Abstract
This paper proposes a set of rules to revise various neural networks for 3D point cloud processing to rotation-equivariant quaternion neural networks (REQNNs). We find that when a neural network uses quaternion features, the network feature naturally has the rotation-equivariance property. Rotation equivariance means that applying a specific rotation transformation to the input point cloud is equivalent to applying the same rotation transformation to all intermediate-layer quaternion features. Besides, the REQNN also ensures that the intermediate-layer features are invariant to the permutation of input points. Compared with the original neural network, the REQNN exhibits higher rotation robustness.
W. Shen, B. Zhang and S. Huang—Have equal contributions.
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Notes
- 1.
The PointNet++ for shape classification used in this paper is slightly revised by concatenating 3D coordinates to input features of the 1-st and 4-th convolution layers, in order to enrich the input information. For fair comparisons, both the REQNN and the original PointNet++ are revised in this way.
- 2.
We add one more convolution layer in the Quaternion2Real module in the REQNN revised from DGCNN, in order to obtain reliable real-valued features considering that the DGCNN has no downsampling operations. For fair comparisons, we add the same convolution layer to the same location of the original DGCNN.
- 3.
The classification accuracy in the scenario of NR/AR in Table 4 and Table 5 was slightly different for PointNet++ [22] (23.57% vs. 21.35%) and DGCNN [33] (30.05% vs. 29.74%). It was because architectures of PointNet++ (see footnote 1) and DGCNN (see footnote 2) examined in Table 4 and Table 5 were slightly different. Nevertheless, this did not essentially change our conclusions.
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Acknowledgments
The work is partially supported by the National Key Research and Development Project (No. 213), the National Nature Science Foundation of China (No. 61976160, U19B2043, and 61906120), the Special Project of the Ministry of Public Security (No. 20170004), and the Key Lab of Information Network Security, Ministry of Public Security (No.C18608).
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Shen, W., Zhang, B., Huang, S., Wei, Z., Zhang, Q. (2020). 3D-Rotation-Equivariant Quaternion Neural Networks. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, JM. (eds) Computer Vision – ECCV 2020. ECCV 2020. Lecture Notes in Computer Science(), vol 12365. Springer, Cham. https://doi.org/10.1007/978-3-030-58565-5_32
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