Extension of the ABC-Procrustes algorithm for 3D affine coordinate transformation
The Procrustes method is a very effective method for determining the Helmert's datum transformation parameters since it requires neither initial starting values nor iteration. Due to these attractive attributes, the ABC-Procrustes algorithm is extended to solve the 3D affine transformation prob...
| Main Authors: | , , , |
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| Format: | Journal Article |
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The Society of Geomagnetism and Earth, Planetary and Space Sciences (published by Terra Scientific Publishing Company)
2010
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/20008 |
| _version_ | 1848750189856161792 |
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| author | Palancz, B. Zaletnyik, P. Awange, Joseph Heck, B. |
| author_facet | Palancz, B. Zaletnyik, P. Awange, Joseph Heck, B. |
| author_sort | Palancz, B. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The Procrustes method is a very effective method for determining the Helmert's datum transformation parameters since it requires neither initial starting values nor iteration. Due to these attractive attributes, the ABC-Procrustes algorithm is extended to solve the 3D affine transformation problem where scale factors are different in the 3 principal directions X,Y,Z. In this study, it is shown that such a direct extension is restricted to cases of mild anisotropy in scaling. For strong anisotropy, however, the procedure fails. The PZ-method is proposed as an extension of the ABC algorithm for this special case. The procedures are applied to determine transformation parameters for; (i) transforming the Australian Geodetic Datum (AGD 84) to the Geocentric Datum Australia (GDA 94), i.e., mild anisotropy and (ii) synthetic data for strong anisotropy. The results indicate that the PZ-algorithm leads to a local multivariate minimization as opposed to the ABC-algorithm, thus requiring slightly longer computational time. However, the ABC-method is found to be useful for computing proper initial values for the PZ-method, thereby increasing its efficiency. |
| first_indexed | 2025-11-14T07:32:53Z |
| format | Journal Article |
| id | curtin-20.500.11937-20008 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:32:53Z |
| publishDate | 2010 |
| publisher | The Society of Geomagnetism and Earth, Planetary and Space Sciences (published by Terra Scientific Publishing Company) |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-200082017-09-13T16:03:34Z Extension of the ABC-Procrustes algorithm for 3D affine coordinate transformation Palancz, B. Zaletnyik, P. Awange, Joseph Heck, B. singular value decomposition anisotropy scaling coordinate transformation global minimization Procrustes Helmert transformation The Procrustes method is a very effective method for determining the Helmert's datum transformation parameters since it requires neither initial starting values nor iteration. Due to these attractive attributes, the ABC-Procrustes algorithm is extended to solve the 3D affine transformation problem where scale factors are different in the 3 principal directions X,Y,Z. In this study, it is shown that such a direct extension is restricted to cases of mild anisotropy in scaling. For strong anisotropy, however, the procedure fails. The PZ-method is proposed as an extension of the ABC algorithm for this special case. The procedures are applied to determine transformation parameters for; (i) transforming the Australian Geodetic Datum (AGD 84) to the Geocentric Datum Australia (GDA 94), i.e., mild anisotropy and (ii) synthetic data for strong anisotropy. The results indicate that the PZ-algorithm leads to a local multivariate minimization as opposed to the ABC-algorithm, thus requiring slightly longer computational time. However, the ABC-method is found to be useful for computing proper initial values for the PZ-method, thereby increasing its efficiency. 2010 Journal Article http://hdl.handle.net/20.500.11937/20008 10.5047/eps.2010.10.004 The Society of Geomagnetism and Earth, Planetary and Space Sciences (published by Terra Scientific Publishing Company) unknown |
| spellingShingle | singular value decomposition anisotropy scaling coordinate transformation global minimization Procrustes Helmert transformation Palancz, B. Zaletnyik, P. Awange, Joseph Heck, B. Extension of the ABC-Procrustes algorithm for 3D affine coordinate transformation |
| title | Extension of the ABC-Procrustes algorithm for 3D affine coordinate transformation |
| title_full | Extension of the ABC-Procrustes algorithm for 3D affine coordinate transformation |
| title_fullStr | Extension of the ABC-Procrustes algorithm for 3D affine coordinate transformation |
| title_full_unstemmed | Extension of the ABC-Procrustes algorithm for 3D affine coordinate transformation |
| title_short | Extension of the ABC-Procrustes algorithm for 3D affine coordinate transformation |
| title_sort | extension of the abc-procrustes algorithm for 3d affine coordinate transformation |
| topic | singular value decomposition anisotropy scaling coordinate transformation global minimization Procrustes Helmert transformation |
| url | http://hdl.handle.net/20.500.11937/20008 |