Repositorio de producción científica de la Universidad de Sevilla

Chain Homotopies for Object Topological Representations


Advanced Search
Opened Access Chain Homotopies for Object Topological Representations

Show item statistics
Export to
Author: Jiménez Rodríguez, María José
Medrano Garfia, Belén
Real Jurado, Pedro
González Díaz, Rocío
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I
Date: 2011
Published in: Discrete Applied Mathematics, 157 (3), 490-499.
Document type: Article
Abstract: This paper presents a set of tools to compute topological information of simplicial complexes, tools that are applicable to extract topological information from digital pictures. A simplicial complex is encoded in a (non-unique) algebraic-topological format called AM-model. An AM-model for a given object K is determined by a concrete chain homotopy and it provides, in particular, integer (co)homology generators of K and representative (co)cycles of these generators. An algorithm for computing an AM-model and the cohomological invariant HB1 (derived from the rank of the cohomology ring) with integer coefficients for a finite simplicial complex in any dimension is designed here. A concept of generators which are "nicely" representative cycles is also presented. Moreover, we extend the definition of AM-models to 3D binary digital images and we design algorithms to update the AM-model information after voxel set operations (union, intersection, difference and inverse).
Size: 280.3Kb
Format: PDF



This work is under a Creative Commons License: 
Atribución-NoComercial-CompartirIgual 4.0 Internacional

This item appears in the following Collection(s)