Point Cloud Registration Based on Multiparameter Functional

Artyom Makovetskii, Sergei Voronin, Vitaly Kober and Aleksei Voronin
Additional contact information
Artyom Makovetskii: Deparment of Mathematics, Chelyabinsk State University, 454001 Chelyabinsk, Russia
Sergei Voronin: Deparment of Mathematics, Chelyabinsk State University, 454001 Chelyabinsk, Russia
Vitaly Kober: Deparment of Mathematics, Chelyabinsk State University, 454001 Chelyabinsk, Russia
Aleksei Voronin: Deparment of Mathematics, Chelyabinsk State University, 454001 Chelyabinsk, Russia

Mathematics, 2021, vol. 9, issue 20, 1-20

Abstract: The registration of point clouds in a three-dimensional space is an important task in many areas of computer vision, including robotics and autonomous driving. The purpose of registration is to find a rigid geometric transformation to align two point clouds. The registration problem can be affected by noise and partiality (two point clouds only have a partial overlap). The Iterative Closed Point (ICP) algorithm is a common method for solving the registration problem. Recently, artificial neural networks have begun to be used in the registration of point clouds. The drawback of ICP and other registration algorithms is the possible convergence to a local minimum. Thus, an important characteristic of a registration algorithm is the ability to avoid local minima. In this paper, we propose an ICP-type registration algorithm ( ? -ICP) that uses a multiparameter functional ( ? -functional). The proposed ? -ICP algorithm generalizes the NICP algorithm (normal ICP). The application of the ? -functional requires a consistent choice of the eigenvectors of the covariance matrix of two point clouds. The paper also proposes an algorithm for choosing the directions of eigenvectors. The performance of the proposed ? -ICP algorithm is compared with that of a standard point-to-point ICP and neural network Deep Closest Points (DCP).

Keywords: variational functionals; global optimization; closed-form solution; iterative closest points (ICP); normal ICP (NICP); neural network; DCP (deep closest points); affine transformations; orthogonal transformations; surface reconstruction; computer geometry (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/20/2589/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/20/2589/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:20:p:2589-:d:656932

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().