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Cubical cohomology ring of 3D photographs

 

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dc.creator González Díaz, Rocío
dc.creator Jiménez Rodríguez, María José
dc.creator Medrano Garfia, Belén
dc.date.accessioned 2015-11-12T12:42:39Z
dc.date.available 2015-11-12T12:42:39Z
dc.date.issued 2011
dc.identifier.uri http://hdl.handle.net/11441/30675
dc.description.abstract Cohomology groups and the cohomology ring of three-dimensional (3D) objects are topological invariants that characterize holes and their relations. Cohomology ring has been traditionally computed on simplicial complexes. Nevertheless, cubical complexes deal directly with the voxels in 3D images, no additional triangulation is necessary. This could facilitate efficient algorithms for the computation of topological invariants in the image context. In this article, we present a constructive process, made up by several algorithms, to compute the cohomology ring of 3D binary-valued digital photographs represented by cubical complexes. Starting from a cubical complex Q that represents such a 3D picture whose foreground has one connected component, we first compute the homological information on the boundary of the object, ∂Q, by an incremental technique; using a face reduction algorithm, we then compute it on the whole object; finally, applying explicit formulas for cubical complexes (without making use of any additional triangulation), the cohomology ring is computed from such information. es
dc.format application/pdf es
dc.language.iso eng es
dc.relation.ispartof International Journal of Imaging Systems and Technology, 21 (1), 76-85. es
dc.rights Atribución-NoComercial-CompartirIgual 4.0 Internacional *
dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/4.0/ *
dc.subject cohomology ring es
dc.subject cubical complexes es
dc.subject 3D digital images es
dc.title Cubical cohomology ring of 3D photographs es
dc.type info:eu-repo/semantics/article es
dc.rights.accessrights info:eu-repo/semantics/openAccess es
dc.contributor.affiliation Universidad de Sevilla. Departamento de Matemática Aplicada I es
dc.identifier.doi http://dx.doi.org/DOI: 10.1002/ima.20271 es
dc.journaltitle International Journal of Imaging Systems and Technology es
dc.publication.volumen 21 es
dc.publication.issue 1 es
dc.publication.initialPage 76 es
dc.publication.endPage 85 es
dc.identifier.idus https://idus.us.es/xmlui/handle/11441/30675
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