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

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