The processing, storage and transmission of large-scale point clouds is an ongoing challenge in the computer vision community which hinders progress in the application of 3D models to real-world settings, such as autonomous driving, virtual reality and remote sensing. We propose a novel, one-shot point cloud simplification method which preserves both the salient structural features and the overall shape of a point cloud without any prior surface reconstruction step. Our method employs Gaussian processes with kernels defined on Riemannian manifolds, allowing us to model the surface variation function across any given point cloud. A simplified version of the original cloud is obtained by sequentially selecting points using a greedy sparsification scheme. The selection criterion used for this scheme ensures that the simplified cloud best represents the surface variation of the original point cloud. We evaluate our method on several benchmark datasets, compare it to a range of existing methods and show that our method is competitive both in terms of empirical performance and computational efficiency.

翻译：大规模点云的处理、存储和传输是计算机视觉领域持续面临的挑战，这阻碍了三维模型在自动驾驶、虚拟现实和遥感等实际场景中的应用。我们提出了一种新型一次性点云简化方法，无需任何表面重建先验步骤即可保留点云的显著结构特征与整体形状。该方法采用定义在黎曼流形上的核函数构建高斯过程，从而能够对任意给定点云的表面变化函数进行建模。通过贪心稀疏化方案顺序选取点，可获得原始点云的简化版本。该方案采用的选取准则确保简化点云能最优地表达原始点云的表面变化。我们在多个基准数据集上对方法进行评估，并与现有多种方法进行对比，结果表明本方法在经验性能与计算效率方面均具有竞争力。