Learning Canonical Embedding for Non-rigid Shape Matching

This paper provides a novel framework that learns canonical embeddings for nonrigid shape matching. In contrast to prior work in this direction, our framework is trained end-to-end and thus avoids instabilities and constraints associated with the commonly-used Laplace-Beltrami basis or sequential optimization schemes. On multiple datasets, we demonstrate that learning self symmetry maps with a deep functional map projects 3D shapes into a low dimensional canonical embedding that facilitates non-rigid shape correspondence via a simple nearest neighbor search. Our framework outperforms multiple recent learning based methods on FAUST and SHREC benchmarks while being computationally cheaper, data efficient, and robust. Shape correspondence is a fundamental problem in computer vision, computer graphics and related fields (Thomas et al., 2021), since it facilitates many applications such as texture or deformation transfer and statistical shape analysis (Bogo et al., 2014) to name a few. Although shape correspondence has been studied from many viewpoints, we focus here on a functional map-based approaches (Ovsjanikov et al., 2012) as this framework is quite general, scalable and thus, has been extended to various other applications such as pose estimation (Neverova et al., 2020), matrix completion (Sharma & Ovsjanikov, 2021) and graph matching (Wang et al., 2020). The progress is mainly hindered by the difficulty of learning a suitable embedding or basis functions for partial 3D data.