A NEW APPROXIMATION ALGORITHM FOR THE MATCHING DISTANCE IN MULTIDIMENSIONAL PERSISTENCE

• 来源期刊: 计算数学（英文版）
• 关键词: Multidimensional persistent topology Matching distance Shape comparison
• 年，卷（期）: 2020,（2）
• 页码范围: 291-309
• 页数: 19页
• 语种: 英文
• DOI: 10.4208/jcm.1809-m2018-0043

摘要

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 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.