  We study the problem of outlier correspondence pruning for non-rigid point
cloud registration. In rigid registration, spatial consistency has been a
commonly used criterion to discriminate outliers from inliers. It measures the
compatibility of two correspondences by the discrepancy between the respective
distances in two point clouds. However, spatial consistency no longer holds in
non-rigid cases and outlier rejection for non-rigid registration has not been
well studied. In this work, we propose Graph-based Spatial Consistency Network
(GraphSCNet) to filter outliers for non-rigid registration. Our method is based
on the fact that non-rigid deformations are usually locally rigid, or local
shape preserving. We first design a local spatial consistency measure over the
deformation graph of the point cloud, which evaluates the spatial compatibility
only between the correspondences in the vicinity of a graph node. An
attention-based non-rigid correspondence embedding module is then devised to
learn a robust representation of non-rigid correspondences from local spatial
consistency. Despite its simplicity, GraphSCNet effectively improves the
quality of the putative correspondences and attains state-of-the-art
performance on three challenging benchmarks. Our code and models are available
at https://github.com/qinzheng93/GraphSCNet.
