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Extension of Procrustes algorithm for 3D affine coordinate transformation

Béla Paláncz
Organization: Budapest University of Technology and Economics
Department: Photogrammetry and Geoinformatics
Piroska Zaletnyik
Organization: Budapest University of Technology and Economics
Department: Department of Geodesy and Surveying
Joseph Awange
Organization: Curtin University of Technology
Department: Spatial Sciences, Division of Resource and Environmental
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Procrustes method is a very effective method to solve the parameter estimation problem for Helmert coordinate transformation, because it requires neither initial start values nor iteration. That is why, it is a very tempting idea to extend it to 3D affine transformation, where scale factors are different in the 3 principal directions. In this study, it will be illustrated, that the direct extension is restricted for cases where the values of these 3 scale factors are just slightly different. We also demonstrate that this fact does not mean that it is unreasonable to use affine transformation model instead of Helmert one, because it can provide improvement in the quality of the transformation even in these restricted cases. However, employing iteration for the scale parameters, the extension can be fully achieved, even for strongly different values of scale parameters. It goes without saying that in this way the computation time will increase considerable, but it is even competitive with those of other methods.

*Applied Mathematics
*Wolfram Technology > Application Packages > Applications from Independent Developers > GeometricalGeodesy

3D affine transformation, Procrustes method
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