Nearest Neighbor Sampling of Point Sets Using Rays
Liangchen Liu , Louis Ly , Colin B. Macdonald , Richard Tsai
Communications on Applied Mathematics and Computation ›› 2023, Vol. 6 ›› Issue (2) : 1131 -1174.
Nearest Neighbor Sampling of Point Sets Using Rays
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.
National Science Foundation(DMS-144041)
Simons Foundation(DMS-172017)
Natural Sciences and Engineering Research Council of Canada
National Science Foundation(DMS-172017)
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