Connectivity forests for homological analysis of digital volumes
In this paper, we provide a graph-based representation of the homology (information related to the different “holes” the object has) of a binary digital volume. We analyze the digital volume AT-model representation [8] from this point of view and the cellular version of the AT-model [5] is precisely...
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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:11441/31743 |
| Acesso em linha: | http://hdl.handle.net/11441/31743 https://doi.org/10.1007/978-3-642-02478-8_52 |
| Access Level: | acceso abierto |
| Palavra-chave: | Computational Biology Bioinformatics Pattern Recognition Artificial Intelligence (incl. Robotics) Data Mining and Knowledge Discovery Models and Principles |
| Resumo: | In this paper, we provide a graph-based representation of the homology (information related to the different “holes” the object has) of a binary digital volume. We analyze the digital volume AT-model representation [8] from this point of view and the cellular version of the AT-model [5] is precisely described here as three forests (connectivity forests), from which, for instance, we can straightforwardly determine representative curves of “tunnels” and “holes”, classify cycles in the complex, computing higher (co)homology operations,... Depending of the order in which we gradually construct these trees, tools so important in Computer Vision and Digital Image Processing as Reeb graphs and topological skeletons appear as results of pruning these graphs. |
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