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

Kurlin, V.

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
• Electronic ISSN: 1872-7344
• 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.
• Public URL: https://durham-repository.worktribe.com/output/1416669