Reducing complexes in multidimensional persistent homology theory

被引：11

作者：

Allili, Madjid ^{[1
]}

Kaczynski, Tomasz ^{[2
]}

Landi, Claudia ^{[3
]}

机构：

[1] Bishops Univ, Dept Math, Sherbrooke, PQ J1M 1Z7, Canada

[2] Univ Sherbrooke, Dept Math, Sherbrooke, PQ J1K 2R1, Canada

[3] Univ Modena & Reggio Emilia, Dipartimento Sci & Metodi Ingn, Reggio Emilia, Italy

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 2017年 / 78卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Multidimensional persistent homology; Discrete Morse theory; Acyclic partial matchings; Matching algorithm; DIGITAL IMAGES; SIZE FUNCTIONS; MORSE-THEORY; DISCRETE; SIMPLIFICATION; COMPUTATION; REDUCTION;

D O I：

10.1016/j.jsc.2015.11.020

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Forman's discrete Morse theory appeared to be useful for providing filtration-preserving reductions of complexes in the study of persistent homology. So far, the algorithms computing discrete Morse matchings have only been used for one-dimensional filtrations. This paper is perhaps the first attempt in the direction of extending such algorithms to multidimensional filtrations. An initial framework related to Morse matchings for the multidimensional setting is proposed, and a matching algorithm given by King, Knudson, and Mramor is extended in this direction. The correctness of the algorithm is proved, and its complexity analyzed. The algorithm is used for establishing a reduction of a simplicial complex to a smaller but not necessarily optimal cellular complex. First experiments with filtrations of triangular meshes are presented. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：61 / 75

页数：15

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