Optimal translational-rotational invariant dictionaries for images

Autores
Barbieri, Davide; Cabrelli, Carlos; Hernández, Eugenio; Molter, Ursula Maria
Año de publicación
2019
Idioma
inglés
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
We provide the construction of a set of square matrices whose translates and rotates provide a Parseval frame that is optimal for approximating a given dataset of images. Our approach is based on abstract harmonic analysis techniques. Optimality is considered with respect to the quadratic error of approximation of the images in the dataset with their projection onto a linear subspace that is invariant under translations and rotations. In addition, we provide an elementary and fully self-contained proof of optimality, and the numerical results from datasets of natural images.
Fil: Barbieri, Davide. Universidad Autónoma de Madrid; España
Fil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Hernández, Eugenio. Universidad Autónoma de Madrid; España
Fil: Molter, Ursula Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Wavelets and Sparsity XVIII
San Diego
Estados Unidos
Society of Photographic Instrumentation Engineers
Materia
IMAGE PROCESSING
GROUP INVARIANCE
OPTIMAL APPROXIMATION
FOURIER ANALYSIS
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:11336/226157
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Optimal translational-rotational invariant dictionaries for imagesBarbieri, DavideCabrelli, CarlosHernández, EugenioMolter, Ursula MariaIMAGE PROCESSINGGROUP INVARIANCEOPTIMAL APPROXIMATIONFOURIER ANALYSIShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We provide the construction of a set of square matrices whose translates and rotates provide a Parseval frame that is optimal for approximating a given dataset of images. Our approach is based on abstract harmonic analysis techniques. Optimality is considered with respect to the quadratic error of approximation of the images in the dataset with their projection onto a linear subspace that is invariant under translations and rotations. In addition, we provide an elementary and fully self-contained proof of optimality, and the numerical results from datasets of natural images.Fil: Barbieri, Davide. Universidad Autónoma de Madrid; EspañaFil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Hernández, Eugenio. Universidad Autónoma de Madrid; EspañaFil: Molter, Ursula Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaWavelets and Sparsity XVIIISan DiegoEstados UnidosSociety of Photographic Instrumentation EngineersSociety of Photographic Instrumentation Engineers2019info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObjectCongresoJournalhttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/226157Optimal translational-rotational invariant dictionaries for images; Wavelets and Sparsity XVIII; San Diego; Estados Unidos; 2019; 1-160277-786XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://doi.org/10.1117/12.2528890info:eu-repo/semantics/altIdentifier/url/https://www.spiedigitallibrary.org/conference-proceedings-of-spie/11138/2528890/Optimal-translational-rotational-invariant-dictionaries-for-images/10.1117/12.2528890.shortinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1909.01887Internacionalinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:57:19Zoai:ri.conicet.gov.ar:11336/226157instacron: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 11:57:20.12CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Optimal translational-rotational invariant dictionaries for images
title Optimal translational-rotational invariant dictionaries for images
spellingShingle Optimal translational-rotational invariant dictionaries for images
Barbieri, Davide
IMAGE PROCESSING
GROUP INVARIANCE
OPTIMAL APPROXIMATION
FOURIER ANALYSIS
title_short Optimal translational-rotational invariant dictionaries for images
title_full Optimal translational-rotational invariant dictionaries for images
title_fullStr Optimal translational-rotational invariant dictionaries for images
title_full_unstemmed Optimal translational-rotational invariant dictionaries for images
title_sort Optimal translational-rotational invariant dictionaries for images
dc.creator.none.fl_str_mv Barbieri, Davide
Cabrelli, Carlos
Hernández, Eugenio
Molter, Ursula Maria
author Barbieri, Davide
author_facet Barbieri, Davide
Cabrelli, Carlos
Hernández, Eugenio
Molter, Ursula Maria
author_role author
author2 Cabrelli, Carlos
Hernández, Eugenio
Molter, Ursula Maria
author2_role author
author
author
dc.subject.none.fl_str_mv IMAGE PROCESSING
GROUP INVARIANCE
OPTIMAL APPROXIMATION
FOURIER ANALYSIS
topic IMAGE PROCESSING
GROUP INVARIANCE
OPTIMAL APPROXIMATION
FOURIER ANALYSIS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We provide the construction of a set of square matrices whose translates and rotates provide a Parseval frame that is optimal for approximating a given dataset of images. Our approach is based on abstract harmonic analysis techniques. Optimality is considered with respect to the quadratic error of approximation of the images in the dataset with their projection onto a linear subspace that is invariant under translations and rotations. In addition, we provide an elementary and fully self-contained proof of optimality, and the numerical results from datasets of natural images.
Fil: Barbieri, Davide. Universidad Autónoma de Madrid; España
Fil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Hernández, Eugenio. Universidad Autónoma de Madrid; España
Fil: Molter, Ursula Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Wavelets and Sparsity XVIII
San Diego
Estados Unidos
Society of Photographic Instrumentation Engineers
description We provide the construction of a set of square matrices whose translates and rotates provide a Parseval frame that is optimal for approximating a given dataset of images. Our approach is based on abstract harmonic analysis techniques. Optimality is considered with respect to the quadratic error of approximation of the images in the dataset with their projection onto a linear subspace that is invariant under translations and rotations. In addition, we provide an elementary and fully self-contained proof of optimality, and the numerical results from datasets of natural images.
publishDate 2019
dc.date.none.fl_str_mv 2019
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/conferenceObject
Congreso
Journal
http://purl.org/coar/resource_type/c_5794
info:ar-repo/semantics/documentoDeConferencia
status_str publishedVersion
format conferenceObject
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/226157
Optimal translational-rotational invariant dictionaries for images; Wavelets and Sparsity XVIII; San Diego; Estados Unidos; 2019; 1-16
0277-786X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/226157
identifier_str_mv Optimal translational-rotational invariant dictionaries for images; Wavelets and Sparsity XVIII; San Diego; Estados Unidos; 2019; 1-16
0277-786X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://doi.org/10.1117/12.2528890
info:eu-repo/semantics/altIdentifier/url/https://www.spiedigitallibrary.org/conference-proceedings-of-spie/11138/2528890/Optimal-translational-rotational-invariant-dictionaries-for-images/10.1117/12.2528890.short
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1909.01887
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
application/pdf
dc.coverage.none.fl_str_mv Internacional
dc.publisher.none.fl_str_mv Society of Photographic Instrumentation Engineers
publisher.none.fl_str_mv Society of Photographic Instrumentation Engineers
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
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score 12.982451

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