Isometric Correspondences Of 3d Models With Geodesic Curves Constrained Functional Maps

Computing isometric correspondences between 3D models is an important research problem in computer graphics.Especially,realize the isometric correspondences between 3D models based on the functional maps framework.However,the existing descriptors in isometric corre spondences based on functional map are mainly limited to point features.In addition,when a registered model is required with mirror symmetry,there will be two correct equidistant registrations,but most existing correspondences methods based on functional map can only detect one correct equidistant registration.Regarding the functional map to detect the intrinsic symmetry of the 3D model,the regularization term of the representation matrix is mainly orthogonal,and the constraint of symmetric not mentioned.In this paper,the isometric correspondences between non-rigid 3D models and the intrinsic symmetry detection of the model are studied.The primary contents are as follows:(1)Proposing an isometric correspondences algorithm based on curve constraint functional map.Based on the framework of functional maps,this paper proposes an isometric correspondences detection method,which can simultaneously detect two isometric correspondences in both direct and symmetric directions by adding geodesic curves constraints.First,two symmetric point pairs on each model are selected using the heat kernel signatures,and four corresponded point pairs in both direct and the symmetric directions are constructed among the symmetric point pairs.This paper theoretically proves that the geodesic curves between the two pairs of corresponded points on the two models are isometric correspondences.Then using the above four pairs of corresponded points to obtain six pairs of geodesic curves.Finally,the above pairs of corresponding geodesic curves are added as geometric descriptor constraints in the framework of the functional maps,which can compute two isometric correspondences in both direct and symmetric directions.(2)The intrinsic symmetry algorithm of 3D model based on geodesic curves constraint symmetric and orthogonal functional map is proposed.First,it is proved theoretically that the functional map representation matrix corresponding to reflection intrinsic symmetry is symmetric and orthogonal.And then,it is added to the functional map framework as the regularization term of the functional map representation matrix based on geodesic curve constraint,and an effective method for intrinsic symmetry detection of 3D model is proposed.(3)Experimental results on public data sets show that the algorithm based on curve constraint functional map can simultaneously calculate two correct equidistant registrations of the same direction and symmetric direction,which can improve the calculation accuracy of the correspondence between 3D models.To a certain extent,the geodesic error is reduced,and the accuracy of the corresponding relationship is effectively improved.For the detection of intrinsic symmetry,the algorithm based on the symmetry and orthogonality of the geodesic curve constraint function mapping can effectively improve the accuracy of the intrinsic symmetry detection of the 3D models.