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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/226157
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T10:24:36Zoai: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:34982025-09-29 10:24:37.141CONICET 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/ |
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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 |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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13.070432 |