基于生物统计模型的智能龈缘修复理论研究

Optimal gingival contours around restored teeth are of critical importance for restorative success and esthetics. By integrating the digital design technology and stomatology restoration, this project presents a novel method for reconstructing the gingival contours in edentulous patients based on biological statistical model to solve the problem of the low-efficiency and inaccuracy in conventional manual design. The main works are as follows: (1) For the issue of the adjacent teeth adhesion of dental meshes, the closed gingival curve of each tooth with no interference between them can be automatically obtained from a morphology modeling algorithm combining the discrete curvature analysis, cellular automaton, granular computing, waved-based B-spline fairing and tangent constraining between teeth, which can establish the foundation for the following statistical sample building of the gingival contour shape; (2) According to the teeth anatomical characteristics, an automatic calibration of the gingival shape is presented in order to building the database of gingival contour shape from large amount of healthy people. The statistical shape model of gingival contour is then build based on the principle component analysis technology to induce the gingival biological anatomical morphing pattern; (3) For restoring the ideal aesthetic gingival contour for edentulous patients, a gingival intelligent inference method combining the multi-objective optimization based on the principle component characteristics of the statistical model and the multiple self-adaption elastic deformation based on the radial basis function is proposed to realize the automated progressive approximation design for the gingival contour. The research results are expected to raise the aesthetic effect of prosthodontics and provide a new idea and theory basis.

理想的龈缘形态对于义齿修复的成功和美学具有极为重要的作用。为解决传统手动设计龈缘效率低和精度差等问题，本项目将数字化设计技术与口腔医学修复紧密结合，提出一种基于生物统计模型的缺牙龈缘智能修复方法，主要工作包括：(1)针对三角网格牙颌模型齿间融合问题，提出基于离散曲率分析、元胞自动机、粒计算、B样条小波光顺以及齿间相切约束的形态建模方法，自动构建出齿间无干涉的封闭龈缘曲线, 为后续龈缘统计样本建立奠定基础；(2)提出基于牙齿解剖标志特征的龈缘形状自动标定方法，以建立大量健康人群龈缘数据库，并基于主成分分析技术建立龈缘统计形状模型，以正确揭示龈缘形态的生物解剖形变规律；(3)为恢复匹配缺牙患者的解剖美学龈缘轮廓，提出基于统计模型多目标优化和基于径向基多重自适应弹性变形的智能推理方法，实现龈缘形态的自动化渐进逼近设计。研究成果可望提高口腔修复美学效果，为龈缘修复提供新思路和理论依据。

理想的龈缘形态对于义齿修复的成功和美学具有极为重要的作用。为解决传统手动设计龈缘效率低和精度差等问题，本研究将数字化设计技术与口腔医学修复紧密结合，提出一种基于生物统计模型的缺牙龈缘智能修复方法，主要创新性工作包括：(1) 针对口腔CT图像的牙齿形态变化和排列特点，提出一种新颖的水平集活动轮廓模型的三维牙齿重建方法，该模型融合边缘梯度能量、先验图像的形状约束能量和先验灰度的局部区域能量，较准确地重建出每颗牙齿独立的三角网格模型，从而为下一步制定口腔修复规划和生物力学分析等奠定坚实的基础；(2) 针对三角网格牙颌模型齿间融合问题，提出结合离散曲率分析、路径规划、形态学运算、B样条拟合相结合的牙齿分割方法，有效避免了牙缝干扰，自动构建出齿间无干涉的封闭龈缘曲线, 为后续龈缘统计样本建立奠定基础；(3) 为恢复患者缺失牙的龈缘轮廓形态，利用基于牙齿解剖标志特征的龈缘形状自动标定方法快速获取龈缘统计样本，并利用主成分分析技术构建龈缘统计形状模型，从而使建立的模型不仅能够充分反映龈缘的解剖形态特征而且能够保证较少的模型参数，在此统计模型基础上，提出基于多目标优化和弹性变形相结合的智能推理方法，实现患者缺失牙龈缘的个性化设计；(4) 为控制牙齿复杂曲面数控加工过程中微线段的速度波动，提出基于过控制顶点的三次B样条曲线的微线段过渡插补方法；为提高系统模型参数的建模精度，提出一种基于信息粒度支持向量机的辨识方法；为满足复杂曲面加工的平稳性和实时要求，提出一种复合式柔性速度规划方法；这些都为三维牙齿模型复杂曲面加工实现高平稳高精度提供理论控制方法。