On the cohomology of 3D digital images

被引：64

作者：

González-Díaz, R ^{[1
]}

Real, P ^{[1
]}

机构：

[1] Univ Seville, Escuela Super Ingn Informat, Depto Matemat Aplicada, E-41012 Seville, Spain

来源：

DISCRETE APPLIED MATHEMATICS | 2005年 / 147卷 / 2-3期

关键词：

digital topology; chain complexes; cohomology ring;

D O I：

10.1016/j.dam.2004.09.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a method for computing the cohomology ring of three-dimensional (31)) digital binaryvalued pictures. We obtain the cohomology ring of a 3D digital binary-valued picture I, via a simplicial complex K (I) topologically representing (up to isomorphisms of pictures) the picture I. The usefulness of a simplicial description of the "digital" cohomology ring of 3D digital binary-valued pictures is tested by means of a small program visualizing the different steps of the method. Some examples concerning topological thinning, the visualization of representative (co)cycles of (co)homology generators and the computation of the cup product on the cohomology of simple pictures are showed. (c) 2004 Elsevier B.V. All rights reserved.

引用

页码：245 / 263

页数：19

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