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This paper proposes a set of rules to revise various neural networks for 3Dpoint cloud processing to rotation-equivariant quaternion neural networks(REQNNs). We find that when a neural network uses quaternion features undercertain conditions, the network feature naturally has the rotation-equivarianceproperty. Rotation equivariance means that applying a specific rotationtransformation to the input point cloud is equivalent to applying the samerotation transformation to all intermediate-layer quaternion features. Besides,the REQNN also ensures that the intermediate-layer features are invariant tothe permutation of input points. Compared with the original neural network, theREQNN exhibits higher rotation robustness.

3D-Rotation-Equivariant Quaternion Neural Networks