We propose VecKM, a novel local point cloud geometry encoder that is
descriptive, efficient and robust to noise. VecKM leverages a unique approach
by vectorizing a kernel mixture to represent the local point clouds. Such
representation is descriptive and robust to noise, which is supported by two
theorems that confirm its ability to reconstruct and preserve the similarity of
the local shape. Moreover, VecKM is the first successful attempt to reduce the
computation and memory costs from $O(n^2+nKd)$ to $O(nd)$ by sacrificing a
marginal constant factor, where $n$ is the size of the point cloud and $K$ is
neighborhood size. The efficiency is primarily due to VecKM's unique
factorizable property that eliminates the need of explicitly grouping points
into neighborhoods. In the normal estimation task, VecKM demonstrates not only
100x faster inference speed but also strongest descriptiveness and robustness
compared with existing popular encoders. In classification and segmentation
tasks, integrating VecKM as a preprocessing module achieves consistently better
performance than the PointNet, PointNet++, and point transformer baselines, and
runs consistently faster by up to 10x.

提出了一种新颖的本地点云几何编码器 VecKM，具有描述性、高效性和鲁棒性。VecKM 利用向量化的核混合来表示本地点云，这种表示具有描述性和鲁棒性，通过两个定理证实了其重构和保持本地形状相似性的能力。此外，VecKM 是首次成功尝试将计算和存储成本从 $O (n^2+nKd)$ 减少到 $O (nd)$ 的编码器，牺牲了边际的常数因子，其中 $n$ 是点云的大小，$K$ 是邻域大小。在法线估计任务中，与现有的流行编码器相比，VecKM 不仅推断速度快 100 倍，而且具有最强的描述性和鲁棒性。在分类和分割任务中，将 VecKM 集成为预处理模块，始终比 PointNet、PointNet++ 和点变换器基线表现更好，并且运行速度始终快 10 倍。