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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研究

Research on Regional Partitioning and Feature Point Retention for Mesh Simplification in 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、修复体设计及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. 现有的网格简化方法在一般场景中表现良好,但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. 为解决这一问题,提出了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. 该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(BFS)对牙齿模型进行区域划分,能够有效地将平坦侧面和复杂咬合面区分开来,并为不同区域制定差异化的简化策略;接着,通过跨区域特征点检测与保留机制,赋予位于区域交界处的顶点更高的保留权重,从而在高简化率下保持牙尖、窝沟和咬合边缘等关键结构. 实验结果表明,该方法在80%、50%和10%的简化率下,均能够实现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,提出的方法在Hausdorff距离、平均距离和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、修复设计和实时交互等应用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 significant burdens on data storage, transmission, and real-time interaction. Existing geometric-driven and attribute-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. This paper proposes a mesh simplification method for dental models that integrates region-adaptive partitioning and cross-region feature preservation. The method first partitions the dental model based on normal similarity and breadth-first search (BFS) of dynamic average normals, distinguishing flat surfaces from complex occlusal surfaces, and formulates differentiated simplification strategies for different regions. Subsequently, a cross-region feature point detection 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 models show that the proposed method achieves low geometric deviation and high normal similarity at simplification rates of 80%, 50%, and 10%. Compared with mainstream methods like QEM, Meshlab, LPM, and ICE, the proposed method performs better in terms of Hausdorff distance, average distance, 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 design, and real-time interactive applications in digital dentistry.

     

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