Capítulo de Libro
Cup products on polyhedral approximations of 3D digital images
Autor/es | González Díaz, Rocío
Lamar León, Javier Umble, Ronald |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I |
Fecha de publicación | 2011 |
Fecha de depósito | 2015-11-18 |
Publicado en |
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Resumen | Let I be a 3D digital image, and let Q(I) be the associated cubical complex. In this paper we show how to simplify the combinatorial structure of Q(I) and obtain a homeomorphic cellular complex P(I) with fewer cells. We ... Let I be a 3D digital image, and let Q(I) be the associated cubical complex. In this paper we show how to simplify the combinatorial structure of Q(I) and obtain a homeomorphic cellular complex P(I) with fewer cells. We introduce formulas for a diagonal approximation on a general polygon and use it to compute cup products on the cohomology H *(P(I)). The cup product encodes important geometrical information not captured by the cohomology groups. Consequently, the ring structure of H *(P(I)) is a finer topological invariant. The algorithm proposed here can be applied to compute cup products on any polyhedral approximation of an object embedded in 3-space. |
Ficheros | Tamaño | Formato | Ver | Descripción |
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Cup products on polyhedral.pdf | 574.8Kb | [PDF] | Ver/ | |