Abstract
Given a real-valued function f defined over a manifold M embedded in Rd, we are interested in recovering structural information about f from the sole information of its values on a finite sample P. Existing methods provide approximation to the persistence diagram of f when geometric noise and functional noise are bounded. However, they fail in the presence of aberrant values, also called outliers, both in theory and practice. We propose a new algorithm that deals with outliers. We handle aberrant functional values with a method inspired from the k-nearest neighbors regression and the local median filtering, while the geometric outliers are handled using the distance to a measure. Combined with topological results on nested filtrations, our algorithm performs robust topological analysis of scalar fields in a wider range of noise models than handled by current methods. We provide theoretical guarantees and experimental results on the quality of our approximation of the sampled scalar field.
Originalsprache | englisch |
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Titel | 31st International Symposium on Computational Geometry, SoCG 2015 |
Herausgeber (Verlag) | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Seiten | 827-841 |
Seitenumfang | 15 |
Band | 34 |
ISBN (elektronisch) | 9783939897835 |
DOIs | |
Publikationsstatus | Veröffentlicht - 1 Juni 2015 |
Extern publiziert | Ja |
Veranstaltung | 31st International Symposium on Computational Geometry: SoCG 2015 - Eindhoven, Niederlande Dauer: 22 Juni 2015 → 25 Juni 2015 |
Konferenz
Konferenz | 31st International Symposium on Computational Geometry |
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Kurztitel | SoCG 2015 |
Land/Gebiet | Niederlande |
Ort | Eindhoven |
Zeitraum | 22/06/15 → 25/06/15 |
ASJC Scopus subject areas
- Software