Fractal Topological Analysis for 2D Binary Digital Images

Fractal dimension is a powerful tool employed as a measurement of geometric aspects. In this work we propose a method of topological fractal analysis for 2D binary digital images by using a graph-based topological model of them, called Homological Spanning Forest (HSF, for short). Defined at interpi...

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Autores: Blanco Trejo, Sergio, Alemán Morillo, C., Díaz del Río, Fernando, Real Jurado, Pedro
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/126295
Acceso en línea:https://hdl.handle.net/11441/126295
https://doi.org/10.1007/s11786-018-0386-9
Access Level:acceso abierto
Palabra clave:Digital image
Region-adjacency tree
Fractal topology
Homological spanning forest
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spelling Fractal Topological Analysis for 2D Binary Digital ImagesBlanco Trejo, SergioAlemán Morillo, C.Díaz del Río, FernandoReal Jurado, PedroDigital imageRegion-adjacency treeFractal topologyHomological spanning forestFractal dimension is a powerful tool employed as a measurement of geometric aspects. In this work we propose a method of topological fractal analysis for 2D binary digital images by using a graph-based topological model of them, called Homological Spanning Forest (HSF, for short). Defined at interpixel level, this set of two trees allows to topologically describe the (black and white) connected component distribution within the image with regards to the relationship “to be surrounded by”. This distribution is condensed into a rooted tree, such that its nodes are connected components determined by some special sub-trees of the previous HSF and the levels of the tree specify the degree of nesting of each connected component. We ask for topological auto-similarity by comparing this topological description of the whole image with a regular rooted tree pattern. Such an analysis can be used to directly quantify some characteristics of biomedical images (e.g. cells samples or clinical images) that are not so noticeable when using geometrical approaches.Ministerio de Economía y Competitividad TEC2016-77785-PMinisterio de Economía y Competitividad MTM2016-81030-PSpringerIngeniería Aeroespacial y Mecánica de FluidosArquitectura y Tecnología de ComputadoresMatemática Aplicada IMinisterio de Economía y Competitividad (MINECO). España2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/126295https://doi.org/10.1007/s11786-018-0386-9reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésMathematics in Computer Science, 13 (1-2), 11-20.TEC2016-77785-PMTM2016-81030-Phttps://link.springer.com/article/10.1007/s11786-018-0386-9info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1262952026-06-17T12:51:07Z
dc.title.none.fl_str_mv Fractal Topological Analysis for 2D Binary Digital Images
title Fractal Topological Analysis for 2D Binary Digital Images
spellingShingle Fractal Topological Analysis for 2D Binary Digital Images
Blanco Trejo, Sergio
Digital image
Region-adjacency tree
Fractal topology
Homological spanning forest
title_short Fractal Topological Analysis for 2D Binary Digital Images
title_full Fractal Topological Analysis for 2D Binary Digital Images
title_fullStr Fractal Topological Analysis for 2D Binary Digital Images
title_full_unstemmed Fractal Topological Analysis for 2D Binary Digital Images
title_sort Fractal Topological Analysis for 2D Binary Digital Images
dc.creator.none.fl_str_mv Blanco Trejo, Sergio
Alemán Morillo, C.
Díaz del Río, Fernando
Real Jurado, Pedro
author Blanco Trejo, Sergio
author_facet Blanco Trejo, Sergio
Alemán Morillo, C.
Díaz del Río, Fernando
Real Jurado, Pedro
author_role author
author2 Alemán Morillo, C.
Díaz del Río, Fernando
Real Jurado, Pedro
author2_role author
author
author
dc.contributor.none.fl_str_mv Ingeniería Aeroespacial y Mecánica de Fluidos
Arquitectura y Tecnología de Computadores
Matemática Aplicada I
Ministerio de Economía y Competitividad (MINECO). España
dc.subject.none.fl_str_mv Digital image
Region-adjacency tree
Fractal topology
Homological spanning forest
topic Digital image
Region-adjacency tree
Fractal topology
Homological spanning forest
description Fractal dimension is a powerful tool employed as a measurement of geometric aspects. In this work we propose a method of topological fractal analysis for 2D binary digital images by using a graph-based topological model of them, called Homological Spanning Forest (HSF, for short). Defined at interpixel level, this set of two trees allows to topologically describe the (black and white) connected component distribution within the image with regards to the relationship “to be surrounded by”. This distribution is condensed into a rooted tree, such that its nodes are connected components determined by some special sub-trees of the previous HSF and the levels of the tree specify the degree of nesting of each connected component. We ask for topological auto-similarity by comparing this topological description of the whole image with a regular rooted tree pattern. Such an analysis can be used to directly quantify some characteristics of biomedical images (e.g. cells samples or clinical images) that are not so noticeable when using geometrical approaches.
publishDate 2019
dc.date.none.fl_str_mv 2019
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/126295
https://doi.org/10.1007/s11786-018-0386-9
url https://hdl.handle.net/11441/126295
https://doi.org/10.1007/s11786-018-0386-9
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Mathematics in Computer Science, 13 (1-2), 11-20.
TEC2016-77785-P
MTM2016-81030-P
https://link.springer.com/article/10.1007/s11786-018-0386-9
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.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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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