Homological tree-based strategies for image analysis
Homological characteristics of digital objects can be obtained in a straightforward manner computing an algebraic map φ over a finite cell complex K (with coefficients in the finite field F2={0,1}) which represents the digital object [9]. Computable homological information includes the Euler charact...
| Autores: | , , |
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| Formato: | capítulo de livro |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2009 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/31981 |
| Acesso em linha: | http://hdl.handle.net/11441/31981 https://doi.org/10.1007/978-3-642-03767-2_40 |
| Access Level: | acceso abierto |
| Palavra-chave: | Cell complex chain homotopy digital volume homology gradient vector field image pyramid tree skeleton |
| Resumo: | Homological characteristics of digital objects can be obtained in a straightforward manner computing an algebraic map φ over a finite cell complex K (with coefficients in the finite field F2={0,1}) which represents the digital object [9]. Computable homological information includes the Euler characteristic, homology generators and representative cycles, higher (co)homology operations, etc. This algebraic map φ is described in combinatorial terms using a mixed three-level forest. Different strategies changing only two parameters of this algorithm for computing φ are presented. Each one of those strategies gives rise to different maps, although all of them provides the same homological information for K. For example, tree-based structures useful in image analysis like topological skeletons and pyramids can be obtained as subgraphs of this forest. |
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