Cup products on polyhedral approximations of 3D digital images
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...
| Autores: | , , |
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| Formato: | capítulo de livro |
| Fecha de publicación: | 2011 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/30805 |
| Acesso em linha: | http://hdl.handle.net/11441/30805 https://doi.org/10.1007/978-3-642-21073-0_12 |
| Access Level: | acceso abierto |
| Palavra-chave: | Cellular complex cohomology cup product diagonal approximation digital image polyhedron |
| Resumo: | 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. |
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