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 RaySe...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.展开更多
基金supported by the National Science Foundation(Grant No.DMS-1440415)partially supported by a grant from the Simons Foundation,NSF Grants DMS-1720171 and DMS-2110895a Discovery Grant from Natural Sciences and Engineering Research Council of Canada.
文摘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.
