Year: 2020
Author: Andrea Cerri, Patrizio Frosini
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 2 : pp. 291–309
Abstract
Topological Persistence has proven to be a promising framework for dealing with problems concerning shape analysis and comparison. In this context, 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1809-m2018-0043
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 2 : pp. 291–309
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Multidimensional persistent topology Matching distance Shape comparison.