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Chain Homotopies for Object Topological Representations

 

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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).
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Format: PDF

URI: http://hdl.handle.net/11441/30726

DOI: http://dx.doi.org/10.1016/j.dam.2008.05.029

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