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林筱韵, 翟羽佳, 吴晓群. 基于“几何-拓扑”迭代优化的三维网格模型修复算法[J]. 计算机辅助设计与图形学学报, 2022, 34(2): 305-314. DOI: 10.3724/SP.J.1089.2022.18865
引用本文: 林筱韵, 翟羽佳, 吴晓群. 基于“几何-拓扑”迭代优化的三维网格模型修复算法[J]. 计算机辅助设计与图形学学报, 2022, 34(2): 305-314. DOI: 10.3724/SP.J.1089.2022.18865
Lin Xiaoyun, Zhai Yujia, Wu Xiaoqun. “Geometry-Topology” Iterative Optimization for Mesh Inpainting[J]. Journal of Computer-Aided Design & Computer Graphics, 2022, 34(2): 305-314. DOI: 10.3724/SP.J.1089.2022.18865
Citation: Lin Xiaoyun, Zhai Yujia, Wu Xiaoqun. “Geometry-Topology” Iterative Optimization for Mesh Inpainting[J]. Journal of Computer-Aided Design & Computer Graphics, 2022, 34(2): 305-314. DOI: 10.3724/SP.J.1089.2022.18865

基于“几何-拓扑”迭代优化的三维网格模型修复算法

“Geometry-Topology” Iterative Optimization for Mesh Inpainting

  • 摘要: 针对三维网格模型孔洞保特征修复问题,提出一种基于"几何-拓扑"迭代优化的三维数据修复算法.给定残缺的三角网格模型,首先识别孔洞区域,利用动态规划方法对孔洞区域进行初始的三角剖分,赋予孔洞区域拓扑连接关系;然后识别孔洞边界一对特征点,基于特征点及其法向粗略拟合特征曲线,在特征曲线的指导下调整孔洞局部的拓扑结构,即孔洞区域拓扑连接关系优化;最后基于孔洞及其N环邻域构建保特征的局部总变分能量函数,迭代求解孔洞及其邻域的顶点几何位置,即局部顶点几何位置的优化,重复局部拓扑连接关系优化和顶点几何位置优化,直到拓扑结构优化处理中不再发生连接关系调整,即完成了三维网格模型的修复.在现有的完整三维网格模型上人为去除部分构造带孔洞的残缺模型,以此作为数据,与其他修复算法进行对比实验的结果表明,所提算法可以有效地恢复孔洞区域的显著特征,并且在修复时间和误差统计上占有明显优势.

     

    Abstract: In this paper, a "geometry-topology" iterative optimization algorithm is proposed for feature preserved mesh inpainting. For a given incomplete triangular mesh model, the hole boundaries are first identified and dynamic programming algorithm is adapted to initialize the hole areas and construct the topology connectivity for the holes. Then, a pair of feature points on the boundary of each hole is identified and roughly fit the feature curve based on the feature points and their normals. The local connectivity of mesh hole is adjusted under the guidance of the feature curve. This is what we named the topology adjustment. For the geometry optimization, a local variational energy function is built based on the hole and its N ring neighborhood based on total variation, and solves this energy function iteratively to get the optimal vertex positions. Finally, local topology adjustment and geometry optimization are alternately repeated until there is no topology adjustment occurs. Parts of the existing complete meshes are manually removed to get the incomplete models with holes. Compared with other algorithms, proposed algorithm can effectively restore the salient features of the hole areas, and has obvious advantages in repair time and error statistics.

     

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