Procrustes based closed-form solution to the point-wise weighted rigid-body transformation in asymmetric and symmetric cases

In the paper, we derive Procrustes-based closed-form solutions to the point-wise weighted rigid-body transformation under different adjustment scenarios. We treat both asymmetric and symmetric cases. By asymmetric (or Gauss-Markov) models we mean those in which either a source system or a target sys...

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Bibliographic Details
Published inJournal of spatial science Vol. 66; no. 3; pp. 445 - 457
Main Authors Ligas, Marcin, Prochniewicz, Dominik
Format Journal Article
LanguageEnglish
Published Taylor & Francis 02.09.2021
Subjects
errors-in-variables
polar decomposition
Procrustes method
rigid-body transformation
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Summary:In the paper, we derive Procrustes-based closed-form solutions to the point-wise weighted rigid-body transformation under different adjustment scenarios. We treat both asymmetric and symmetric cases. By asymmetric (or Gauss-Markov) models we mean those in which either a source system or a target system is subject to random errors. On the other hand, by the symmetric model (Gauss-Helmert or errors-in-variables) we mean the one in which points of both coordinate systems are considered erroneous. The solutions are universal in the sense that they fit both 2D and 3D transformation cases without modifications of computational algorithms. Presented results are also attractive because the solutions require neither linearisation nor iteration.
ISSN:1449-8596
1836-5655
DOI:10.1080/14498596.2019.1684394