A Graph-with-Loop Structure for a Topological Representation of 3D Objects

Given a cell complex K whose geometric realization |K| is embedded in R 3 and a continuous function h: |K|→R (called the height function), we construct a graph G h (K) which is an extension of the Reeb graph R h (|K|). More concretely, the graph G h (K) without loops is a subdivision of R h (|K|). T...

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Detalles Bibliográficos
Autores: González Díaz, Rocío, Jiménez Rodríguez, María José, Medrano Garfia, Belén, Real Jurado, Pedro
Tipo de recurso: capítulo de libro
Fecha de publicación:2007
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/30657
Acceso en línea:http://hdl.handle.net/11441/30657
https://doi.org/10.1007/978-3-540-74272-2_63
Access Level:acceso abierto
Palabra clave:Pattern Recognition
Image Processing and Computer Vision
Artificial Intelligence
Robotics Computer Graphics Algorithm Analysis and Problem Complexity
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spelling A Graph-with-Loop Structure for a Topological Representation of 3D ObjectsGonzález Díaz, RocíoJiménez Rodríguez, María JoséMedrano Garfia, BelénReal Jurado, PedroPattern RecognitionImage Processing and Computer VisionArtificial IntelligenceRobotics Computer Graphics Algorithm Analysis and Problem ComplexityGiven a cell complex K whose geometric realization |K| is embedded in R 3 and a continuous function h: |K|→R (called the height function), we construct a graph G h (K) which is an extension of the Reeb graph R h (|K|). More concretely, the graph G h (K) without loops is a subdivision of R h (|K|). The most important difference between the graphs G h (K) and R h (|K|) is that G h (K) preserves not only the number of connected components but also the number of “tunnels” (the homology generators of dimension 1) of K. The latter is not true in general for R h (|K|). Moreover, we construct a map ψ: G h (K)→K identifying representative cycles of the tunnels in K with the ones in G h (K) in the way that if e is a loop in G h (K), then ψ(e) is a cycle in K such that all the points in |ψ(e)| belong to the same level set in |K|.Matemática Aplicada I2007info:eu-repo/semantics/bookPartapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/30657https://doi.org/10.1007/978-3-540-74272-2_63reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésComputer Analysis of Images and Patterns (CAIP 2007), Lecture Notes in Computer Science, Vol. 4673, p. 506-513info:eu-repo/semantics/openAccessoai:idus.us.es:11441/306572026-06-17T12:51:07Z
dc.title.none.fl_str_mv A Graph-with-Loop Structure for a Topological Representation of 3D Objects
title A Graph-with-Loop Structure for a Topological Representation of 3D Objects
spellingShingle A Graph-with-Loop Structure for a Topological Representation of 3D Objects
González Díaz, Rocío
Pattern Recognition
Image Processing and Computer Vision
Artificial Intelligence
Robotics Computer Graphics Algorithm Analysis and Problem Complexity
title_short A Graph-with-Loop Structure for a Topological Representation of 3D Objects
title_full A Graph-with-Loop Structure for a Topological Representation of 3D Objects
title_fullStr A Graph-with-Loop Structure for a Topological Representation of 3D Objects
title_full_unstemmed A Graph-with-Loop Structure for a Topological Representation of 3D Objects
title_sort A Graph-with-Loop Structure for a Topological Representation of 3D Objects
dc.creator.none.fl_str_mv González Díaz, Rocío
Jiménez Rodríguez, María José
Medrano Garfia, Belén
Real Jurado, Pedro
author González Díaz, Rocío
author_facet González Díaz, Rocío
Jiménez Rodríguez, María José
Medrano Garfia, Belén
Real Jurado, Pedro
author_role author
author2 Jiménez Rodríguez, María José
Medrano Garfia, Belén
Real Jurado, Pedro
author2_role author
author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
dc.subject.none.fl_str_mv Pattern Recognition
Image Processing and Computer Vision
Artificial Intelligence
Robotics Computer Graphics Algorithm Analysis and Problem Complexity
topic Pattern Recognition
Image Processing and Computer Vision
Artificial Intelligence
Robotics Computer Graphics Algorithm Analysis and Problem Complexity
description Given a cell complex K whose geometric realization |K| is embedded in R 3 and a continuous function h: |K|→R (called the height function), we construct a graph G h (K) which is an extension of the Reeb graph R h (|K|). More concretely, the graph G h (K) without loops is a subdivision of R h (|K|). The most important difference between the graphs G h (K) and R h (|K|) is that G h (K) preserves not only the number of connected components but also the number of “tunnels” (the homology generators of dimension 1) of K. The latter is not true in general for R h (|K|). Moreover, we construct a map ψ: G h (K)→K identifying representative cycles of the tunnels in K with the ones in G h (K) in the way that if e is a loop in G h (K), then ψ(e) is a cycle in K such that all the points in |ψ(e)| belong to the same level set in |K|.
publishDate 2007
dc.date.none.fl_str_mv 2007
dc.type.none.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/30657
https://doi.org/10.1007/978-3-540-74272-2_63
url http://hdl.handle.net/11441/30657
https://doi.org/10.1007/978-3-540-74272-2_63
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Computer Analysis of Images and Patterns (CAIP 2007), Lecture Notes in Computer Science, Vol. 4673, p. 506-513
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 15.300719

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