  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.
