  Removing outlier correspondences is one of the critical steps for successful
feature-based point cloud registration. Despite the increasing popularity of
introducing deep learning methods in this field, spatial consistency, which is
essentially established by a Euclidean transformation between point clouds, has
received almost no individual attention in existing learning frameworks. In
this paper, we present PointDSC, a novel deep neural network that explicitly
incorporates spatial consistency for pruning outlier correspondences. First, we
propose a nonlocal feature aggregation module, weighted by both feature and
spatial coherence, for feature embedding of the input correspondences. Second,
we formulate a differentiable spectral matching module, supervised by pairwise
spatial compatibility, to estimate the inlier confidence of each correspondence
from the embedded features. With modest computation cost, our method
outperforms the state-of-the-art hand-crafted and learning-based outlier
rejection approaches on several real-world datasets by a significant margin. We
also show its wide applicability by combining PointDSC with different 3D local
descriptors.
