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Three-dimensional (3-D) data have many applications in the field of computer vision and a point cloud is one of the most popular modalities. Therefore, how to establish a good representation for a point cloud is a core issue in computer vision, especially for 3-D object recognition tasks. Existing approaches mainly focus on the invariance of representation under the group of permutations. However, for point cloud data, it should also be rotation invariant. To address such invariance, in this article, we introduce a relation of equivalenc
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