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在线期刊

基于测地曲线约束函数映射的三维模型等距配准

王辉1), 朱冰洁1), 李楠楠2)*, 曹俊杰3), 王胜法4), 郝存明5), 刘秀平3)
1) (石家庄铁道大学信息科学与技术学院 石家庄 050043)2) (大连海事大学信息科学技术学院 大连 116026)3) (大连理工大学数学科学学院 大连 116024)4) (大连理工大学国际信息与软件学院 大连 116620)5) (河北省科学院应用数学研究所 石家庄 050051)
分类号: TP391.41 DOI: 10.3724/SP.J.1089.2021.18768
出版年,卷(期):页码: 2021 , 33 ( 10 ): 1582-1594 王辉
摘要: 针对三维模型之间的等距配准问题, 基于函数映射框架, 提出了一种测地曲线约束能同时检测同方向和对称方向2个等距配准的方法. 首先, 计算模型上的2组对称点对, 进而建立2个模型间同方向和对称方向上的4组对应点对; 其次, 理论上证明2个模型上4组对应点之间的测地曲线是等距配准的, 进一步利用以上4组对应点对得到配准的6组测地曲线对; 最后, 将以上测地曲线作为几何描述子约束添加到函数映射框架中, 可以同时求解三维模型间同方向和对称方向上2个等距配准. 同时从理论上证明镜面型内蕴对称对应的函数映射表示矩阵是对称正交的, 并将其作为表示矩阵的正则化项添加到基于测地曲线约束的函数映射框架中检测三维模型内蕴对称. 在公开的非刚性三维模型数据库的实验结果表明, 所提方法在三维模型等距配准和内蕴对称上的测地距离误差小于以前的工作.
关键词: 三维模型; 等距配准; 内蕴对称; 函数映射
Isometric Correspondences of 3D Models with Geodesic Curves Constrained Functional Maps
Wang Hui1), Zhu Bingjie1), Li Nannan2)*, Cao Junjie3), Wang Shengfa4), Hao Cunming5), and Liu Xiuping3)
1) (School of Information Science and Technology, Shijiazhuang Tiedao University, Shijiazhuang 050043)2) (School of Information Science and Technology, Dalian Maritime University, Dalian 116026)3) (School of Mathematical Sciences, Dalian University of Technology, Dalian 116024)4) (International School of Information Science & Engineering, Dalian University of Technology, Dalian 116620)5) (Institute of Applied Mathematics, Hebei Academy of Sciences, Shijiazhuang 050051)
abstract: For the isometric correspondences between 3D models problem, a method of isometric correspondences based on the functional maps framework is proposed, which can simultaneously detect two isometric correspondences in both direct and symmetric directions by adding geodesic curves constraints. Firstly, two symmetric point pairs on each model are selected, and four corresponded point pairs in both direct and the symmetric directions are constructed among the symmetric point pairs. Secondly, it theoretically proves that the geodesic curves between the four pairs of corresponded points on the two models are isometric correspondences, and then using the above four pairs of corresponded points to obtain six pairs of corresponded geodesic curves. Finally, the above pairs of corresponded geodesic curves are added as geometric descriptor constraints in the functional maps framework, which can compute two isometric correspondences in both direct and symmetric directions. At the same time, it theoretically proves that the functional maps representation matrix of a reflection intrinsic symmetry is symmetric and orthogonal, and by adding it as a regularized item of the representation matrix to the functional maps framework based on geodesic curves constraint to detect the intrinsic symmetry of the 3D model. Experiments on the open non-rigid 3D model databases demonstrate that the geodesic distance error of this method is smaller than previous works in the detection results of isometric correspondences and intrinsic symmetry of the 3D models.
keyword: 3D models; isometric correspondences; intrinsic symmetries; functional maps
 
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