
F. Chazal, L. J. Guibas, S. Y. Oudot,
P. Skraba. Analysis of Scalar Fields over Point Cloud
Data.
Abstract:
Given a realvalued function f
defined over some metric space X, is it possible to recover some
structural information about f from the sole information of its
values at a finite set L of sample points, whose pairwise
distances in X are given? We provide a positive answer to this
question. More precisely, taking advantage of recent advances on
the front of stability for persistence diagrams, we introduce a
novel algebraic construction, based on a pair of nested families
of simplicial complexes built on top of the point cloud L, from
which the persistence diagram of f can be faithfully
approximated. We derive from this construction a series of
algorithms for the analysis of scalar fields from point cloud
data. These algorithms are simple and easy to implement, they have
reasonable complexities, and they come with theoretical
guarantees. To illustrate the genericity and practicality of the
approach, we also present some experimental results obtained in
various applications, ranging from clustering to sensor
networks.
Bibtex:
@inproceedings{cgosasfop08
, title = "Analysis of Scalar Fields over Point Cloud Data"
, author = "F. Chazal and L. J. Guibas and S. Y. Oudot and P. Skraba"
, booktitle = "Proc. 19th ACMSIAM Sympos. on Discrete Algorithms"
, pages = "10211030"
, year = "2009"
}
@article{cgosasfop11
, title = "Analysis of Scalar Fields over Point Cloud Data"
, author = "F. Chazal and L. J. Guibas and S. Y. Oudot and P. Skraba"
, journal = "Discrete and Computational Geometry"
, volume = 46
, number = 4
, pages = "743775"
, month = "December"
, year = "2011"
}

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