Topological Analysis of Scalar Fields with Outliers

Mickaël Buchet, Frédéric Chazal, Tamal K. Dey, Fengtao Fan, Steve Y. Oudot, Yusu Wang

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandForschungBegutachtung

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.

Originalspracheenglisch
Titel31st International Symposium on Computational Geometry, SoCG 2015
Herausgeber (Verlag)Schloss Dagstuhl, Leibniz-Zentrum fü Informatik GmbH
Seiten827-841
Seitenumfang15
Band34
ISBN (elektronisch)9783939897835
DOIs
PublikationsstatusVeröffentlicht - 1 Jun 2015
Extern publiziertJa
Veranstaltung31st International Symposium on Computational Geometry - Eindhoven, Niederlande
Dauer: 22 Jun 201525 Jun 2015

Konferenz

Konferenz31st International Symposium on Computational Geometry
KurztitelSoCG 2015
LandNiederlande
OrtEindhoven
Zeitraum22/06/1525/06/15

Schlagwörter

    ASJC Scopus subject areas

    • Software

    Dieses zitieren

    Buchet, M., Chazal, F., Dey, T. K., Fan, F., Oudot, S. Y., & Wang, Y. (2015). Topological Analysis of Scalar Fields with Outliers. in 31st International Symposium on Computational Geometry, SoCG 2015 (Band 34, S. 827-841). Schloss Dagstuhl, Leibniz-Zentrum fü Informatik GmbH. https://doi.org/10.4230/LIPIcs.SOCG.2015.827