Nearest Neighbor Sampling of Point Sets using Rays

TL;DR

This paper introduces RaySense, a novel tensor-based framework for sampling, compressing, and analyzing point sets in Euclidean spaces by capturing nearest neighbor information along rays, enabling efficient data analysis and geometric computations.

Contribution

The paper presents RaySense, a new tensor sketching method that captures geometric and statistical properties of point sets through ray-based nearest neighbor sampling, with broad applications.

Findings

Efficient computation of line integrals on point sets using RaySense.

Ability to extract statistical data from the sketch independent of ray selection.

Demonstrated practical applications of the RaySense framework.

Abstract

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.