We propose a new framework for the sampling, compression, and analysis of distributions of point sets and other geometric objects embedded in Euclidean spaces. Our approach involves constructing a tensor called the RaySense sketch, which captures nearest neighbors from the underlying geometry of points along a set of rays. We explore various operations that can be performed on the RaySense sketch, leading to different properties and potential applications. Statistical information about the data set can be extracted from the sketch, independent of the ray set. Line integrals on point sets can be efficiently computed using the sketch. We also present several examples illustrating applications of the proposed strategy in practical scenarios.

翻译：我们提出了一种新的框架，用于嵌入欧几里得空间的点集及其他几何对象的分布采样、压缩与分析。该方法构建了一个名为RaySense摘要的张量，该张量沿一组射线捕捉点集底层几何结构中的最近邻信息。我们探索了可在RaySense摘要上执行的多种操作，这些操作衍生出不同的性质与潜在应用。该摘要可独立于射线集合提取数据集的统计信息，并能高效计算点集上的线积分。此外，我们通过若干实例展示了所提策略在实际场景中的应用。