Irregular graph pyramids and representative cocycles of cohomology generators

Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide more refined algebraic invariants to a topological space than d...

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Detalles Bibliográficos
Autores: González Díaz, Rocío, Ion, Adrián, Iglesias Ham, Mabel, Kropatsch, Walter G.
Tipo de recurso: artículo
Fecha de publicación:2009
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/30786
Acceso en línea:http://hdl.handle.net/11441/30786
https://doi.org/10.1007/978-3-642-02124-4_27
Access Level:acceso abierto
Palabra clave:Graph pyramids
Representative cocycles of cohomology generators
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spelling Irregular graph pyramids and representative cocycles of cohomology generatorsGonzález Díaz, RocíoIon, AdriánIglesias Ham, MabelKropatsch, Walter G.Graph pyramidsRepresentative cocycles of cohomology generatorsStructural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide more refined algebraic invariants to a topological space than does homology. It assigns ‘quantities’ to the chains used in homology to characterize holes of any dimension. Graph pyramids can be used to describe subdivisions of the same object at multiple levels of detail. This paper presents cohomology in the context of structural pattern recognition and introduces an algorithm to efficiently compute representative cocycles (the basic elements of cohomology) in 2D using a graph pyramid. Extension to nD and application in the context of pattern recognition are discussed.Matemática Aplicada I2009info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/30786https://doi.org/10.1007/978-3-642-02124-4_27reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésGraph-Based Representations in Pattern Recognition, 5534, 263-272.info:eu-repo/semantics/openAccessoai:idus.us.es:11441/307862026-06-17T12:51:07Z
dc.title.none.fl_str_mv Irregular graph pyramids and representative cocycles of cohomology generators
title Irregular graph pyramids and representative cocycles of cohomology generators
spellingShingle Irregular graph pyramids and representative cocycles of cohomology generators
González Díaz, Rocío
Graph pyramids
Representative cocycles of cohomology generators
title_short Irregular graph pyramids and representative cocycles of cohomology generators
title_full Irregular graph pyramids and representative cocycles of cohomology generators
title_fullStr Irregular graph pyramids and representative cocycles of cohomology generators
title_full_unstemmed Irregular graph pyramids and representative cocycles of cohomology generators
title_sort Irregular graph pyramids and representative cocycles of cohomology generators
dc.creator.none.fl_str_mv González Díaz, Rocío
Ion, Adrián
Iglesias Ham, Mabel
Kropatsch, Walter G.
author González Díaz, Rocío
author_facet González Díaz, Rocío
Ion, Adrián
Iglesias Ham, Mabel
Kropatsch, Walter G.
author_role author
author2 Ion, Adrián
Iglesias Ham, Mabel
Kropatsch, Walter G.
author2_role author
author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
dc.subject.none.fl_str_mv Graph pyramids
Representative cocycles of cohomology generators
topic Graph pyramids
Representative cocycles of cohomology generators
description Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide more refined algebraic invariants to a topological space than does homology. It assigns ‘quantities’ to the chains used in homology to characterize holes of any dimension. Graph pyramids can be used to describe subdivisions of the same object at multiple levels of detail. This paper presents cohomology in the context of structural pattern recognition and introduces an algorithm to efficiently compute representative cocycles (the basic elements of cohomology) in 2D using a graph pyramid. Extension to nD and application in the context of pattern recognition are discussed.
publishDate 2009
dc.date.none.fl_str_mv 2009
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/30786
https://doi.org/10.1007/978-3-642-02124-4_27
url http://hdl.handle.net/11441/30786
https://doi.org/10.1007/978-3-642-02124-4_27
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Graph-Based Representations in Pattern Recognition, 5534, 263-272.
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 15.300724

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