Abstract:

Aiming at the problems of incomplete feature descriptors information and unsatisfactory mapping matrix optimization when constructing the shape correspondence between non-rigid deformation 3D shapes,a novel approach is presented using the Unsupervised Siamese Deep Functional Maps Network(USDFMN) to calculate the shape correspondence.First,the source and target shapes are input to the USDFMN to learn the original 3D geometric traits,which are respectively projected to the Laplacian-Beltrami bases to get the corresponding spectral feature descriptors.Second,the spectral feature descriptors are input in the functional mapping layer to calculate the more robust correspondence where an optimal functional matrix is obtained.Third,an unsupervised learning model is employed to calculate the chamfer distance metric for designing the unsupervised loss function,which estimates the similarity between shapes and evaluates the final calculated correspondence.Finally,the function mapping matrices are restored to point-to-point correspondences using the ZoomOut algorithm.Qualitative and quantitative experimental results show that the proposed algorithm for the shape correspondence of the SURREAL and TOSCA datasets contributes to a uniform visualization in correspondence distributions and a reduction in the geodesic errors.It can not only reduce the time complexity but also improve the accuracy of the shape correspondence calculation to a certain extent.Moreover,the ability of the USDFMN to be generalized,as well as its scalability,is greatly enhanced on different datasets.

Key words: machine vision, shape correspondence, siamese deep functional maps, unsupervised loss function, chamfer distance