Rotation-Invariant Convolution With Point Sort and Curvature Radius for Point Cloud Classification and Segmentation

Recently, the distance-based and angle-based geometric descriptors and local reference axes have been used widely to explore the rotation invariance of point clouds. However, they tend to encounter with two challenges. (i) Similar distances and angles among different points would lead to ambiguous descriptions of local regions. (ii) Establishing a local reference axis may reduce the number of neighbor points, resulting in information loss in local regions. To this end, a Rotation-invariant Convolution with Point Sorting and Curvature Radius $\text {(RCPC)}$ is proposed. Firstly, to solve the challenge (i), a neighbor point sorting module $\text {(NPS)}$ is introduced. Neighbor points on the local tangent disk are sorted according to the local reference axis at the first step. When neighbor points occlude each other along the local reference axis direction, NPS calculates the Euclidean distances from the sampling point to each neighbor point. With these distances, neighbor points in the local region are reorganized to establish multiple triangles to retain as much information. To solve the challenge (ii), a curvature-based geometric descriptor $\text {(CGD)}$ is developed. It calculates the Euclidean distance and angle between the points within established triangles. Further, the CGD constructs a curvature circle for each triangle and calculate the curvature radius which is highly sensitive to small local shape changes. Even Euclidean distances and angles are similar, the CGD can maintain high uniqueness for local regions. Experiments on ModelNet40, ScanObjectNN, and ShapeNet have proved that the proposed approach outperforms other state-of-the-art methods.