基于颌位空间约束的缺损牙体曲面统计重建算法

doi:10.3901/JME.2016.01.165

摘要/Abstract

摘要： 重建符合牙齿咬合接触关系的缺损牙体曲面是全冠、嵌体、贴面等多类修复体造型过程中均需要解决的关键问题。针对规模有限的标准模板牙冠难以表达牙齿自然形态多样性的不足，提出了基于颌位空间约束的缺损牙齿曲面统计重建算法。采用广义普氏分析构建样本牙冠曲面之间的对应关系，在主要特征近似对齐的基础上计算平均牙冠；结合样本牙冠与平均牙冠对应点间的欧氏距离，建立可以表达样本牙冠与平均牙冠形态区别的差异矩阵，利用主成分分析方法求解影响平均牙冠形态的主要特征矢量，在此基础上建立基于参数表达的统计牙冠模型；根据缺损牙体的残留区域形态及其颌位接触关系采集局部约束特征点，以此反求统计模型的形变参数，构建基于颌位空间约束的统计牙冠，实现缺损牙体曲面的形态重建。下颌第一磨牙的重建试验表明，所建立的统计牙冠不仅具有足够的解剖形态特征，而且能与缺损牙体的残留形态以及邻牙、对颌牙相适应，具有良好的颌位接触关系，后期设计不需要复杂的调颌检测。

关键词: 广义普氏分析, 口腔修复CAD/CAM, 统计牙冠模型, 形变参数

Abstract: Restoring the broken tooth surface which should coincide with the occlusal contact is a common essential problem in the modelling of dental restorations, such as crowns, inlays/onlays and veneers. Traditional modelling technologies have one obvious limitation: the size of standard template tooth library is limited, so it is hard to describe the diversity of natural tooth. To solve these problems, a novel statistical reconstruction algorithm for restoring broken tooth surface based on occlusion spatial constraint is presented. The correspondence between all sample crown models is established by means of generalized Procrustes analysis, whereby a number of corresponding landmarks are selected and the average crown model is calculated. The covariance matrix is established and principal component analysis is carried out which describing the differences between sample crown models and average crown model, so a mathematical representation of statistical crown morphology can be defined by a quantitative formulation. Finally, the broken tooth surface can be inferred with the statistical crown model by using occlusion spatial constraint points, which determine the deformable parameters of statistical deformable model. An experiment on the first lower molar demonstrates that the proposed method can describe enough anatomical morphology, the pose and anatomical features of the tooth will work well for chewing without need more complicated occlusion inspection.

Key words: deformable parameters, dental CAD/CAM, generalized Procrustes analysis, statistical crown model

中图分类号:

TP391

张长东, 刘婷婷, 廖文和, 张凯. 基于颌位空间约束的缺损牙体曲面统计重建算法[J]. 机械工程学报, 2016, 52(1): 165-174.

ZHANG Changdong, LIU Tingting, LIAO Wenhe, ZHANG Kai. Statistical Reconstruction Algorithm for Restoring Broken Tooth Surface Based on Occlusion Spatial Constraint[J]. Journal of Mechanical Engineering, 2016, 52(1): 165-174.

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