Modelos variacionais aplicados a computação visual
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações do LNCC |
Texto Completo: | https://tede.lncc.br/handle/tede/316 |
Resumo: | In this master’s thesis, we explore analytical and numerical approaches that allow us to bring together variational techniques applied to visual computing (image processing and computer graphics). In this way, we study a version of the functional proposed by Mumford and Shah that is simply rewritten as an energy functional defined by two arguments, these being the piecewise continuous version of an input data and its respective discontinuity points. Then, we explore schems of numerical solutions based on finite elements and finite differences, in addition, we seek possible simplifications for the functional in order to expand the Bourdin’s model applications. In the area of computer graphics we focus on fluid animation. We examined the model named Gradient Vector Flow (GVF), which is defined by a diffusion-reaction vector equation. In this line, we dedicate the studies and analyzes to the preservation of a singular point, in the original field. In this line, we dedicate the studies and analyzes to the preservation of a singular point in the original field, with respect to boundary conditions of the GVF solution, assuming a compact domain, with rectangular geometry. In this respect, we use approximations based on well-collocation method using Haar wavelet functions compared to methods based on explicit finite differences and, a new method, based on implicit finite differences, developed in this dissertation. The focus was to find the method that best preserve the topology of the initial vector field. In these models, the parameters chosen are important for the quality of the results. In this sense, we carried out a study with respect to the sensitivity of the methods to the variation of the parameters and we presented a parameterization model based on inverse problems, directing the research towards the calibration of the methods presented in this dissertation. |
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Giraldi, Gilson AntonioLoula, Abimael Fernando DouradoGiraldi, Gilson AntonioJavier Blanco, PabloVieira, Marcelo BernardesSantos, Ítalo Messias Félix2023-03-06T18:17:26Z2020-08-03SANTOS, I. M. F. Modelos variacionais aplicados a computação visual. 2020. 121 f. Dissertação (Programa de Pós-Graduação em Modelagem Computacional) - Laboratório Nacional de Computação Científica, Petrópolis, 2020.https://tede.lncc.br/handle/tede/316In this master’s thesis, we explore analytical and numerical approaches that allow us to bring together variational techniques applied to visual computing (image processing and computer graphics). In this way, we study a version of the functional proposed by Mumford and Shah that is simply rewritten as an energy functional defined by two arguments, these being the piecewise continuous version of an input data and its respective discontinuity points. Then, we explore schems of numerical solutions based on finite elements and finite differences, in addition, we seek possible simplifications for the functional in order to expand the Bourdin’s model applications. In the area of computer graphics we focus on fluid animation. We examined the model named Gradient Vector Flow (GVF), which is defined by a diffusion-reaction vector equation. In this line, we dedicate the studies and analyzes to the preservation of a singular point, in the original field. In this line, we dedicate the studies and analyzes to the preservation of a singular point in the original field, with respect to boundary conditions of the GVF solution, assuming a compact domain, with rectangular geometry. In this respect, we use approximations based on well-collocation method using Haar wavelet functions compared to methods based on explicit finite differences and, a new method, based on implicit finite differences, developed in this dissertation. The focus was to find the method that best preserve the topology of the initial vector field. In these models, the parameters chosen are important for the quality of the results. In this sense, we carried out a study with respect to the sensitivity of the methods to the variation of the parameters and we presented a parameterization model based on inverse problems, directing the research towards the calibration of the methods presented in this dissertation.Nesta dissertação de mestrado, exploramos abordagens analíticas e numéricas que permitem reunir técnicas variacionais aplicadas a computação visual (processamento de imagens e computação gráfica). Neste caminho, estudamos uma versão do funcional proposto por Mumford e Shah que é reescrito de maneira simples como um funcional de energia definido por dois argumentos, sendo estes a versão contínua por partes de um dado de entrada e seus respectivos pontos de descontinuidade. Em seguida, exploramos formas de soluções numéricas baseadas em elementos finitos e diferenças finitas bem como possíveis simplificações para o funcional com o intuito de expandir as aplicações do modelo de Bourdin. Na área de computação gráfica focamos em animação de fluidos. Examinamos o modelo denominado Fluxo do Vetor Gradiente (GVF), que é definido por uma equação vetorial de difusão-reação. Nesta linha, dedicamos os estudos e análises à preservação de um ponto singular, no campo original, em relação à condição de fronteira do campo inicial na solução do GVF, supondo um domínio compacto, com geometria retangular. Neste aspecto, utilizamos aproximações baseadas no método da boa colocação utilizando funções wavelets de Haar em comparação com métodos baseados em diferenças finitas explícitos e, um novo método, baseado em diferenças finitas implícito, desenvolvido nesta dissertação. O foco foi a busca do método que melhor preserva a topologia do campo inicial. Nestes modelos, os parâmetros escolhidos são importantes para a qualidade dos resultados. Neste sentido, realizamos um estudo com respeito a sensibilidade dos métodos à variação dos parâmetros e apresentamos um modelo de parametrização baseado em problemas inversos, direcionando a pesquisa à parametrização dos métodos abordados nesta dissertação.Submitted by Patrícia Vieira Silva (library@lncc.br) on 2023-03-06T18:14:09Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_Ítalo Santos2020.pdf: 4718182 bytes, checksum: 324b9b270e7062cf75649bf006df5065 (MD5)Approved for entry into archive by Patrícia Vieira Silva (library@lncc.br) on 2023-03-06T18:14:40Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_Ítalo Santos2020.pdf: 4718182 bytes, checksum: 324b9b270e7062cf75649bf006df5065 (MD5)Made available in DSpace on 2023-03-06T18:17:26Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_Ítalo Santos2020.pdf: 4718182 bytes, checksum: 324b9b270e7062cf75649bf006df5065 (MD5) Previous issue date: 2020-08-03Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorFundação de Amparo à Pesquisa do Estado do Rio de Janeiroapplication/pdfhttp://tede-server.lncc.br:8080/retrieve/1204/Dissertacao_%c3%8dtalo%20Santos2020.pdf.jpgporLaboratório Nacional de Computação CientíficaPrograma de Pós-Graduação em Modelagem ComputacionalLNCCBrasilCoordenação de Pós-Graduação e Aperfeiçoamento (COPGA)http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessProcessamento de imagem - Técnicas digitaisComputação gráficaCNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::METODOLOGIA E TECNICAS DA COMPUTACAOModelos variacionais aplicados a computação visualinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisreponame:Biblioteca Digital de Teses e Dissertações do LNCCinstname:Laboratório Nacional de Computação Científica (LNCC)instacron:LNCCLICENSElicense.txtlicense.txttext/plain; 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dc.title.por.fl_str_mv |
Modelos variacionais aplicados a computação visual |
title |
Modelos variacionais aplicados a computação visual |
spellingShingle |
Modelos variacionais aplicados a computação visual Santos, Ítalo Messias Félix Processamento de imagem - Técnicas digitais Computação gráfica CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::METODOLOGIA E TECNICAS DA COMPUTACAO |
title_short |
Modelos variacionais aplicados a computação visual |
title_full |
Modelos variacionais aplicados a computação visual |
title_fullStr |
Modelos variacionais aplicados a computação visual |
title_full_unstemmed |
Modelos variacionais aplicados a computação visual |
title_sort |
Modelos variacionais aplicados a computação visual |
author |
Santos, Ítalo Messias Félix |
author_facet |
Santos, Ítalo Messias Félix |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Giraldi, Gilson Antonio |
dc.contributor.advisor2.fl_str_mv |
Loula, Abimael Fernando Dourado |
dc.contributor.referee1.fl_str_mv |
Giraldi, Gilson Antonio |
dc.contributor.referee2.fl_str_mv |
Javier Blanco, Pablo |
dc.contributor.referee3.fl_str_mv |
Vieira, Marcelo Bernardes |
dc.contributor.author.fl_str_mv |
Santos, Ítalo Messias Félix |
contributor_str_mv |
Giraldi, Gilson Antonio Loula, Abimael Fernando Dourado Giraldi, Gilson Antonio Javier Blanco, Pablo Vieira, Marcelo Bernardes |
dc.subject.por.fl_str_mv |
Processamento de imagem - Técnicas digitais Computação gráfica |
topic |
Processamento de imagem - Técnicas digitais Computação gráfica CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::METODOLOGIA E TECNICAS DA COMPUTACAO |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::METODOLOGIA E TECNICAS DA COMPUTACAO |
description |
In this master’s thesis, we explore analytical and numerical approaches that allow us to bring together variational techniques applied to visual computing (image processing and computer graphics). In this way, we study a version of the functional proposed by Mumford and Shah that is simply rewritten as an energy functional defined by two arguments, these being the piecewise continuous version of an input data and its respective discontinuity points. Then, we explore schems of numerical solutions based on finite elements and finite differences, in addition, we seek possible simplifications for the functional in order to expand the Bourdin’s model applications. In the area of computer graphics we focus on fluid animation. We examined the model named Gradient Vector Flow (GVF), which is defined by a diffusion-reaction vector equation. In this line, we dedicate the studies and analyzes to the preservation of a singular point, in the original field. In this line, we dedicate the studies and analyzes to the preservation of a singular point in the original field, with respect to boundary conditions of the GVF solution, assuming a compact domain, with rectangular geometry. In this respect, we use approximations based on well-collocation method using Haar wavelet functions compared to methods based on explicit finite differences and, a new method, based on implicit finite differences, developed in this dissertation. The focus was to find the method that best preserve the topology of the initial vector field. In these models, the parameters chosen are important for the quality of the results. In this sense, we carried out a study with respect to the sensitivity of the methods to the variation of the parameters and we presented a parameterization model based on inverse problems, directing the research towards the calibration of the methods presented in this dissertation. |
publishDate |
2020 |
dc.date.issued.fl_str_mv |
2020-08-03 |
dc.date.accessioned.fl_str_mv |
2023-03-06T18:17:26Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
SANTOS, I. M. F. Modelos variacionais aplicados a computação visual. 2020. 121 f. Dissertação (Programa de Pós-Graduação em Modelagem Computacional) - Laboratório Nacional de Computação Científica, Petrópolis, 2020. |
dc.identifier.uri.fl_str_mv |
https://tede.lncc.br/handle/tede/316 |
identifier_str_mv |
SANTOS, I. M. F. Modelos variacionais aplicados a computação visual. 2020. 121 f. Dissertação (Programa de Pós-Graduação em Modelagem Computacional) - Laboratório Nacional de Computação Científica, Petrópolis, 2020. |
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https://tede.lncc.br/handle/tede/316 |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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openAccess |
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Laboratório Nacional de Computação Científica |
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Programa de Pós-Graduação em Modelagem Computacional |
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LNCC |
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Brasil |
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Coordenação de Pós-Graduação e Aperfeiçoamento (COPGA) |
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Laboratório Nacional de Computação Científica |
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