Vietoris–Rips complex

Known as: Rips complex, Vietoris complex, Vietoris-Rips complex 
In topology, the Vietoris–Rips complex, also called the Vietoris complex or Rips complex, is an abstract simplicial complex that can be defined from… (More)
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Papers overview

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2018
2018
In this work, we present a memory efficient representation of the roadmap that approximates the underlying topology of the Cfree… (More)
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2018
2018
A Vietoris–Rips complex is a way to thicken a (possibly discrete) metric space into a larger space containing more topological… (More)
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2018
2018
We study Vietoris–Rips and Čech complexes of metric wedge sums and metric gluings. We show that the Vietoris–Rips (resp. Čech… (More)
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2015
2015
Given a metric space X and a distance threshold r > 0, the Vietoris–Rips simplicial complex has as its simplices the finite… (More)
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2014
2014
Given a finite discrete point set X ⊂ R and distance parameter δ, we may generate the Vietoris-Rips Complex Rδ(X); the simplicial… (More)
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2013
2013
Given a point set that samples a shape, we formulate conditions under which the Rips complex of the point set at some scale… (More)
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2011
2011
We associate with each compact set X of Rn two real-valued functions cX and hX defined on R+ which provide two measures of how… (More)
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2011
2011
Upper bounds on the Betti numbers over an arbitrary field of Vietoris–Rips complexes are established, and examples of such… (More)
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Review
2010
Review
2010
The Vietoris-Rips complex characterizes the topology of a point set. This complex is popular in topological data analysis as its… (More)
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2010
2010
Fix a finite set of points in Euclidean n-space En, thought of as a point-cloud sampling of a certain domain D ⊂ En. The… (More)
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