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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2022, Volume 7, Issue 1, Pages 97–112
DOI: https://doi.org/10.47475/2500-0101-2022-17107 (Mi chfmj273) 		 
Mathematics

Algorithms to solve absolute orientation problem for GL(3), O(3), and SO(3) groups

A. Yu. Makovetskiia, S. M. Voronina, A. S. Voronina, T. Makavetskayab

a Chelyabinsk State University, Chelyabinsk, Russia
b South Ural State University (National Research University), Chelyabinsk, Russia
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DOI: https://doi.org/10.47475/2500-0101-2022-17107
Abstract: The most popular algorithm for aligning of 3D point data is the Iterative Closest Point (ICP). The point-to-point variational problem for orthogonal transformations is mathematically equivalent to the absolute orientation problem in photogrammetry. In this paper the survey of the known closed form methods to solve point-to-point ICP variation problem is proposed. Also, the new extension of the Horn algorithm for O(3) group to SO(3) group is obtained. Computer simulation illustrates the difference of performance for considered methods.
Keywords: absolute orientation problem, Iterative Closest Points (ICP), point-to-point, closed form solution, exact solution, orthogonal transformation, affine transformation.
Funding agency Grant number
Russian Foundation for Basic Research 20-47-740007
The work was supported by the RFBR (grant 20-47-740007).
Received: 18.01.2022
Revised: 28.02.2022
Document Type: Article
UDC: 519.7
Language: English
Citation: A. Yu. Makovetskii, S. M. Voronin, A. S. Voronin, T. Makavetskaya, “Algorithms to solve absolute orientation problem for GL(3), O(3), and SO(3) groups”, Chelyab. Fiz.-Mat. Zh., 7:1 (2022), 97–112
Citation in format AMSBIB
\Bibitem{MakVorVor22}
\by A.~Yu.~Makovetskii, S.~M.~Voronin, A.~S.~Voronin, T.~Makavetskaya
\paper Algorithms to solve absolute orientation problem for GL(3), O(3), and SO(3) groups
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2022
\vol 7
\issue 1
\pages 97--112
\mathnet{http://mi.mathnet.ru/chfmj273}
\crossref{https://doi.org/10.47475/2500-0101-2022-17107}
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