虚拟正畸治疗中的错位牙齿自动排列方法

2019年4月图 学 学 报 April2019第40卷第2期JOURNAL OF GRAPHICS V ol.40No.2虚拟正畸治疗中的错位牙齿自动排列方法

李占利1，付敬鼎1，李洪安1，周康1，惠巧娟2

(1. 西安科技大学计算机科学与技术学院，陕西西安 710054；

2. 中国矿业大学银川学院机电动力与信息工程系，宁夏银川 750021)

摘要：针对虚拟正畸技术中人工排牙效率低下问题，提出一种基于拟合优化的错位牙齿自动排列方法。对输入的牙列模型建立排牙坐标系，定义单颗牙齿特征点并建立牙齿局部坐标系。在此基础上，从低维角度分析牙列中各颗牙齿的位置和姿态，采用加权拟合优化的方法分别计算牙齿的坐标平移量与局部坐标轴旋转量，形成牙齿位姿与空间牙列曲线的关联约束，并结合矩形包围盒的碰撞检测方法，设计基于最速下降法的迭代算法在空间牙列曲线约束范围内调整牙齿位姿，完成牙齿的自动排列。实验结果表明，排好的牙列与人工排牙结果相差无异，排牙效率大大提高；与现有排牙方法相比，更贴近临床牙齿矫治，且牙齿移动代价总量明显降低。

关键词：虚拟正畸；自动排牙；加权拟合；优化

中图分类号：TP 391 DOI：10.11996/JG.j.2095-302X.2019020225

文献标识码：A 文章编号：2095-302X(2019)02-0225-10

Automatic Alignment Method for Malocclusion in

Virtual Orthodontics Treatment

LI Zhan-li1, FU Jing-ding1, LI Hong-an1, ZHOU Kang1, HUI Qiao-juan2

(1. College of Computer Science and Technology, Xi’an University of Science and Technology, Xi’an Shaanxi 710054, China; 2. Department of

Mechatronics Power and Information Engineering, China University of Mining and Technology Yinchuan College, Yinchuan Ningxia 750021, China)

Abstract: Aiming at the problem of low efficiency of teeth arrangement by artificial teeth in virtual orthodontics treatment technology, this paper proposes an automatic alignment method for malocclusion based on fitting optimization. Firstly, we create a coordinate system for the input dental model, define single tooth feature points and establish the local coordinate system of teeth. On this basis, the position and posture of each tooth in the dentition is analyzed from a lower dimension. The weighted fitting optimization method is employed to calculate the coordinate translation and local axis rotation of tooth which forms the association constraints of the position, posture of teeth and the spatial dental curves. Then, combined with the collision detection method of rectangular bounding box, we design an iterative algorithm based on method of steepest descent to adjust the position and posture of teeth within the constraints of spatial dental curves. The experimental results show that the teeth alignment is similar to artificial alignment of teeth, and the alignment efficiency is highly improved. The proposed method is not only more like clinical orthodontics, but also reduces the total cost of teeth movement compared with the existing teeth alignment method.

Keywords: virtual orthodontics; automatic teeth alignment; weighted fitting; optimization

收稿日期：2018-09-03；定稿日期：2018-09-14

基金项目：宁夏高等学校科学研究项目(NGY2017234)；陕西高等教育教学改革研究项目(17BY040)；西安科技大学博士启动金项目(2019QDJ007)；

陕西省自然科学基础研究计划项目(2019JM-162)

第一作者：李占利(1964-)，男，陕西周至人，教授，博士，博士生导师。主要研究方向为计算机图形学、图像处理等。E-mail：lizl@

通信作者：李洪安(1978-)，男，山东武城人，副教授，博士，硕士生导师。主要研究方向为图形图像处理、机器视觉等。E-mail：an6860@