A NEW APPROXIMATION ALGORITHM FOR THE MATCHING DISTANCE IN MULTIDIMENSIONAL PERSISTENCE

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 proper ties of shapes,coded by vect or-valued functions.This extension has led to int roduce suitable shape descrip tors,named the multidimensional persis tence 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.