Topological Analysis of Scalar Fields with Outliers

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

研究成果: Conference contribution

6 被引用数 (Scopus)

抄録

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.

本文言語English
ホスト出版物のタイトル31st International Symposium on Computational Geometry, SoCG 2015
編集者Janos Pach, Janos Pach, Lars Arge
出版社Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ページ827-841
ページ数15
ISBN(電子版)9783939897835
DOI
出版ステータスPublished - 2015 6月 1
イベント31st International Symposium on Computational Geometry, SoCG 2015 - Eindhoven, Netherlands
継続期間: 2015 6月 222015 6月 25

出版物シリーズ

名前Leibniz International Proceedings in Informatics, LIPIcs
34
ISSN(印刷版)1868-8969

Other

Other31st International Symposium on Computational Geometry, SoCG 2015
国/地域Netherlands
CityEindhoven
Period15/6/2215/6/25

ASJC Scopus subject areas

  • ソフトウェア

引用スタイル