orthodontics and biomechanical analysis. Therefore, this thesis proposed a simulation method of tooth root based on the characteristics of the crown. Firstly, this method simulated the two types of tooth roots as single root and multiple roots respectively, divided the single root and multiple root teeth into segments, and designed different simulation schemes for each segment. Then, for multi-root simulation, based on the spatial distribution of multi-root roots and the intersection characteristics of spatial curves, a method for multi-root root selection based on geometric features and a curve fusion method for improving fast intersection selection are proposed. The roots are selected according to the number of roots, and the root simulation is completed. Finally, the machine learning method was used to learn the characteristics of the surface of the real crown model and transfer the style of the root, so that the simulation effect of the tooth is closer to the real tooth. This method compared single root and multiple roots before and after simulation treatment in terms of crown-to-root ratio and roughness, and compares the effects before and after the style transfer. Experimental results show that the tooth root model constructed in this thesis is very close to real teeth.

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