Rotation-InvariantLocal-to-GlobalRepresentation Learningfor3DPointCloud SupplementaryDocument

In each hierarchy, the number of neighbors for the stochastic dilatedk-NNs, denoted byk, is sampled from the following three different uniform distributions:U(32,96),U(16,48),andU(8,24). Meanwhile,thenumberofedgesinthe graph, ˆk, is given by sampling fromU(8,24),U(4,12), andU(2,8). Thedilationrateemployed in the first descriptor extraction stage is sampled fromU(2,4). Figure 1 visualizes the local axes constructed in the descriptor extraction step. The figures on the left present the original point clouds and the right ones illustrate the local reference frames for the downsampled points.