WTFM Layer: An Effective Map Extractor for Unsupervised Shape Correspondence

Abstract

We propose a novel unsupervised learning approach for computing correspondences between non-rigid 3D shapes. The core idea is that we integrate a novel structural constraint into the deep functional map pipeline, a recently dominant learning framework for shape correspondence, via a powerful spectral manifold wavelet transform (SMWT). As SMWT is isometrically invariant operator and can analyze features from multiple frequency bands, we use the multiscale SMWT results of the learned features as function preservation constraints to optimize the functional map by assuming each frequency-band information of the descriptors should be correspondingly preserved by the functional map. Such a strategy allows extracting significantly more deep feature information than existing approaches which only use the learned descriptors to estimate the functional map. And our formula strongly ensure the isometric properties of the underlying map. We also prove that our computation of the functional map amounts to filtering processes only referring to matrix multiplication. Then, we leverage the alignment errors of intrinsic embedding between shapes as a loss function and solve it in an unsupervised way using the Sinkhorn algorithm. Finally, we utilize DiffusionNet as a feature extractor to ensure that discretization-resistant and directional shape features are produced. Experiments on multiple challenging datasets prove that our method can achieve state-of-the-art correspondence quality. Furthermore, our method yields significant improvements in robustness to shape discretization and generalization across the different datasets. The source code and trained models will be available at https://github.com/HJ-Xu/ WTFM-Layer.