This paper proposes a correspondence-free method for point cloud rotational
registration. We learn an embedding for each point cloud in a feature space
that preserves the SO(3)-equivariance property, enabled by recent developments
in equivariant neural networks. The proposed shape registration method achieves
three major advantages through combining equivariant feature learning with
implicit shape models. First, the necessity of data association is removed
because of the permutation-invariant property in network architectures similar
to PointNet. Second, the registration in feature space can be solved in
closed-form using Horn's method due to the SO(3)-equivariance property. Third,
the registration is robust to noise in the point cloud because of the joint
training of registration and implicit shape reconstruction. The experimental
results show superior performance compared with existing correspondence-free
deep registration methods.

本文提出了一种基于等变特征学习和隐式形状模型的无对应点云旋转配准方法，可实现无需数据关联、在特征空间中闭式求解和对噪声鲁棒。实验结果表明，该方法优于现有基于深度学习的无对应点云配准方法。