@Article{JCM-38-2,
author = {Cerri, Andrea and Patrizio, Frosini},
title = {A New Approximation Algorithm for the Matching Distance in Multidimensional Persistence},
journal = {Journal of Computational Mathematics},
year = {2020},
volume = {38},
number = {2},
pages = {291--309},
abstract = {<p style="text-align: justify;">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.<br/>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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1809-m2018-0043},
url = {https://global-sci.com/article/84309/a-new-approximation-algorithm-for-the-matching-distance-in-multidimensional-persistence}
}