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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Abstract

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.

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

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