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标题：Extension of the ABC-Procrustes algorithm for 3D affine coordinate transformation
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作者：B. Paláncz ; P. Zaletnyik ; J. L. Awange 等
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