基于波前思想的三维牙齿复杂孔洞修补
Three-Dimensional Tooth Complex Hole Repair Based on Advancing Front Idea
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摘要: 三维牙齿模型表面的孔洞既影响美观, 又干扰牙齿正畸治疗过程. 针对已有算法修补牙齿孔洞效果不佳且效率低的问题, 提出基于波前思想的牙齿复杂孔洞修补算法. 首先对孔洞边界中过小内角和过短边进行坍缩, 对过长边进行分段; 然后采用顶点的法向信息与局部Taubin曲率结合的方法初步修补孔洞; 再利用拉普拉斯-贝尔特拉米算子降低模型表面噪点干扰; 最后将顶点高斯曲率作为约束, 结合Sqrt3算法细分网格, 获得形态自然的孔洞修补结果. 对含有孔洞的下牙颌模型以及不同形态的单颗牙齿模型进行修补实验, 与其他算法对比修补效率, 并采用网格质量评估算法评价修补结果, 结果表明, 所提方法修补模型中各种孔洞的效率以及效果明显优于对比方法, 最大限度地保留了牙齿表面微小特征.Abstract: The holes on the surface of the three-dimensional tooth model not only affect the aesthetics, but also interfere with the orthodontic treatment process. Aiming at the problem that the existing algorithms have a poor effect and low efficiency in repairing tooth holes, a complex tooth hole repair algorithm based on an advancing front idea is proposed. Firstly, the overly small inner angles and short edges within the hole boundary are collapsed, while excessively long edges are segmented. Then, the hole is initially repaired by combining the normal information of the vertices with the local Taubin curvature. The Laplace-Beltrami operator is used to reduce surface noise in the model. Finally, the vertex Gaussian curvature is used as a constraint, and the Sqrt3 algorithm is used to subdivide the mesh to obtain a natural hole repair result. The repair experiments were carried out on the mandibular model with holes and the single tooth model with different shapes. The repair efficiency was compared with other algorithms, and the mesh quality evaluation algorithm was used to evaluate the repair results. The results show that the efficiency and effectiveness of the proposed method in repairing various holes in the model are significantly better than those of the comparative method, and the tiny features of the tooth surface are retained to the maximum extent.