Artículo
Chain Homotopies for Object Topological Representations
Autor/es | Jiménez Rodríguez, María José
Medrano Garfia, Belén Real Jurado, Pedro González Díaz, Rocío |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I |
Fecha de publicación | 2011 |
Fecha de depósito | 2015-11-13 |
Publicado en |
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Resumen | 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 ... 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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Chain homotopies.pdf | 280.3Kb | [PDF] | Ver/ | |