A regularized point cloud registration approach for orthogonal transformations

Artyom Makovetskii (), Sergei Voronin, Vitaly Kober and Aleksei Voronin
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Artyom Makovetskii: Chelyabinsk State University
Sergei Voronin: Chelyabinsk State University
Vitaly Kober: Chelyabinsk State University
Aleksei Voronin: Chelyabinsk State University

Journal of Global Optimization, 2022, vol. 83, issue 3, No 6, 497-519

Abstract: Abstract An important part of the well-known iterative closest point algorithm (ICP) is the variational problem. Several variants of the variational problem are known, such as point-to-point, point-to-plane, generalized ICP, and normal ICP (NICP). This paper proposes a closed-form exact solution for orthogonal registration of point clouds based on the generalized point-to-point ICP algorithm. We use points and normal vectors to align 3D point clouds, while the common point-to-point approach uses only the coordinates of points. The paper also presents a closed-form approximate solution to the variational problem of the NICP. In addition, the paper introduces a regularization approach and proposes reliable algorithms for solving variational problems using closed-form solutions. The performance of the algorithms is compared with that of common algorithms for solving variational problems of the ICP algorithm. The proposed paper is significantly extended version of Makovetskii et al. (CCIS 1090, 217–231, 2019).

Keywords: Variational functionals; Global optimization; Exact solution; Closed-form solution; Iterative closest points (ICP); Normal ICP (NICP); Affine transformations; Orthogonal transformations; Surface reconstruction; Computer geometry (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-020-00934-8

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