Persistent Homology as Stopping-Criterion for Voronoi Interpolation

Melodia L, Lenz R (2020)

Publication Language: English

Publication Type: Conference contribution, Original article

Publication year: 2020

Publisher: Springer

City/Town: Berlin

Pages Range: 1-14

Conference Proceedings Title: Proceedings of the 20th International Workshop on Combinatorial Image Analysis

Event location: Novi Sad RS

ISBN: 978-3-030-51002-2

URI: https://link.springer.com/book/10.1007/978-3-030-51002-2

DOI: 10.1007/978-3-030-51002-2

Abstract

In this study the Voronoi interpolation is used to interpolate a set of points drawn from a topological space with higher homology groups on its filtration. The technique is based on Voronoi tesselation, which induces a natural dual map to the Delaunay triangulation. Advantage is taken from this fact calculating the persistent homology on it after each iteration to capture the changing topology of the data. The boundary points are identified as critical. The Bottleneck and Wasserstein distance serve as a measure of quality between the original point set and the interpolation. If the norm of two distances exceeds a heuristically determined threshold, the algorithm terminates. We give the theoretical basis for this approach and justify its validity with numerical experiments.

Authors with CRIS profile

Luciano Melodia Professur für evolutionäres Datenmanagement Richard Lenz Professur für evolutionäres Datenmanagement

Related research project(s)

Schema Inference and Machine Learning (SIML) Aug. 1, 2018 - Aug. 1, 2021

How to cite

APA:

Melodia, L., & Lenz, R. (2020). Persistent Homology as Stopping-Criterion for Voronoi Interpolation. In Tibor Lukić, Reneta P. Barneva, Valentin E. Brimkov, Lidija Čomić, Nataša Sladoje (Eds.), Proceedings of the 20th International Workshop on Combinatorial Image Analysis (pp. 1-14). Novi Sad, RS: Berlin: Springer.

MLA:

Melodia, Luciano, and Richard Lenz. "Persistent Homology as Stopping-Criterion for Voronoi Interpolation." Proceedings of the 20th International Workshop on Combinatorial Image Analysis, Novi Sad Ed. Tibor Lukić, Reneta P. Barneva, Valentin E. Brimkov, Lidija Čomić, Nataša Sladoje, Berlin: Springer, 2020. 1-14.

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