Abstract:

The focus of this paper is on the accuracy of existing shape correspondence methods which is easily degenerated by the topological changes of the near-isometric non-rigid 3D shapes.The novel approach we propose in this paper is based on a Mixed Supervision Deep Functional Maps Network (MSDFMNet).First,in the weakly supervised feature extraction module,the 3D point clouds representation forms of both source and target shapes are approximately rigidly aligned through weakly supervised learning,and then the features are learned directly from raw shape geometry,which leads to more discriminative features while solving the problem that the symmetry of the shape itself affects the accuracy of the correspondence.Second,by turning the extracted features into their corresponding spectral feature descriptors in the unsupervised functional map module,we build the matrix of functional maps.We then apply the weighted regularization to obtain the optimal functional maps matrix.In solving the problem of insufficient constraint of the functional maps matrix,the need for labeled data and the labor cost of the algorithm is also reduced.Finally,the optimal functional maps matrix is refined in the post-processing module by using the ZoomOut algorithm to recover the precise point-to-point mappings.Experimental results have shown that the geodesic errors of the 3D shape correspondence constructed by this algorithm on the FAUST,SCAPE and SURREAL dataset are smaller than those of the current commonly used methods,and that the correspondence results are more accurate,and texture mapping results are smoother.Our algorithm has a good generalization ability.

Key words: shape correspondence, weakly supervised learning, unsupervised learning, mixed supervision, deep functional maps