首页|Nearest Neighbor Sampling of Point Sets Using Rays

Nearest Neighbor Sampling of Point Sets Using Rays

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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 neigh-bors from the underlying geometry of points along a set of rays.We explore various opera-tions 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.

Point cloudsSamplingClassificationRegistrationDeep learningVoronoi cell analysis

Liangchen Liu、Louis Ly、Colin B.Macdonald、Richard Tsai

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Department of Mathematics,The University of Texas at Austin,2515 Speedway,Austin,TX 78712,USA

Oden Institute for Computational Engineering and Sciences,The University of Texas at Austin,201 E 24th St,Austin,TX 78712,USA

Department of Mathematics,University of British Columbia,1984 Mathematics Rd,Vancouver,BC V6T 1Z2,Canada

National Science FoundationSimons FoundationNSF GrantsNSF GrantsDiscovery Grant from Natural Sciences and Engineering Research Council of Canada

DMS-1440415DMS-1720171DMS-2110895

2024

应用数学与计算数学学报
上海大学

应用数学与计算数学学报

影响因子:0.165
ISSN:1006-6330
年,卷(期):2024.6(2)