Nearest Neighbor Sampling of Point Sets Using Rays  

作　　者：Liangchen Liu Louis Ly Colin B.Macdonald Richard Tsai 

机构地区：[1]Department of Mathematics,The University of Texas at Austin,2515 Speedway,Austin,TX 78712,USA [2]Oden Institute for Computational Engineering and Sciences,The University of Texas at Austin,201 E24th St,Austin,TX 78712,USA [3]Department of Mathematics,University of British Columbia,1984 Mathematics Rd,Vancouver,BCV6T1Z2,Canada

出　　处：《Communications on Applied Mathematics and Computation》2024年第2期1131-1174,共44页应用数学与计算数学学报（英文）

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-2110895;a Discovery Grant from Natural Sciences and Engineering Research Council of Canada.

摘　　要：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.

关 键 词：Point clouds Sampling CLASSIFICATION REGISTRATION Deep learning Voronoi cell analysis 

分 类 号：O17[理学—数学] O24[理学—基础数学]