A fast persistence-based segmentation of noisy 2D clouds with provable guarantees

Kurlin, V.

doi:10.1016/j.patrec.2015.11.025

A fast persistence-based segmentation of noisy 2D clouds with provable guarantees

Kurlin, V.

Authors

V. Kurlin

Abstract

We design a new fast algorithm to automatically segment a 2D cloud of points into persistent regions. The only input is a dotted image without any extra parameters, say a scanned black-and-white map with almost closed curves or any image with detected edge points. The output is a hierarchy of segmentations into regions whose boundaries have a long enough life span (persistence) in a sequence of nested neighborhoods of the input points. We give conditions on a noisy sample of a graph, when the boundaries of resulting regions are geometrically close to original cycles in the unknown graph.

Citation

Kurlin, V. (2016). A fast persistence-based segmentation of noisy 2D clouds with provable guarantees. Pattern Recognition Letters, 83(Part 1), 3-12. https://doi.org/10.1016/j.patrec.2015.11.025

Journal Article Type	Article
Acceptance Date	Nov 30, 2015
Online Publication Date	Dec 19, 2015
Publication Date	Nov 1, 2016
Deposit Date	Dec 14, 2015
Publicly Available Date	Dec 19, 2016
Journal	Pattern Recognition Letters
Print ISSN	0167-8655
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	83
Issue	Part 1
Pages	3-12
DOI	https://doi.org/10.1016/j.patrec.2015.11.025
Keywords	Persistent homology, Delaunay triangulation.

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Publisher Licence URL
http://creativecommons.org/licenses/by-nc-nd/4.0/

Copyright Statement
© 2015 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/