Application of simulated annealing algorithm for 3D coordinate transformation problem solution
Transformation of spatial coordinates (3D) is a common computational task in photogrammetry, engineering geodesy, geographical information systems or computer vision. In the most frequently used variant, transformation of point coordinates requires knowledge of seven transformation parameters, of wh...
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| Format: | Article |
| Language: | English |
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De Gruyter
2020-07-01
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| Series: | Open Geosciences |
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| Online Access: | https://doi.org/10.1515/geo-2020-0038 |
| _version_ | 1818594443234639872 |
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| author | Odziemczyk Waldemar |
| author_facet | Odziemczyk Waldemar |
| author_sort | Odziemczyk Waldemar |
| collection | DOAJ |
| description | Transformation of spatial coordinates (3D) is a common computational task in photogrammetry, engineering geodesy, geographical information systems or computer vision. In the most frequently used variant, transformation of point coordinates requires knowledge of seven transformation parameters, of which three determine translation, another three rotation and one change in scale. As these parameters are commonly determined through iterative methods, it is essential to know their initial approximation. While determining approximate values of the parameters describing translation or scale change is relatively easy, determination of rotation requires more advanced methods. This study proposes an original, two-step procedure of estimating transformation parameters. In the initial step, a modified version of simulated annealing algorithm is used for identifying the approximate value of the rotation parameter. In the second stage, traditional least squares method is applied to obtain the most probable values of transformation parameters. The way the algorithm works was checked on two numerical examples. The computational experiments proved that proposed algorithm is efficient even in cases characterised by very disadvantageous configuration of common points. |
| first_indexed | 2024-12-16T11:00:12Z |
| format | Article |
| id | doaj.art-5ff0bae116c74840917b5ff891148dcc |
| institution | Directory Open Access Journal |
| issn | 2391-5447 |
| language | English |
| last_indexed | 2024-12-16T11:00:12Z |
| publishDate | 2020-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Geosciences |
| spelling | doaj.art-5ff0bae116c74840917b5ff891148dcc2022-12-21T22:34:01ZengDe GruyterOpen Geosciences2391-54472020-07-0112149150210.1515/geo-2020-0038geo-2020-0038Application of simulated annealing algorithm for 3D coordinate transformation problem solutionOdziemczyk Waldemar0Chair of Engineering Geodesy and Control-Measuring Systems, Faculty of Geodesy and Cartography, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warszawa, room. 304, Warsaw 00-661, PolandTransformation of spatial coordinates (3D) is a common computational task in photogrammetry, engineering geodesy, geographical information systems or computer vision. In the most frequently used variant, transformation of point coordinates requires knowledge of seven transformation parameters, of which three determine translation, another three rotation and one change in scale. As these parameters are commonly determined through iterative methods, it is essential to know their initial approximation. While determining approximate values of the parameters describing translation or scale change is relatively easy, determination of rotation requires more advanced methods. This study proposes an original, two-step procedure of estimating transformation parameters. In the initial step, a modified version of simulated annealing algorithm is used for identifying the approximate value of the rotation parameter. In the second stage, traditional least squares method is applied to obtain the most probable values of transformation parameters. The way the algorithm works was checked on two numerical examples. The computational experiments proved that proposed algorithm is efficient even in cases characterised by very disadvantageous configuration of common points.https://doi.org/10.1515/geo-2020-00383d coordinate transformationrodrigues matrixquaternionsinitial valuessimulated annealingmetaheuristic method |
| spellingShingle | Odziemczyk Waldemar Application of simulated annealing algorithm for 3D coordinate transformation problem solution Open Geosciences 3d coordinate transformation rodrigues matrix quaternions initial values simulated annealing metaheuristic method |
| title | Application of simulated annealing algorithm for 3D coordinate transformation problem solution |
| title_full | Application of simulated annealing algorithm for 3D coordinate transformation problem solution |
| title_fullStr | Application of simulated annealing algorithm for 3D coordinate transformation problem solution |
| title_full_unstemmed | Application of simulated annealing algorithm for 3D coordinate transformation problem solution |
| title_short | Application of simulated annealing algorithm for 3D coordinate transformation problem solution |
| title_sort | application of simulated annealing algorithm for 3d coordinate transformation problem solution |
| topic | 3d coordinate transformation rodrigues matrix quaternions initial values simulated annealing metaheuristic method |
| url | https://doi.org/10.1515/geo-2020-0038 |
| work_keys_str_mv | AT odziemczykwaldemar applicationofsimulatedannealingalgorithmfor3dcoordinatetransformationproblemsolution |