@Article{JCM-38-291, author = {Cerri , Andrea and Frosini , Patrizio}, 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 = {
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.