Isometric Correspondences of 3D Models with Geodesic Curves Constrained Functional Maps

For the isometric correspondences between 3D models problem,a method of isometric correspon-dences 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 correspon-dences,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 sym-metric 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 repre-sentation 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 geo-desic distance error of this method is smaller than previous works in the detection results of isometric corre-spondences and intrinsic symmetry of the 3D models.