Skeletonisation algorithms with theoretical guarantees for unorganised point clouds with high levels of noise

Smith, P and Kurlin, V ORCID: 0000-0001-5328-5351 (2021) Skeletonisation algorithms with theoretical guarantees for unorganised point clouds with high levels of noise. [Report]

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Abstract

Data Science aims to extract meaningful knowledge from unorganised data. Real datasets usually come in the form of a cloud of points with only pairwise distances. Numerous applications require to visualise an overall shape of a noisy cloud of points sampled from a non-linear object that is more complicated than a union of disjoint clusters. The skeletonisation problem in its hardest form is to find a 1-dimensional skeleton that correctly represents a shape of the cloud. This paper compares several algorithms that solve the above skeletonisation problem for any point cloud and guarantee a successful reconstruction. For example, given a highly noisy point sample of an unknown underlying graph, a reconstructed skeleton should be geometrically close and homotopy equivalent to (has the same number of independent cycles as) the underlying graph. One of these algorithm produces a Homologically Persistent Skeleton (HoPeS) for any cloud without extra parameters. This universal skeleton contains sub-graphs that provably represent the 1-dimensional shape of the cloud at any scale. Other subgraphs of HoPeS reconstruct an unknown graph from its noisy point sample with a correct homotopy type and within a small offset of the sample. The extensive experiments on synthetic and real data reveal for the first time the maximum level of noise that allows successful graph reconstructions.

Item Type:	Report
Additional Information:	This paper has been published in the journal Pattern Recognition
Uncontrolled Keywords:	Data skeletonisation, Noisy point sample, Persistent homology
Depositing User:	Symplectic Admin
Date Deposited:	24 Jan 2019 10:08
Last Modified:	19 Jan 2023 01:07
DOI:	10.1016/j.patcog.2021.107902
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3031137