@inproceedings{d835d525199d4357be7129c8c51dabef,
title = "Morse Theory for the k-NN Distance Function",
abstract = "We study the k-th nearest neighbor distance function from a finite point-set in Rd. We provide a Morse theoretic framework to analyze the sub-level set topology. In particular, we present a simple combinatorial-geometric characterization for critical points and their indices, along with detailed information about the possible changes in homology at the critical levels. We conclude by computing the expected number of critical points for a homogeneous Poisson process. Our results deliver significant insights and tools for the analysis of persistent homology in order-k Delaunay mosaics, and random k-fold coverage.",
keywords = "Applied topology, Distance function, Morse theory, k-nearest neighbor",
author = "Yohai Reani and Omer Bobrowski",
note = "Publisher Copyright: {\textcopyright} Yohai Reani and Omer Bobrowski.; 40th International Symposium on Computational Geometry, SoCG 2024 ; Conference date: 11-06-2024 Through 14-06-2024",
year = "2024",
month = jun,
doi = "10.4230/LIPIcs.SoCG.2024.75",
language = "الإنجليزيّة",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
editor = "Wolfgang Mulzer and Phillips, \{Jeff M.\}",
booktitle = "40th International Symposium on Computational Geometry, SoCG 2024",
}