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)
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.
3D models; isometric correspondences; intrinsic symmetries; functional maps