Topological Analysis of Scalar Fields with Outliers

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

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.

Original languageEnglish
Title of host publication31st International Symposium on Computational Geometry, SoCG 2015
EditorsJanos Pach, Janos Pach, Lars Arge
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages827-841
Number of pages15
ISBN (Electronic)9783939897835
DOIs
Publication statusPublished - 2015 Jun 1
Event31st International Symposium on Computational Geometry, SoCG 2015 - Eindhoven, Netherlands
Duration: 2015 Jun 222015 Jun 25

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume34
ISSN (Print)1868-8969

Other

Other31st International Symposium on Computational Geometry, SoCG 2015
CountryNetherlands
CityEindhoven
Period15/6/2215/6/25

Keywords

  • Distance to a Measure
  • Nested Rips Filtration
  • Persistent Homology
  • Scalar Field Analysis
  • Topological Data Analysis

ASJC Scopus subject areas

  • Software

Cite this

Buchet, M., Chazal, F., Dey, T. K., Fan, F., Oudot, S. Y., & Wang, Y. (2015). Topological Analysis of Scalar Fields with Outliers. In J. Pach, J. Pach, & L. Arge (Eds.), 31st International Symposium on Computational Geometry, SoCG 2015 (pp. 827-841). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 34). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.SOCG.2015.827