Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds

Autores
Zhang, Kewei; Orlando, Antonio; Crooks, Elaine
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We apply compensated convex transforms to define a multiscale Hausdorff stable method to extract intersections between smooth compact manifolds represented by their characteristic functions or as point clouds embedded in Rn. We prove extraction results on intersections of smooth compact manifolds and for points of high curvature. As a result of the Hausdorff?Lipschitz continuity of our transforms, we show that our method is stable against dense sampling of smooth manifolds with noise. Examples of explicitly calculated prototype models for some simple cases are presented, which are also used in the proofs of our main results. Numerical experiments in two- and three-dimensional space, and applications to geometric objects are also shown.
Fil: Zhang, Kewei. The University of Nottingham; Reino Unido
Fil: Orlando, Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Tucuman. Facultad de Ciencias Exactas y Tecnologia. Instituto de Estructuras ; Argentina
Fil: Crooks, Elaine. Swansea University; Reino Unido
Materia
Compensated Convex Transforms
Hausdorff Stability
Stable Ridges
Random Samples
Valleys
Edges
Corners Transforms
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/45546
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/45546
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Compensated convexity and Hausdorff stable extraction of intersections for smooth manifoldsZhang, KeweiOrlando, AntonioCrooks, ElaineCompensated Convex TransformsHausdorff StabilityStable RidgesRandom SamplesValleysEdgesCorners Transformshttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1We apply compensated convex transforms to define a multiscale Hausdorff stable method to extract intersections between smooth compact manifolds represented by their characteristic functions or as point clouds embedded in Rn. We prove extraction results on intersections of smooth compact manifolds and for points of high curvature. As a result of the Hausdorff?Lipschitz continuity of our transforms, we show that our method is stable against dense sampling of smooth manifolds with noise. Examples of explicitly calculated prototype models for some simple cases are presented, which are also used in the proofs of our main results. Numerical experiments in two- and three-dimensional space, and applications to geometric objects are also shown.Fil: Zhang, Kewei. The University of Nottingham; Reino UnidoFil: Orlando, Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Tucuman. Facultad de Ciencias Exactas y Tecnologia. Instituto de Estructuras ; ArgentinaFil: Crooks, Elaine. Swansea University; Reino UnidoWorld Scientific2015-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/45546Zhang, Kewei; Orlando, Antonio; Crooks, Elaine; Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds; World Scientific; Mathematical Models And Methods In Applied Sciences; 25; 05; 5-2015; 839-8730218-2025CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1142/S0218202515500207info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0218202515500207info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:10:27Zoai:ri.conicet.gov.ar:11336/45546instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 12:10:28.014CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds
title Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds
spellingShingle Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds
Zhang, Kewei
Compensated Convex Transforms
Hausdorff Stability
Stable Ridges
Random Samples
Valleys
Edges
Corners Transforms
title_short Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds
title_full Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds
title_fullStr Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds
title_full_unstemmed Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds
title_sort Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds
dc.creator.none.fl_str_mv Zhang, Kewei
Orlando, Antonio
Crooks, Elaine
author Zhang, Kewei
author_facet Zhang, Kewei
Orlando, Antonio
Crooks, Elaine
author_role author
author2 Orlando, Antonio
Crooks, Elaine
author2_role author
author
dc.subject.none.fl_str_mv Compensated Convex Transforms
Hausdorff Stability
Stable Ridges
Random Samples
Valleys
Edges
Corners Transforms
topic Compensated Convex Transforms
Hausdorff Stability
Stable Ridges
Random Samples
Valleys
Edges
Corners Transforms
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We apply compensated convex transforms to define a multiscale Hausdorff stable method to extract intersections between smooth compact manifolds represented by their characteristic functions or as point clouds embedded in Rn. We prove extraction results on intersections of smooth compact manifolds and for points of high curvature. As a result of the Hausdorff?Lipschitz continuity of our transforms, we show that our method is stable against dense sampling of smooth manifolds with noise. Examples of explicitly calculated prototype models for some simple cases are presented, which are also used in the proofs of our main results. Numerical experiments in two- and three-dimensional space, and applications to geometric objects are also shown.
Fil: Zhang, Kewei. The University of Nottingham; Reino Unido
Fil: Orlando, Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Tucuman. Facultad de Ciencias Exactas y Tecnologia. Instituto de Estructuras ; Argentina
Fil: Crooks, Elaine. Swansea University; Reino Unido
description We apply compensated convex transforms to define a multiscale Hausdorff stable method to extract intersections between smooth compact manifolds represented by their characteristic functions or as point clouds embedded in Rn. We prove extraction results on intersections of smooth compact manifolds and for points of high curvature. As a result of the Hausdorff?Lipschitz continuity of our transforms, we show that our method is stable against dense sampling of smooth manifolds with noise. Examples of explicitly calculated prototype models for some simple cases are presented, which are also used in the proofs of our main results. Numerical experiments in two- and three-dimensional space, and applications to geometric objects are also shown.
publishDate 2015
dc.date.none.fl_str_mv 2015-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/45546
Zhang, Kewei; Orlando, Antonio; Crooks, Elaine; Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds; World Scientific; Mathematical Models And Methods In Applied Sciences; 25; 05; 5-2015; 839-873
0218-2025
CONICET Digital
CONICET
url http://hdl.handle.net/11336/45546
identifier_str_mv Zhang, Kewei; Orlando, Antonio; Crooks, Elaine; Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds; World Scientific; Mathematical Models And Methods In Applied Sciences; 25; 05; 5-2015; 839-873
0218-2025
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218202515500207
info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0218202515500207
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv World Scientific
publisher.none.fl_str_mv World Scientific
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1846782490580090880
score 12.982451

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