Recently, various works that attempted to introduce rotation invariance to point cloud analysis have devised point-pair features, such as angles and distances. In these methods, however, the point-pair is only comprised of the center point and its adjacent points in a vicinity, which may bring information loss to the local feature representation. In this paper, we instead connect each point densely with all other points in a local neighborhood to compose the point-pairs. Specifically, we present a simple but effective local feature representation, called sorted Gram matrix(SGM), which is not only invariant to arbitrary rotations, but also models the pair-wise relationship of all the points in a neighbor-hood. In more detail, we utilize vector inner product to model distance- and angle-information between two points, and in a local patch it naturally forms a Gram matrix. In order to guarantee permutation invariance, we sort the correlation value in Gram matrix for each point, therefore this geometric feature names sorted Gram matrix. Furthermore, we mathematically prove that the Gram matrix is rotation-invariant and sufficient to model the inherent structure of a point cloud patch. We then use SGM as features in convolution, which can be readily integrated as a drop-in module into any point-based networks. Finally, we evaluated the proposed method on two widely used datasets, and it outperforms previous state-of-the-arts on both shape classification and part segmentation tasks by a large margin.

Point clouds can be represented in many forms (views), typically, point-based sets, voxel-based cells or range-based images(i.e., panoramic view). The point-based view is geometrically accurate, but it is disordered, which makes it difficult to find local neighbors efficiently. The voxel-based view is regular, but sparse, and computation grows cubicly when voxel resolution increases. The range-based view is regular and generally dense, however spherical projection makes physical dimensions distorted. Both voxel-and range-based views suffer from quantization loss, especially for voxels when facing large-scale scenes. In order to utilize different view’s advantages and alleviate their own shortcomings in fine-grained segmentation task, we propose a novel range-point-voxel fusion network, namely RPVNet. In this network, we devise a deep fusion framework with multiple and mutual information interactions among these three views, and propose a gated fusion module (termed as GFM), which can adaptively merge the three features based on concurrent inputs. Moreover, the proposed RPV interaction mechanism is highly efficient, and we summarize it to a more general formulation. By leveraging this efficient interaction and relatively lower voxel resolution, our method is also proved to be more efficient. Finally, we evaluated the proposed model on two large-scale datasets, i.e., SemanticKITTI and nuScenes, and it shows state-of-the-art performance on both of them. Note that, our method currently ranks 1st on SemanticKITTI leaderboard without any extra tricks.