Solution of The Variational Registration Problem Based on Iterative Closest Point Algorithms for Various Types of Geometric Transformations

• Published in: Journal of communications technology & electronics Vol. 67; no. Suppl 1; pp. S119 - S128
• Main Authors: Makovetskii, A. Yu, Kober, V. I., Voronin, S. M., Voronin, A. V., Karnaukhov, V. N., Mozerov, M. G.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.12.2022; Springer; Springer Nature B.V
• Subjects: Algorithms; Communications Engineering; Engineering; Geometric transformation; Horns; Iterative algorithms; Networks; Photogrammetry; Simulation methods; Theory and Methods of Information Processing; Three dimensional models; absolute orientation problem; exact solution; iterative closest point algorithm; orthogonal transformation; point-to-point matching; closed-form solution; affine transformation
• ISSN: 1064-2269; 1555-6557
• DOI: 10.1134/S1064226922130198

The most popular algorithm for registering clouds of points in 3D space is the iterative closest point (ICP) algorithm. The point-to-point variational problem for orthogonal transformations is mathematically equivalent to the absolute orientation problem in photogrammetry. In this paper, we briefly overview closed-form solutions to the point-to-point variational problem. The well-known Horn algorithm solves the problem for the O (3) group. We propose a modified Horn algorithm that makes it possible to solve the problem for the SO (3) group. Computer simulation illustrates the registration accuracy of the considered methods for various geometric transformations.