In this paper, we propose a fully differentiable pipeline for estimating
accurate dense correspondences between 3D point clouds. The proposed pipeline
is an extension and a generalization of the functional maps framework. However,
instead of using the Laplace-Beltrami eigenfunctions as done in virtually all
previous works in this domain, we demonstrate that learning the basis from data
can both improve robustness and lead to better accuracy in challenging
settings. We interpret the basis as a learned embedding into a higher
dimensional space. Following the functional map paradigm the optimal
transformation in this embedding space must be linear and we propose a separate
architecture aimed at estimating the transformation by learning optimal
descriptor functions. This leads to the first end-to-end trainable functional
map-based correspondence approach in which both the basis and the descriptors
are learned from data. Interestingly, we also observe that learning a
\emph{canonical} embedding leads to worse results, suggesting that leaving an
extra linear degree of freedom to the embedding network gives it more
robustness, thereby also shedding light onto the success of previous methods.
Finally, we demonstrate that our approach achieves state-of-the-art results in
challenging non-rigid 3D point cloud correspondence applications.

本文提出了一种全可微的流程，用于估计三维点云之间的准确密集对应，基于从数据学习基础并使用嵌入网络，实现端到端可训练的对应方法，在挑战性的非刚性三维点云对应应用中实现了最新的结果。