Rotation-Invariant Point Cloud Segmentation With Kernel Principal Component Analysis and Geometry-Based Weighted Convolution

Learning a rotation-invariant (RI) representation is of significant importance for real-world point cloud segmentation that is perturbed by arbitrary rotations. Recent principal component analysis (PCA)-based methods provide an effective alternative to align point clouds and produce the RI representation under the preservation of global information. However, conventional PCA with 3-D coordinates cannot fully represent high-dimensional geometric structures like surfaces and curves and cannot uniformly align these structures for learning RI representation. In this paper, we propose a novel rotation-invariant method for point cloud segmentation, which leverages kernel PCA (KPCA) for aligning point clouds in a projected high-dimensional space via non-linear mapping and develops a Geometry-based Weighted Convolution (GWConv) to distinguish part boundaries during segmentation. Specifically, the KPCA produces a RI representation with polynomial kernels for effectively representing complicated geometric structures in point clouds. Moreover, the GWConv incorporates geometric structures into convolution and enhances neighboring points with similar geometry for fine-grained segmentation based on the RI representation. Experimental results demonstrate that the proposed method can achieve competitive performance with the state-of-the-arts and outperforms existing PCA-based methods in part segmentation on ShapeNet. Furthermore, it achieves evident performance gains on complicated 3-D shapes such as Earphone and Car and facilitates segmentation around the part boundaries.