  Learning rotation-invariant distinctive features is a fundamental requirement
for point cloud registration. Existing methods often use rotation-sensitive
networks to extract features, while employing rotation augmentation to learn an
approximate invariant mapping rudely. This makes networks fragile to rotations,
overweight, and hinders the distinctiveness of features. To tackle these
problems, we propose a novel position-aware rotation-equivariant network, for
efficient, light-weighted, and robust registration. The network can provide a
strong model inductive bias to learn rotation-equivariant/invariant features,
thus addressing the aforementioned limitations. To further improve the
distinctiveness of descriptors, we propose a position-aware convolution, which
can better learn spatial information of local structures. Moreover, we also
propose a feature-based hypothesis proposer. It leverages rotation-equivariant
features that encode fine-grained structure orientations to generate reliable
model hypotheses. Each correspondence can generate a hypothesis, thus it is
more efficient than classic estimators that require multiple reliable
correspondences. Accordingly, a contrastive rotation loss is presented to
enhance the robustness of rotation-equivariant features against data
degradation. Extensive experiments on indoor and outdoor datasets demonstrate
that our method significantly outperforms the SOTA methods in terms of
registration recall while being lightweight and keeping a fast speed. Moreover,
experiments on rotated datasets demonstrate its robustness against rotation
variations. Code is available at https://github.com/yaorz97/PARENet.
