
Mickaël Buchet, Frédéric Chazal, Tamal K. Dey, Fengtao Fan,
Steve Y. Oudot, and Yusu Wang. Topological analysis of scalar fields
with outliers. Proc. Sympos. on Computational Geometry,
2015. To appear.
Abstract:
Given a realvalued 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 in M. 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 knearest 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.
Bibtex:
@inproceedings{bcdfowtasfo15,
author = {M. Buchet and F. Chazal and T. K. Dey and F. Fan and S. Y. Oudot and Y. Wang},
title = {Topological analysis of scalar fields with outliers},
booktitle = {Proc. Sympos. on Computational Geometry},
year = {2015}
}

