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...

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Detalles Bibliográficos
Autores: Molina Abril, Helena, Real Jurado, Pedro
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
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spelling Advanced homology computation of digital volumes via cell complexesMolina Abril, HelenaReal Jurado, PedroPattern RecognitionDiscrete Mathematics in Computer ScienceProbability and Statistics in Computer ScienceImage Processing and Computer VisionArtificial Intelligence (incl. Robotics)Computer GraphicsGiven 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.Matemática Aplicada I2008info:eu-repo/semantics/bookPartinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/31738https://doi.org/10.1007/978-3-540-89689-0_40reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésStructural, Syntactic, and Statistical Pattern Recognition, Lecture Notes in Computer Science, Vol. 5342 p. 361-371info:eu-repo/semantics/openAccessoai:idus.us.es:11441/317382026-06-17T12:51:07Z
dc.title.none.fl_str_mv Advanced homology computation of digital volumes via cell complexes
title Advanced homology computation of digital volumes via cell complexes
spellingShingle Advanced homology computation of digital volumes via cell complexes
Molina Abril, Helena
Pattern Recognition
Discrete Mathematics in Computer Science
Probability and Statistics in Computer Science
Image Processing and Computer Vision
Artificial Intelligence (incl. Robotics)
Computer Graphics
title_short Advanced homology computation of digital volumes via cell complexes
title_full Advanced homology computation of digital volumes via cell complexes
title_fullStr Advanced homology computation of digital volumes via cell complexes
title_full_unstemmed Advanced homology computation of digital volumes via cell complexes
title_sort Advanced homology computation of digital volumes via cell complexes
dc.creator.none.fl_str_mv Molina Abril, Helena
Real Jurado, Pedro
author Molina Abril, Helena
author_facet Molina Abril, Helena
Real Jurado, Pedro
author_role author
author2 Real Jurado, Pedro
author2_role author
dc.contributor.none.fl_str_mv Matemática Aplicada I
dc.subject.none.fl_str_mv Pattern Recognition
Discrete Mathematics in Computer Science
Probability and Statistics in Computer Science
Image Processing and Computer Vision
Artificial Intelligence (incl. Robotics)
Computer Graphics
topic Pattern Recognition
Discrete Mathematics in Computer Science
Probability and Statistics in Computer Science
Image Processing and Computer Vision
Artificial Intelligence (incl. Robotics)
Computer Graphics
description 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.
publishDate 2008
dc.date.none.fl_str_mv 2008
dc.type.none.fl_str_mv info:eu-repo/semantics/bookPart
info:eu-repo/semantics/submittedVersion
format bookPart
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/31738
https://doi.org/10.1007/978-3-540-89689-0_40
url http://hdl.handle.net/11441/31738
https://doi.org/10.1007/978-3-540-89689-0_40
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Structural, Syntactic, and Statistical Pattern Recognition, Lecture Notes in Computer Science, Vol. 5342 p. 361-371
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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