Nearest Neighbor Sampling of Point Sets Using Rays
作者机构：Department of MathematicsThe University of Texas at Austin2515 SpeedwayAustinTX 78712USA Oden Institute for Computational Engineering and SciencesThe University of Texas at Austin201 E24th StAustinTX 78712USA Department of MathematicsUniversity of British Columbia1984 Mathematics RdVancouverBCV6T1Z2Canada
出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)
年 卷 期：2024年第6卷第2期
页 面：1131-1174页
核心收录：
学科分类：0710[理学-生物学] 07[理学] 0836[工学-生物工程] 0701[理学-数学] 070101[理学-基础数学]
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
主 题：Point clouds Sampling Classification Registration Deep learning Voronoi cell analysis
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 *** approach involves constructing a tensor called the RaySense sketch,which captures nearest neighbors from the underlying geometry of points along a set of *** explore various operations that can be performed on the RaySense sketch,leading to different properties and potential *** information about the data set can be extracted from the sketch,independent of the ray *** integrals on point sets can be efficiently computed using the *** also present several examples illustrating applications of the proposed strategy in practical scenarios.
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