A new approximation Algorithm for the Matching Distance in Multidimensional Persistence

Cerri, Andrea ; Frosini, Patrizio (2011) A new approximation Algorithm for the Matching Distance in Multidimensional Persistence. p. 15. DOI 10.6092/unibo/amsacta/2971.
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Topological Persistence has proven to be a promising framework for dealing with problems concerning shape analysis and comparison. In this contexts, it was originally introduced by taking into account 1-dimensional properties of shapes, modeled by real-valued functions. More recently, Topological Persistence has been generalized to consider multidimensional properties of shapes, coded by vector-valued functions. This extension has led to introduce suitable shape descriptors, named the multidimensional persistence Betti numbers functions, and a distance to compare them, the so-called multidimensional matching distance. In this paper we propose a new computational framework to deal with the multidimensional matching distance. We start by proving some new theoretical results, and then we use them to formulate an algorithm for computing such a distance up to an arbitrary threshold error.

Document type
Monograph (Technical Report)
Cerri, Andrea
Frosini, Patrizio
Multidimensional persistent topology, matching distance, shape comparison
Deposit date
18 Feb 2011 10:14
Last modified
16 May 2011 12:16

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