1D and 2D Fourier-based approaches to numeric curvature estimation and their comparative performance assessment.
Autor(a) principal: | |
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Data de Publicação: | 2003 |
Outros Autores: | , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFOP |
Texto Completo: | http://www.repositorio.ufop.br/handle/123456789/1050 |
Resumo: | A careful comparison of three numeric techniques for estimation of the curvature along spatially quantized contours is reported. Two of the considered techniques are based on the Fourier transform (operating over 1D and 2D signals) and Gaussian regularization required to attenuate the spatial quantization noise. While the 1D approach has been reported before and used in a series of applications, the 2D Fourier transform-based method is reported in this article for the first time. The third approach, based on splines, represents a more traditional alternative. Three classes of parametric curves are investigated: analytical, B-splines, and synthesized in the Fourier domain. Four quantization schemes are considered: grid intersect quantization, square box quantization, a table scanner, and a video camera. The performances of the methods are evaluated in terms of their execution speed, curvature error, and sensitivity to the involved parameters. The third approach resulted the fastest, but implied larger errors; the Fourier methods allowed higher accuracy and were robust to parameter configurations. The 2D Fourier method provides the curvature values along the whole image, but exhibits interference in some situations. Such results are important not only for characterizing the relative performance of the considered methods, but also for providing practical guidelines for those interested in applying those techniques to real problems. |
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Estrozi, Leandro FariasRios Filho, Luiz GonzagaBianchi, Andrea Gomes CamposCésar Júnior, Roberto MarcondesCosta, Luciano da Fontoura2012-07-10T15:44:55Z2012-07-10T15:44:55Z2003ESTROZI, L. F. et al. 1D and 2D Fourier-based approaches to numeric curvature estimation and their comparative performance assessment. Digital Signal Processing, v. 13, n.1, p.172-197, jan. 2003. Disponível em: <http://www.sciencedirect.com/science/article/pii/S105120040200012X>. Acesso em: 10 jul. 2012.10512004http://www.repositorio.ufop.br/handle/123456789/1050A careful comparison of three numeric techniques for estimation of the curvature along spatially quantized contours is reported. Two of the considered techniques are based on the Fourier transform (operating over 1D and 2D signals) and Gaussian regularization required to attenuate the spatial quantization noise. While the 1D approach has been reported before and used in a series of applications, the 2D Fourier transform-based method is reported in this article for the first time. The third approach, based on splines, represents a more traditional alternative. Three classes of parametric curves are investigated: analytical, B-splines, and synthesized in the Fourier domain. Four quantization schemes are considered: grid intersect quantization, square box quantization, a table scanner, and a video camera. The performances of the methods are evaluated in terms of their execution speed, curvature error, and sensitivity to the involved parameters. The third approach resulted the fastest, but implied larger errors; the Fourier methods allowed higher accuracy and were robust to parameter configurations. The 2D Fourier method provides the curvature values along the whole image, but exhibits interference in some situations. Such results are important not only for characterizing the relative performance of the considered methods, but also for providing practical guidelines for those interested in applying those techniques to real problems.Performance assessmentGaussian regularizationDigital signal processingCurvature estimationDifferential geometry1D and 2D Fourier-based approaches to numeric curvature estimation and their comparative performance assessment.info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleO Periódico Digital Signal Processing concede permissão para depósito do artigo no Repositório Institucional da UFOP. Número da licença: 3337590439746.info:eu-repo/semantics/openAccessengreponame:Repositório Institucional da UFOPinstname:Universidade Federal de Ouro Preto (UFOP)instacron:UFOPLICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://www.repositorio.ufop.br/bitstream/123456789/1050/5/license.txt8a4605be74aa9ea9d79846c1fba20a33MD55ORIGINALARTIGO_FourierBasedApproaches.pdfARTIGO_FourierBasedApproaches.pdfapplication/pdf813506http://www.repositorio.ufop.br/bitstream/123456789/1050/1/ARTIGO_FourierBasedApproaches.pdf4ea94646ece8f84064d961f2abd92b7eMD51123456789/10502015-03-10 17:03:22.559oai:localhost: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Repositório InstitucionalPUBhttp://www.repositorio.ufop.br/oai/requestrepositorio@ufop.edu.bropendoar:32332015-03-10T21:03:22Repositório Institucional da UFOP - Universidade Federal de Ouro Preto (UFOP)false |
dc.title.pt_BR.fl_str_mv |
1D and 2D Fourier-based approaches to numeric curvature estimation and their comparative performance assessment. |
title |
1D and 2D Fourier-based approaches to numeric curvature estimation and their comparative performance assessment. |
spellingShingle |
1D and 2D Fourier-based approaches to numeric curvature estimation and their comparative performance assessment. Estrozi, Leandro Farias Performance assessment Gaussian regularization Digital signal processing Curvature estimation Differential geometry |
title_short |
1D and 2D Fourier-based approaches to numeric curvature estimation and their comparative performance assessment. |
title_full |
1D and 2D Fourier-based approaches to numeric curvature estimation and their comparative performance assessment. |
title_fullStr |
1D and 2D Fourier-based approaches to numeric curvature estimation and their comparative performance assessment. |
title_full_unstemmed |
1D and 2D Fourier-based approaches to numeric curvature estimation and their comparative performance assessment. |
title_sort |
1D and 2D Fourier-based approaches to numeric curvature estimation and their comparative performance assessment. |
author |
Estrozi, Leandro Farias |
author_facet |
Estrozi, Leandro Farias Rios Filho, Luiz Gonzaga Bianchi, Andrea Gomes Campos César Júnior, Roberto Marcondes Costa, Luciano da Fontoura |
author_role |
author |
author2 |
Rios Filho, Luiz Gonzaga Bianchi, Andrea Gomes Campos César Júnior, Roberto Marcondes Costa, Luciano da Fontoura |
author2_role |
author author author author |
dc.contributor.author.fl_str_mv |
Estrozi, Leandro Farias Rios Filho, Luiz Gonzaga Bianchi, Andrea Gomes Campos César Júnior, Roberto Marcondes Costa, Luciano da Fontoura |
dc.subject.por.fl_str_mv |
Performance assessment Gaussian regularization Digital signal processing Curvature estimation Differential geometry |
topic |
Performance assessment Gaussian regularization Digital signal processing Curvature estimation Differential geometry |
description |
A careful comparison of three numeric techniques for estimation of the curvature along spatially quantized contours is reported. Two of the considered techniques are based on the Fourier transform (operating over 1D and 2D signals) and Gaussian regularization required to attenuate the spatial quantization noise. While the 1D approach has been reported before and used in a series of applications, the 2D Fourier transform-based method is reported in this article for the first time. The third approach, based on splines, represents a more traditional alternative. Three classes of parametric curves are investigated: analytical, B-splines, and synthesized in the Fourier domain. Four quantization schemes are considered: grid intersect quantization, square box quantization, a table scanner, and a video camera. The performances of the methods are evaluated in terms of their execution speed, curvature error, and sensitivity to the involved parameters. The third approach resulted the fastest, but implied larger errors; the Fourier methods allowed higher accuracy and were robust to parameter configurations. The 2D Fourier method provides the curvature values along the whole image, but exhibits interference in some situations. Such results are important not only for characterizing the relative performance of the considered methods, but also for providing practical guidelines for those interested in applying those techniques to real problems. |
publishDate |
2003 |
dc.date.issued.fl_str_mv |
2003 |
dc.date.accessioned.fl_str_mv |
2012-07-10T15:44:55Z |
dc.date.available.fl_str_mv |
2012-07-10T15:44:55Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
ESTROZI, L. F. et al. 1D and 2D Fourier-based approaches to numeric curvature estimation and their comparative performance assessment. Digital Signal Processing, v. 13, n.1, p.172-197, jan. 2003. Disponível em: <http://www.sciencedirect.com/science/article/pii/S105120040200012X>. Acesso em: 10 jul. 2012. |
dc.identifier.uri.fl_str_mv |
http://www.repositorio.ufop.br/handle/123456789/1050 |
dc.identifier.issn.none.fl_str_mv |
10512004 |
identifier_str_mv |
ESTROZI, L. F. et al. 1D and 2D Fourier-based approaches to numeric curvature estimation and their comparative performance assessment. Digital Signal Processing, v. 13, n.1, p.172-197, jan. 2003. Disponível em: <http://www.sciencedirect.com/science/article/pii/S105120040200012X>. Acesso em: 10 jul. 2012. 10512004 |
url |
http://www.repositorio.ufop.br/handle/123456789/1050 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
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info:eu-repo/semantics/openAccess |
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openAccess |
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UFOP |
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Repositório Institucional da UFOP |
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