PDConv: Rigid transformation invariant convolution for 3D point clouds[Formula presented]

Rigid transformation poses a big challenge for many deep learning models on 3D point clouds as the point coordinates can be drastically changed. To tackle this issue, we proposed Point Distance Convolution (PDConv). Relying on distance information, it extracts invariant features from the set of points regardless of the rigid transformations it undergoes. By stacking PDConv layers, we construct a novel deep learning network for 3D point clouds that is intrinsically invariant to rigid transformation, termed PDConvNet. Experiment results on point cloud classification and segmentation demonstrate that our model can achieve not only the desired invariance but also obtain competitive performances. Extensive ablation studies further validate our choice of Point Distance Representation (PDR) and hierarchical network architecture.