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  • 标题:Extension of the ABC-Procrustes algorithm for 3D affine coordinate transformation
  • 本地全文:下载
  • 作者:B. Paláncz ; P. Zaletnyik ; J. L. Awange
  • 期刊名称:Earth, Planets and Space
  • 电子版ISSN:1880-5981
  • 出版年度:2010
  • 卷号:62
  • 期号:11
  • 页码:857-862
  • DOI:10.5047/eps.2010.10.004
  • 出版社:Springer Verlag
  • 摘要: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.
  • 关键词:Procrustes ;coordinate transformation ;anisotropy scaling ;Helmert transformation ;singular value decomposition ;global minimization
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