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CORR
2010
Springer

Invariance properties of the multidimensional matching distance in Persistent Topology and Homology

10 years 4 months ago
Invariance properties of the multidimensional matching distance in Persistent Topology and Homology
Abstract. Persistent Topology studies topological features of shapes by analyzing the lower level sets of suitable functions, called filtering functions, and encoding the arising information in a parameterized version of the Betti numbers, i.e. the ranks of persistent homology groups. Initially introduced by considering real-valued filtering functions, Persistent Topology has been subsequently generalized to a multidimensional setting, i.e. to the case of Rnvalued filtering functions, leading to studying the ranks of multidimensional homology groups. In particular, a multidimensional matching distance has been defined, in order to compare these ranks. The definition of the multidimensional matching distance is based on foliating the domain of the ranks of multidimensional homology groups by a collection of half-planes, and hence it formally depends on a subset of Rn
Andrea Cerri, Patrizio Frosini
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CORR
Authors Andrea Cerri, Patrizio Frosini
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