  In this work, we present a novel learning-based framework that combines the
local accuracy of contrastive learning with the global consistency of geometric
approaches, for robust non-rigid matching. We first observe that while
contrastive learning can lead to powerful point-wise features, the learned
correspondences commonly lack smoothness and consistency, owing to the purely
combinatorial nature of the standard contrastive losses. To overcome this
limitation we propose to boost contrastive feature learning with two types of
smoothness regularization that inject geometric information into correspondence
learning. With this novel combination in hand, the resulting features are both
highly discriminative across individual points, and, at the same time, lead to
robust and consistent correspondences, through simple proximity queries. Our
framework is general and is applicable to local feature learning in both the 3D
and 2D domains. We demonstrate the superiority of our approach through
extensive experiments on a wide range of challenging matching benchmarks,
including 3D non-rigid shape correspondence and 2D image keypoint matching.
