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.

导出引用管理器 EndNote|Reference Manager|ProCite|BibTeX|RefWorks

链接本文: http://www.cjmenet.com.cn/CN/10.3901/JME.2016.01.165

http://www.cjmenet.com.cn/CN/Y2016/V52/I1/165

参考文献

[1] 刘明丽，王勇，吕培军. 以三维B样条曲线网格构建嵌体轴面[J]. 北京大学学报，2006，38(4)：438-440. LIU Mingli，WANG Yong，Lü Peijun. Construction of inlay axial surface using B-spline curve network[J]. Journal of Peking University，2006，38(4)：438-440.
[2] 吕培军，李彦生，王勇，等. 国产口腔修复CAD/CAM系统的研究与开发[J]. 中华口腔医学杂志，2002， 37(5)：367-370.
Lü Peijun，LI Yansheng，WANG Yong，et al. The research and development of CAD/CAM system in restorative dentistry[J]. Chinese Journal of Stomatology， 2002，37(5)：367-370.
[3] ADOLPH S，GURKE S. Modeling of a fitting inlay from various information[C]// Proceedings of 2001 Conference on Vision，Modelling and Visualization. Amerstdam： IOS Press，2001，309-316.
[4] YOO K，HA J，YOO J. Modeling inlay/onlay prostheses with mesh deformation techniques[C]// Proceedings of 7th International Conference on Computational Science. Berlin：Springer-Verlag，2007：154-157.
[5] STEINBRECHER T，GERTH M. Dental inlay and onlay construction by iterative Laplacian surface editing[J]. Eurographics Symposium on Geometry Processing，2008，27(5)：1441-1447.
[6] 张长东，戴宁，廖文和，等. 部分缺失牙齿咬合面自适应重建算法[J]. 中国生物医学工程学报，2012，31(2)： 203-210. ZHANG Changdong，DAI Ning，LIAO Wenhe，et al. Partially missing dental occlusion surface adaptive reconstruction algorithm[J]. Chinese Journal of Biomedical Engineering，2012，31(2)：203-210.
[7] 郑淑贤，李佳，孙庆丰. 基于特征映射的义齿表面三维变形设计方法[J]. 机械工程学报，2011，47(3)：129-134. ZHENG Shuxian，LI Jia，SUN Qingfeng. 3D deformation design method for prosthetic dental surface based on feature mapping[J]. Journal of Mechanical Engineering，2011，47(3)：129-134.
[8] ZHENG Shuxian，LI Jia，SUN Qingfeng. A novel 3D morphing approach for tooth occlusal surface reconstruction[J]. Computer-Aided Design，2011，43(3)：293-302.
[9] 范然，金小刚. 模板特征线匹配的牙齿形状修复[J]. 计算机辅助设计与图形学学报，2014，26(2)：280-286. FAN Ran，JIN Xiaogang. Tooth shape restoration with template feature line matching[J]. Journal of Computer-Aided Design&Computer Graphics，2014，26(2)：280-286.
[10] MEHL A，BLANZ V，HICKEL R. Biogeneric tooth: a new mathematical representation for tooth morphology in lower first molars[J]. European Journal of Oral Sciences， 2005，113(4)：333-340.
[11] BLANZ V，MEHL A，VETTER Y，et al. A statistical method for robust 3D surface reconstruction from sparse data[C]// The 2nd International Symposium on 3D Data Processing，Visualization and Transmission. Los Alamitos：IEEE Computer Society，2004，293-300.
[12] RADMAN A，ALKHOLIDI A，HAMAM H. A new approach improving the quality of 3D face recognition[J]. Advances in Computer Science and Engineering，2011，6(1)：1-32.
[13] BLANZ V，SCHERBAUM K，SEIDEL H P. Fitting a morphable model to 3D scans of faces[J]. Computer Vision，2007：1-8.
[14] 胡永利，尹宝才，谷春亮，等. 基于形变模型的三维人脸重建方法及其改进[J]. 计算机学报，2005，28(10)：1671-1679. HU Yongli，YIN Baocai，GU Chunliang，et al. 3D face reconstruction based on the improved morphable model[J]. Chinese Journal of Computers，2005，28(10)：1671-1679.
[15] 龚勋，王国胤. 基于特征点的三维人脸形变模型[J]. 软件学报，2009，20(3)：724-733. GONG Xun，WANG Guoyin. 3D face deformable model based on feature points[J]. Journal of Software，2009，20(3)：724-733.
[16] HASLER N，STOLL C，SUNKEL M，et al. A statistical model of human pose and body shape[J]. Computer Graphics Forum，2009，28(2)：337-346.
[17] CHAIBI Y，CRESSON T，AUBERT B. Fast 3D reconstruction of the lower limb using a parametric model and statistical inferences and clinical measurements calculation from biplanar X-rays[J]. Computer Methods in Biomechanics and Biomedical Engineering，2012，15(5)：457-466.
[18] PIZARRO D，BARTOLI A. Global optimization for optimal generalized procrustes analysis[J]. Computer Vision and Pattern Recognition (CVPR)，2011：2409-2415.
[19] WILLIAM H P，SAUL A T，WILLIAM T V，et al. Numerical recipes in C[M]. London：Cambridge University Press，1999.
[20] 张旭，戴宁，廖文和，等. 基于三维渐变的牙齿磨耗可视化仿真[J]. 机械工程学报，2013，49(3)：95-100. ZHANG Xu，DAI Ning，LIAO Wenhe，et al. Visual simulation of tooth wear based on 3D morphing techniques[J]. Journal of Mechanical Engineering，2013，49(3)：95-100.
[21] MIN T，SEAN C，SUNGEUI Y，et al. Interactive continuous collision detection between deformable models using connectivity-based culling[C]// Proceedings of SPM'08，New York：ACM，2008：25-36.