An implementation of the partitioned Levenberg-Marquardt algorithm for applications in computer vision.

Bibliographic Details
Main Author: França, José Alexandre de
Publication Date: 2009
Other Authors: França, Maria Bernadete de Morais, Koyama, Marcela Hitomi, Silva, Tiago Polizer da
Format: Article
Language: por
Source: Revista Semina: Ciências Exatas e Tecnológicas (Online)
Download full: https://ojs.uel.br/revistas/uel/index.php/semexatas/article/view/4734
Summary: At several applications of computer vision is necessary to estimate parameters for a specific model which best fits an experimental data set. For these cases, a minimization algorithm might be used and one of the most popular is the Levenberg-Marquardt algorithm. Although several free applies from this algorithm are available, any of them has great features when the resolution of problem has a sparse Jacobian matrix . In this case, it is possible to have a great reduce in the algorithm's complexity. This work presents a Levenberg-Marquardt algorithm implemented in cases which has a sparse Jacobian matrix. To illustrate this algorithm application, the camera calibration with 1D pattern is applied to solve the problem. Empirical results show that this method is able to figure out satisfactorily with few iterations, even with noise presence.
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spelling An implementation of the partitioned Levenberg-Marquardt algorithm for applications in computer vision.Uma implementação do algoritmo Levenberg-Marquardt dividido para aplicações em visão computacional.Levenberg-Marquardt algorithmMonocular CalibrationNewton's.Software systemAlgoritmo Levenberg-MarquardtCalibração MonocularAlgoritmo de Newton.Sistema de softwareAt several applications of computer vision is necessary to estimate parameters for a specific model which best fits an experimental data set. For these cases, a minimization algorithm might be used and one of the most popular is the Levenberg-Marquardt algorithm. Although several free applies from this algorithm are available, any of them has great features when the resolution of problem has a sparse Jacobian matrix . In this case, it is possible to have a great reduce in the algorithm's complexity. This work presents a Levenberg-Marquardt algorithm implemented in cases which has a sparse Jacobian matrix. To illustrate this algorithm application, the camera calibration with 1D pattern is applied to solve the problem. Empirical results show that this method is able to figure out satisfactorily with few iterations, even with noise presence.Em diversas aplicações da visão computacional, é necessário estimar-se, em um modelo, os parâmetros que melhor se ajustam a um conjunto de dados experimentais. Nesses casos, um algoritmo de minimização pode ser utilizado. Dentre estes, um dos mais conhecidos é o Levenberg-Marquardt. Apesar de diversas implementações de tal algoritmo estarem disponíveis livremente, nenhuma delas leva em consideração quando a solução do problema conduz a uma matriz jacobiana esparsa. Nesses casos, é possível reduzir significativamente a complexidade do algoritmo. Neste trabalho, apresenta-se uma implementação do algoritmo Levenberg-Marquardt para os casos em que a matriz jacobiana do problema é esparsa. Além disso, para ilustrar a aplicação do algoritmo, ele é aplicado a solução do problema de calibração monocular com gabaritos de uma única dimensão. Resultados empíricos mostram que o método converge satisfatoriamente em apenas algumas poucas iterações, mesmo na presença de ruído.State University of Londrina2009-07-15info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionAvaliado pelos paresapplication/pdfhttps://ojs.uel.br/revistas/uel/index.php/semexatas/article/view/473410.5433/1679-0375.2009v30n1p51Semina: Ciências Exatas e Tecnológicas; Vol. 30 No. 1 (2009); 51-62Semina: Ciências Exatas e Tecnológicas; v. 30 n. 1 (2009); 51-621679-03751676-5451reponame:Revista Semina: Ciências Exatas e Tecnológicas (Online)instname:Universidade Estadual de Londrina (UEL)instacron:UELporhttps://ojs.uel.br/revistas/uel/index.php/semexatas/article/view/4734/4092Copyright (c) 2018 Semina: Exact and Technological Sciencesinfo:eu-repo/semantics/openAccessFrança, José Alexandre deFrança, Maria Bernadete de MoraisKoyama, Marcela HitomiSilva, Tiago Polizer da2010-09-21T19:37:53Zoai:ojs2.ojs.uel.br:article/4734Revistahttps://ojs.uel.br/revistas/uel/index.php/semexatas/indexPUBhttps://ojs.uel.br/revistas/uel/index.php/semexatas/oaiseminaexatas@uel.br || periodicosuel@uel.br1679-03751676-5451opendoar:2010-09-21T19:37:53Revista Semina: Ciências Exatas e Tecnológicas (Online) - Universidade Estadual de Londrina (UEL)false
dc.title.none.fl_str_mv An implementation of the partitioned Levenberg-Marquardt algorithm for applications in computer vision.
Uma implementação do algoritmo Levenberg-Marquardt dividido para aplicações em visão computacional.
title An implementation of the partitioned Levenberg-Marquardt algorithm for applications in computer vision.
spellingShingle An implementation of the partitioned Levenberg-Marquardt algorithm for applications in computer vision.
França, José Alexandre de
Levenberg-Marquardt algorithm
Monocular Calibration
Newton's.
Software system
Algoritmo Levenberg-Marquardt
Calibração Monocular
Algoritmo de Newton.
Sistema de software
title_short An implementation of the partitioned Levenberg-Marquardt algorithm for applications in computer vision.
title_full An implementation of the partitioned Levenberg-Marquardt algorithm for applications in computer vision.
title_fullStr An implementation of the partitioned Levenberg-Marquardt algorithm for applications in computer vision.
title_full_unstemmed An implementation of the partitioned Levenberg-Marquardt algorithm for applications in computer vision.
title_sort An implementation of the partitioned Levenberg-Marquardt algorithm for applications in computer vision.
author França, José Alexandre de
author_facet França, José Alexandre de
França, Maria Bernadete de Morais
Koyama, Marcela Hitomi
Silva, Tiago Polizer da
author_role author
author2 França, Maria Bernadete de Morais
Koyama, Marcela Hitomi
Silva, Tiago Polizer da
author2_role author
author
author
dc.contributor.author.fl_str_mv França, José Alexandre de
França, Maria Bernadete de Morais
Koyama, Marcela Hitomi
Silva, Tiago Polizer da
dc.subject.por.fl_str_mv Levenberg-Marquardt algorithm
Monocular Calibration
Newton's.
Software system
Algoritmo Levenberg-Marquardt
Calibração Monocular
Algoritmo de Newton.
Sistema de software
topic Levenberg-Marquardt algorithm
Monocular Calibration
Newton's.
Software system
Algoritmo Levenberg-Marquardt
Calibração Monocular
Algoritmo de Newton.
Sistema de software
description At several applications of computer vision is necessary to estimate parameters for a specific model which best fits an experimental data set. For these cases, a minimization algorithm might be used and one of the most popular is the Levenberg-Marquardt algorithm. Although several free applies from this algorithm are available, any of them has great features when the resolution of problem has a sparse Jacobian matrix . In this case, it is possible to have a great reduce in the algorithm's complexity. This work presents a Levenberg-Marquardt algorithm implemented in cases which has a sparse Jacobian matrix. To illustrate this algorithm application, the camera calibration with 1D pattern is applied to solve the problem. Empirical results show that this method is able to figure out satisfactorily with few iterations, even with noise presence.
publishDate 2009
dc.date.none.fl_str_mv 2009-07-15
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Avaliado pelos pares
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://ojs.uel.br/revistas/uel/index.php/semexatas/article/view/4734
10.5433/1679-0375.2009v30n1p51
url https://ojs.uel.br/revistas/uel/index.php/semexatas/article/view/4734
identifier_str_mv 10.5433/1679-0375.2009v30n1p51
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv https://ojs.uel.br/revistas/uel/index.php/semexatas/article/view/4734/4092
dc.rights.driver.fl_str_mv Copyright (c) 2018 Semina: Exact and Technological Sciences
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Copyright (c) 2018 Semina: Exact and Technological Sciences
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv State University of Londrina
publisher.none.fl_str_mv State University of Londrina
dc.source.none.fl_str_mv Semina: Ciências Exatas e Tecnológicas; Vol. 30 No. 1 (2009); 51-62
Semina: Ciências Exatas e Tecnológicas; v. 30 n. 1 (2009); 51-62
1679-0375
1676-5451
reponame:Revista Semina: Ciências Exatas e Tecnológicas (Online)
instname:Universidade Estadual de Londrina (UEL)
instacron:UEL
instname_str Universidade Estadual de Londrina (UEL)
instacron_str UEL
institution UEL
reponame_str Revista Semina: Ciências Exatas e Tecnológicas (Online)
collection Revista Semina: Ciências Exatas e Tecnológicas (Online)
repository.name.fl_str_mv Revista Semina: Ciências Exatas e Tecnológicas (Online) - Universidade Estadual de Londrina (UEL)
repository.mail.fl_str_mv seminaexatas@uel.br || periodicosuel@uel.br
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