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Topological analysis of scalar fields with outliers

Abstract : Given a real-valued function f defined over a manifold M embedded in R d , 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 the noise is bounded in both the functional and geometric domains. 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 on the quality of our approximation and some experimental results illustrating its behavior.
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https://hal.inria.fr/hal-01092874
Contributor : Mickaël Buchet <>
Submitted on : Tuesday, December 9, 2014 - 4:22:55 PM
Last modification on : Tuesday, June 18, 2019 - 2:36:02 PM
Long-term archiving on: : Saturday, April 15, 2017 - 7:11:48 AM

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  • HAL Id : hal-01092874, version 1
  • ARXIV : 1412.1680

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Mickaël Buchet, Frédéric Chazal, Tamal K. Dey, Fengtao Fan, Steve Y. Oudot, et al.. Topological analysis of scalar fields with outliers. Symposium on Computational Geometry 2015, Jun 2015, Eindhoven, Netherlands. ⟨hal-01092874⟩

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