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Interpretable Rotation-Equivariant Quaternion Neural Networks for 3D Point Cloud Processing.

Wen Shen, Zhihua Wei, Qihan Ren

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |January 8, 2024
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    This study introduces rotation-equivariant quaternion neural networks (REQNNs) for 3D point cloud processing. REQNNs improve feature representation, classification accuracy, and robustness against rotation compared to traditional networks.

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    Area of Science:

    • Computer Vision
    • Machine Learning
    • 3D Data Analysis

    Background:

    • Traditional neural networks struggle with rotation invariance in 3D point cloud data.
    • Feature representations need to be both rotation-equivariant and permutation-invariant for robust 3D processing.

    Purpose of the Study:

    • To develop a method for revising existing neural networks into rotation-equivariant quaternion neural networks (REQNNs).
    • To ensure feature representations are rotation-equivariant and permutation-invariant for 3D point clouds.

    Main Methods:

    • Proposed generic rules to transform standard neural networks into REQNNs.
    • Utilized quaternion features to naturally achieve rotation equivariance.
    • Proved rotation equivariance of features and gradients, and rotation invariance of training.

    Main Results:

    • REQNNs demonstrate naturally satisfied rotation equivariance of features using quaternion representations.
    • Demonstrated rotation equivariance of gradients and rotation invariance of training w.r.t. inputs.
    • Evaluated knowledge representation stability and robustness against adversarial rotation attacks.

    Conclusions:

    • REQNNs significantly outperform traditional neural networks in classification accuracy on rotated data.
    • REQNNs exhibit enhanced robustness against adversarial rotation attacks.
    • The proposed revision rules provide a general method for creating rotation-equivariant networks for 3D point cloud processing.