Tuning of conic parameters using Tikhonov regularization and L-Curve simulation
In this article, a method to infer the parameters of a conic given a set of rectangular coordinates that belong to the geometric entity is shown. The methodology consists of solving a Tikhonov regulation problem where the unregulated term introduces the non-linear nature of the conical body and the...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Universidad Nacional de Colombia
2019-07-01
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| Series: | Dyna |
| Subjects: | |
| Online Access: | https://revistas.unal.edu.co/index.php/dyna/article/view/75996 |
| _version_ | 1818663808566034432 |
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| author | Andrés Felipe Calvo-Salcedo Carlos Alberto Henao Baena Hugo Armando Becerra-Gallego |
| author_facet | Andrés Felipe Calvo-Salcedo Carlos Alberto Henao Baena Hugo Armando Becerra-Gallego |
| author_sort | Andrés Felipe Calvo-Salcedo |
| collection | DOAJ |
| description | In this article, a method to infer the parameters of a conic given a set of rectangular coordinates that belong to the geometric entity is shown. The methodology consists of solving a Tikhonov regulation problem where the unregulated term introduces the non-linear nature of the conical body and the regulated the restriction associated to the discriminant of the quadratic equation, then the solution is computed minimizing the resulting cost function where the Regularization parameter is tuned using the L-Curve technique. The model was validated with synthetic and real data from digital images, as well as subject to comparison against other state of the art alternatives. The results show that the method is robust against atypical values and the phenomenon of occlusion present in the data. |
| first_indexed | 2024-12-17T05:22:44Z |
| format | Article |
| id | doaj.art-103c7730dd054ce885d0916ab74075ea |
| institution | Directory Open Access Journal |
| issn | 0012-7353 2346-2183 |
| language | English |
| last_indexed | 2024-12-17T05:22:44Z |
| publishDate | 2019-07-01 |
| publisher | Universidad Nacional de Colombia |
| record_format | Article |
| series | Dyna |
| spelling | doaj.art-103c7730dd054ce885d0916ab74075ea2022-12-21T22:01:58ZengUniversidad Nacional de ColombiaDyna0012-73532346-21832019-07-018621019420310.15446/dyna.v86n210.7599651693Tuning of conic parameters using Tikhonov regularization and L-Curve simulationAndrés Felipe Calvo-Salcedo0Carlos Alberto Henao Baena1Hugo Armando Becerra-Gallego2Universidad Tecnológica de PereiraTecnoparque Nodo PereiraUniversidad Tecnológica de PereiraIn this article, a method to infer the parameters of a conic given a set of rectangular coordinates that belong to the geometric entity is shown. The methodology consists of solving a Tikhonov regulation problem where the unregulated term introduces the non-linear nature of the conical body and the regulated the restriction associated to the discriminant of the quadratic equation, then the solution is computed minimizing the resulting cost function where the Regularization parameter is tuned using the L-Curve technique. The model was validated with synthetic and real data from digital images, as well as subject to comparison against other state of the art alternatives. The results show that the method is robust against atypical values and the phenomenon of occlusion present in the data.https://revistas.unal.edu.co/index.php/dyna/article/view/75996segmentationoptimizationparameter estimation |
| spellingShingle | Andrés Felipe Calvo-Salcedo Carlos Alberto Henao Baena Hugo Armando Becerra-Gallego Tuning of conic parameters using Tikhonov regularization and L-Curve simulation Dyna segmentation optimization parameter estimation |
| title | Tuning of conic parameters using Tikhonov regularization and L-Curve simulation |
| title_full | Tuning of conic parameters using Tikhonov regularization and L-Curve simulation |
| title_fullStr | Tuning of conic parameters using Tikhonov regularization and L-Curve simulation |
| title_full_unstemmed | Tuning of conic parameters using Tikhonov regularization and L-Curve simulation |
| title_short | Tuning of conic parameters using Tikhonov regularization and L-Curve simulation |
| title_sort | tuning of conic parameters using tikhonov regularization and l curve simulation |
| topic | segmentation optimization parameter estimation |
| url | https://revistas.unal.edu.co/index.php/dyna/article/view/75996 |
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