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

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.