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Endowing Deep 3D Models with Rotation Invariance Based on Principal Component Analysis

In this paper, we propose a simple yet effective method to endow deep 3D models with rotation invariance by expressing the coordinates in an intrinsic frame determined by the object shape itself. Key to our approach is to find such an intrinsic frame which should be unique to the identical object shape and consistent across different instances of the same category, e.g. the frame axes of desks should be all roughly along the edges. Interestingly, the principal component analysis exactly provides an effective way to define such a frame, i.e. setting the principal components as the frame axes. As the principal components have direction ambiguity caused by the sign-ambiguity of eigenvector computation, there exist several intrinsic frames for each object. In order to achieve absolute rotation invariance for a deep model, we adopt the coordinates expressed in all intrinsic frames as inputs to obtain multiple output features, which will be further aggregated as a final feature via a self-attention module. Our method is theoretically rotation-invariant and can be flexibly embedded into the current network architectures. Comprehensive experiments demonstrate that our approach can achieve near state-of-the-art performance on rotation-augmented dataset for ModelNet40 classification and outperform other models on SHREC'17 perturbed retrieval task.

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