  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.
