Advanced homology computation of digital volumes via cell complexes
Given a 3D binary voxel-based digital object V, an algorithm for computing homological information for V via a polyhedral cell complex is designed. By homological information we understand not only Betti numbers, representative cycles of homology classes and homological classification of cycles but...
| Autores: | , |
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| Tipo de recurso: | capítulo de libro |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2008 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/31738 |
| Acceso en línea: | http://hdl.handle.net/11441/31738 https://doi.org/10.1007/978-3-540-89689-0_40 |
| Access Level: | acceso abierto |
| Palabra clave: | Pattern Recognition Discrete Mathematics in Computer Science Probability and Statistics in Computer Science Image Processing and Computer Vision Artificial Intelligence (incl. Robotics) Computer Graphics |
| Sumario: | Given a 3D binary voxel-based digital object V, an algorithm for computing homological information for V via a polyhedral cell complex is designed. By homological information we understand not only Betti numbers, representative cycles of homology classes and homological classification of cycles but also the computation of homology numbers related additional algebraic structures defined on homology (coproduct in homology, product in cohomology, (co)homology operations,...). The algorithm is mainly based on the following facts: a) a local 3D-polyhedrization of any 2×2×2 configuration of mutually 26-adjacent black voxels providing a coherent cell complex at global level; b) a description of the homology of a digital volume as an algebraic-gradient vector field on the cell complex (see Discrete Morse Theory [5], AT-model method [7,5]). Saving this vector field, we go further obtaining homological information at no extra time processing cost. |
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