TY - JOUR
T1 - A New Approximation Algorithm for the Matching Distance in Multidimensional Persistence
AU - Cerri , Andrea
AU - Frosini , Patrizio
JO - Journal of Computational Mathematics
VL - 2
SP - 291
EP - 309
PY - 2020
DA - 2020/02
SN - 38
DO - http://doi.org/10.4208/jcm.1809-m2018-0043
UR - https://global-sci.org/intro/article_detail/jcm/14518.html
KW - Multidimensional persistent topology, Matching distance, Shape comparison.
AB - <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>