Cavazza, Niccolò ;
Ferri, Massimo ;
Landi, Claudia
(2010)
Estimating multidimensional persistent homology through a finite sampling.
p. 11.
DOI
10.6092/unibo/amsacta/2861.
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Abstract
An exact computation of the persistent Betti numbers of a submanifold X of a Euclidean space is possible only in a theoretical setting. In practical situations, only a finite sample of X is available. We show that, under suitable density conditions, it is possible to estimate the multidimensional persistent Betti numbers of X from the ones of a union of balls centered on the sample points;
this even yields the exact value in restricted areas of the domain.
Similar inequalities are proved for the multidimensional persistent Betti numbers of the ball union and the one of a combinatorial description of it.
Abstract
An exact computation of the persistent Betti numbers of a submanifold X of a Euclidean space is possible only in a theoretical setting. In practical situations, only a finite sample of X is available. We show that, under suitable density conditions, it is possible to estimate the multidimensional persistent Betti numbers of X from the ones of a union of balls centered on the sample points;
this even yields the exact value in restricted areas of the domain.
Similar inequalities are proved for the multidimensional persistent Betti numbers of the ball union and the one of a combinatorial description of it.
Document type
Monograph
(Technical Report)
Creators
Subjects
DOI
Deposit date
23 Nov 2010 11:33
Last modified
16 May 2011 12:14
URI
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Document type
Monograph
(Technical Report)
Creators
Subjects
DOI
Deposit date
23 Nov 2010 11:33
Last modified
16 May 2011 12:14
URI
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