Nearest Neighbor Sampling of Point Sets using Rays
This provides a new framework for geometric data analysis, though it appears incremental as it builds on existing nearest neighbor and sampling techniques.
The paper tackles the problem of sampling, compressing, and analyzing point sets in Euclidean spaces by introducing the RaySense sketch, a tensor that captures nearest neighbors along rays, enabling efficient computation of line integrals and extraction of statistical information.
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.