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A non‐iterative method for approximation of the exact solution to the point‐to‐plane variational problem for orthogonal transformations
Author(s) -
Makovetskii Artyom,
Voronin Sergei,
Kober Vitaly,
Voronin Aleksei
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5173
Subject(s) - mathematics , affine transformation , transformation (genetics) , orthonormal basis , algorithm , orthogonal matrix , iterative method , point cloud , matrix (chemical analysis) , transformation matrix , iterative closest point , translation (biology) , point (geometry) , orthogonal transformation , mathematical analysis , geometry , orthogonal basis , computer science , artificial intelligence , biochemistry , chemistry , physics , materials science , kinematics , quantum mechanics , classical mechanics , messenger rna , composite material , gene
The most popular algorithm for aligning of three‐dimensional point data is the iterative closest point (ICP). In this paper, a new algorithm for orthogonal registration of point clouds based on the point‐to‐plane ICP algorithm is proposed. The algorithm consists of three steps: first, a matrix of affine transformation between two given point clouds are calculated; second, the affine transformation matrix is projected onto the manifold S O (3) of orthonormal matrices; finally, a translation vector is reestimated. The proposed algorithm does not require an approximate initial estimate. At each iterative step of the ICP algorithm, an approximated closed‐form solution for the orthogonal transformation is derived. The performance of the proposed algorithm is compared with that of common algorithms for the geometrical transformations estimation.