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面向数字牙科的区域划分与特征点保留网格简化方法

Mesh Simplification with Region Partitioning and Feature Point Preservation for Digital Dentistry

  • 摘要: 随着数字牙科与三维口腔医学的发展,高精度牙齿三维模型在正畸规划、修复体设计和手术仿真中得到了广泛应用。然而,牙齿模型通常包含数万三角面片,这种高密度网格在数据存储、传输和实时交互过程中带来了巨大的负担。针对现有的网格简化方法在面对牙齿这种具有显著特征的模型时仍然存在特征丢失和边界断裂等问题,提出一种融合区域自适应划分与跨区域特征保护的牙齿模型网格简化方法。首先基于法线相似度和动态平均法线的广度优先搜索对牙齿模型进行区域划分,有效地区分平坦侧面和复杂咬合面,并为不同区域制定差异化的简化策略;然后通过跨区域特征点检测和保留机制赋予位于区域交界处的顶点更高的保留权重,在高简化率下保持牙尖、窝沟、咬合边缘等关键结构。在真实牙齿数据上的实验结果表明,在80%、50%和10%的简化率下,所提方法的Hausdorff距离最低可达0.042 202、平均距离最低可达0.001 617、法线相似度均接近1,实现了低几何偏差和高法线相似度;与QEM、MeshLab、LPM、ICE等主流简化方法相比,该方法在Hausdorff距离、平均距离、Chamfer距离等指标上具有更好的性能,且在高简化率下能够有效地保留临床关心的几何特征,为数字牙科在正畸模拟、修复设计、实时交互等应用中提供了强有力的支持。

     

    Abstract: With the advancement of digital dentistry and 3D oral medicine, high-precision 3D dental models have been widely used in orthodontic planning, prosthetic design, and surgical simulation. However, dental models often consist of tens of thousands of triangular meshes, and such high-density meshes pose signifi-cant burdens on data storage, transmission, and real-time interaction. Existing geometric-driven and attrib-ute-driven mesh simplification methods perform well in general scenarios, but they still face the challenges of feature loss and boundary breakage when dealing with the pronounced regional geometric heterogeneity and clinical feature centralization in dental models. A mesh simplification method for dental models is proposed, which integrates adaptive region segmentation and cross-region feature preservation. The method first partitions the dental model based on normal similarity and breadth-first search (BFS) of dy-namic average normals, distinguishing flat surfaces from complex occlusal surfaces, and formulates dif-ferentiated simplification strategies for different regions. Subsequently, a cross-region feature point detec-tion and preservation mechanism is employed, giving higher preservation weights to vertices located at the boundaries between multiple regions, thus retaining key structures such as cusps, grooves, and occlusal edges under high simplification rates. Experimental results on real dental datasets show that at simplifica-tion rates of 80%, 50%, and 10%, the proposed method achieves a minimum Hausdorff distance of 0.042 202, a minimum mean distance of 0.001 617, and normal similarity values close to 1, realizing low geometric deviation and high normal consistency. Compared with mainstream methods like QEM, MeshLab, LPM, and ICE, the proposed method performs better in terms of Hausdorff distance, average dis-tance, and Chamfer distance, and it effectively preserves clinically relevant geometric features even under high simplification rates. This method provides strong support for orthodontic simulation, prosthetic de-sign, and real-time interactive applications in digital dentistry.

     

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