Many point cloud classification methods are developed under the assumption that all point clouds in the dataset are well aligned with the canonical axes so that the 3D Cartesian point coordinates can be employed to learn features. When input point clouds are not aligned, the classification performance drops significantly. In this work, we focus on a mathematically transparent point cloud classification method called PointHop, analyze its reason for failure due to pose variations, and solve the problem by replacing its pose dependent modules with rotation invariant counterparts. The proposed method is named SO(3)-Invariant PointHop (or S3I-PointHop in short). We also significantly simplify the PointHop pipeline using only one single hop along with multiple spatial aggregation techniques. The idea of exploiting more spatial information is novel. Experiments on the ModelNet40 dataset demonstrate the superiority of S3I-PointHop over traditional PointHop-like methods.
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